1950's tax preparation: plugboard programming with an IBM 403 Accounting Machine

Long before computers existed, businesses used electromechanical accounting machines for data processing. These one-ton accounting machines were "programmed" through wiring on a plugboard control panel, allowing them to generate complex business reports from records stored on punched cards. Even though they lacked electronics and used spinning mechanical wheels to add up data, these machines could process more than two cards a second.

This plugboard for an IBM 403 implements tax deduction computation. Board courtesy of Carl Claunch.

In honor of April 151, I examine a plugboard that was used for tax preparation in the 1950s9 and explain the forgotten art of plugboard programming, showing how a tangle of wiring implemented a data processing algorithm. By mounting the plugboard on an accounting machine, a particular data processing task could be performed. Although the plugboard looks like spaghetti code made physical, tracing out the connections shows its function: it computed deductions by summing records across multiple fields, printed a report with subtotals and totals, and punched a smaller card deck with the subtotals.

Overview of punched card data processing

Punched cards were a key part of data processing from 1890 until the 1970s, used for accounting, inventory, payroll and many other tasks. Typically, each 80-column punched card held one record, with data stored in fixed fields on the card. The example below shows an example card with columns divided into fields such as date, vendor number, order number and amount. An accounting machine would process these cards: totaling the amounts, and generating a report with subtotals by account and department, as shown below.

Example of a punched card holding a 'unit record', and a report generated from these cards. The accounting machine can group records based on a field to produce subtotals, intermediate totals, and totals. From Manual of Operation.

Punched-card data processing was invented by Herman Hollerith for the 1890 US census, which used a simple tabulating machine that counted records indicated by holes in the cards.2 These machines steadily accumulated features, becoming complex "accounting machines" that could generate business reports.6 These machines became popular with businesses and by 1944, IBM had 10,000 tabulating and accounting machines in the field.3 In July 1948, IBM introduced the 402 Accounting Machine, which used the plugboard I'm examining. The 402 (and the similar 4035) were feature-rich machines that had 16 counters, multiple levels of subtotals, vertical spacing control to support forms, comparisons and conditional operations, and leading zero elimination.

IBM 403 accounting machine, with Type 82 card sorter at right.4 These machines are on display at the Computer History Museum.

The surprising thing about this history is that businesses were performing data processing with punched cards decades before the first computers, using machinery that was entirely electro-mechanical, not even using vacuum tubes. This equipment was built from components such as wire brushes to read holes in punch cards, relays to control the circuits, and mechanical counter wheels to add values. Even though these systems were technologically primitive, they revolutionized business data processing and paved the way for electronic business computers such as the popular IBM 1401.

Plugboard programming

The accounting machines were programmed by wiring up a plugboard for a specific task. Since each application used cards with fields in different positions, accounting machines needed a way to define each field. Different reports would be formatted with values in different locations on the page. Applications would need to total and subtotal different values. Before stored-program computing existed, a technique was needed to easily customize the system for a particular application. The result was wiring on control panel plugboards.

Closeup of the plugboard for an IBM 403. The accounting machine is "programmed" by plugging in wires to form connections.

The photo above shows a closeup of the plugboard. The plugboard has a grid of holes (which are called hubs), with their functions labeled. By inserting a wire into the board, two hubs are connected, causing the accounting machine to perform a particular operation. The collection of wires specifies the operations that are performed on each card.

The back of the plugboard for an IBM 403 accounting machine.

When a wire is inserted into the plugboard, the jack on the end of the wire sticks out the back of the plugboard, as shown above. When the plugboard is mounted in the accounting machine (below), these jacks make contact with a grid of connectors on the accounting machine, completing the desired circuits. (Note the "setup change" switches above the plugboard; these switches will be relevant later.)

A plugboard inserted into the side of an IBM 403 at the Computer History Museum. Note the control switches above the plugboard. These can be used to change what the plugboard does.

Since the plugboard is removable, companies could easily switch plugboards to perform different tasks. (Rewiring a plugboard for each function would be much too time-consuming.) As a consequence, companies might have shelves full of plugboards for all the operations they performed; with plugboards, the "software" takes up considerable physical space. The photo below shows one company's collection of plugboards to perform different tasks.

Shelves full of plugboards for the IBM 402, courtesy of IBM 1401 restoration team.

The tax program

I closely examined the wiring of the tax plugboard to determine what it does. The first step was to trace out each wire to draw a schematic wiring diagram (below) that shows all the connections on the plugboard. If you compare the diagram with the plugboard photo at the start of the article, you can see that it shows the same wiring, but in a much easier to follow format.

A wiring diagram for an IBM 403 plugboard to compute tax deductions. (Click for full size.)

I found that the program wired into the board reads cards and computes subtotals and totals from the cards. In more detail, each card has seven fields that are read. The first field is an identifier, and all cards with the same identifier are totaled together to give totals for each of five fields. My hypothesis is that this field is an employee id, and each card corresponds to one pay period.7 Summing the records for each employee id gives the employee's total deductions (or year-to-date deductions). The totaled five fields could be payroll deductions such as federal income tax, state tax, social security tax, Medicare tax and retirement contributions. After reading the cards for an employee, the accounting machine punches a new summary card with the employee's total deductions prints a line on the report. The per-employee totals are then summed together to give overall totals at the end.

Here's how the plugboard works, step by step. When an 80-column card is read, each digit is available in one of the reading hubs, labeled 1 through 80. By putting a wire in a hub, the digit is transmitted to another part of the machine. For instance, suppose there is a 6-digit number punched into columns 28 to 33 of the card and we want to total these numbers. This is done by connecting a wire from reading column 28 to the upper digit of the counter, a wire from column 29 to the second digit of the counter, and so forth, for 6 wires in total.

The wires transferring the field to counter 6C are the six red wires in the photo below. The 80 card columns are available in the two rows of hubs below the label "Third reading". The inputs to the counters are the four rows of hubs below the "Counter entry" labels. Other fields are wired to counters similarly.

The six red wires connect six columns read from the card (right) to the entry of counter 6C (left).

Trying to figure out the wiring from the photo is difficult, so plugboard wiring is typically indicated in a diagram. The diagram below shows the wiring between the columns read (right) and the counter 6C (left). The six wires are compressed into one line on the diagram, using IBM's style of representing plugboards. The horizontal bars connected by a line indicate six parallel wires.

A diagram representing the connection between the card read (right) and the counter (left).

To print a total, a counter "exit" is wired to the desired printer columns. On the plugboard, the printer columns are labeled print entries: 43 "alphamerical print entry" positions that can print alphabetical or numerical characters, followed by 45 "numerical print entry" positions that only print numbers. The diagram below shows four wires from counter 4C to print columns 1 through 4 (yellow), and six wires from counter 6C (red) to print columns 35 through 40.

Wiring a counter to a "print exit" causes the counter value to be printed.

The accounting machine contains 16 decimal counters in all. Four of them are 8-digit counters, named 8A, 8B, 8C and 8D. Four are 6-digit counters (6A to 6D), four are 4-digit counters (4A to 4D), and four are 2-digit counters (2A to 2D). In addition, two counters can be joined together to form a larger counter. There are also connections between counters for subtotals. For instance, counter 8A accumulates a per-employee subtotal. These subtotals are added to counter 8B to form the final total.

Another important operation is to compare two cards to see if they have the same id (and should be counted together) or if they have different ids (so a subtotal should be printed and the counters reset). A comparison is done by wiring two fields to the two "comparing entry" rows. If the fields are different, the "comparing exit" will trigger a signal. Since we want to compare each card with the next card, we get one field from the "second reading" and one from the "third reading"; the card we are processing will be at the third reading stage while the card behind it will be at the second reading stage. Finally, the comparison output is wired to the "program start (minor)" hub. This causes the accounting machine to start an additional cycle to print the subtotals (i.e. minor totals) and reset the counters. (There are also "intermediate" and "major" program start hubs, which provide two additional levels of totals.)

Columns 1-4 of the cards are compared to determine if subtotals should be printed.

On the diagram above, columns 1-4 from the second reading and from the third reading are wired to the comparing entry hubs. The four corresponding comparing exit hubs are wired together (gray) and connected to the minor (MI) program start hub (yellow wire to PRG START in upper right). The closeup of the plugboard below shows the wiring on the plugboard.

Columns 1-4 of the cards are compared to determine if subtotals should be printed.

Another interesting feature of the plugboard is conditional behavior, using "selectors". Connections can be switched based on a different signal, allowing behavior to change based on a comparison, or a panel switch. This plugboard changes behavior based on the "setup change 1" panel switch, one of the switches on the accounting machine above the panel. (You can think of this as the plugboard version of command-line options.) According to the label on the plugboard (below), this switch selects "year to date". On the board, this switch enables processing of one field, as well as switching between the constant 2 and 5 for addition to counter 2B. (The reason for this constant is a mystery to me.)

The label on the plugboard shows it computes tax deductions.9 "S/P" is presumably "summary punch". The setup 1 switch selects "year to date".

The wiring on the right side of the plugboard controls the counter behavior, such as accumulating subtotals versus final totals. It also wires some of the counters together to form larger counters. For instance, counters 2C and 4D are combined to form a single 6-digit counter. 8 I won't explain the counter control wiring here; the manuals15 explain how it works.

"Summary punching" is another interesting feature of the accounting machine. This lets you take a large file of cards and punch a smaller summary file. For the tax plugboard, one summary card is punched for each employee, with the totals for that employee. Thus, a card file with one record for each employee's pay period is reduced to a much smaller file with one card for the employee's yearly totals. This smaller card file can then be used for further processing.

IBM 403 accounting machine connected to a 519 summary punch. Courtesy Columbia University Computing History.

Summary punching is accomplished by connecting a summary punch machine (above right) to the accounting machine (left) through a thick cable. A hub on the plugboard is wired to enable summary punching, and another hub is wired to control when to punch a card. For the tax plugboard, a summary card is punched for each minor total with the wiring below. A separate plugboard on the summary punch machine controlled which columns were punched on the summary card.

Summary punch wiring on the IBM 403 plugboard. The summary punch control pickup (SP Control PU on the left) is wired to punch a summary card on a minor total. The summary punch switch (SP.SW) hubs are connected by the gray wire (lower left).

Inside the 403 Accounting Machine

Its amazing how much functionality these accounting machines could provide without the benefit of electronics, purely through clever electromechanical systems. Inside the accounting machine is a maze of motors, rotating shafts, cams and clutches, making it seem more like a car than a computer—it even contained an oil pump! With all these mechanical parts a 403 accounting machine weighed over a ton (2515 pounds / 1143 kg).

Inside an IBM 403 Accounting Machine, front view. From the 402/403 Field Engineering Manual, fig. 5.

On the plugboard, a wire is used to route a column of the card. How does a character on the card get sent across this wire? How does a counter perform addition? And how does the result get printed? The accounting machines use clever mechanisms, closely tied to the structure of a punched card, to perform these operations.

In modern terms, a character is encoded serially over a wire, by a single pulse whose timing depends on the position of the hole. These pulses start and stop the counters used to add values. These pulses also control the timing of the typebars that print the result. How these pulses are generated and how they electromechanically control the system will be described more below.

The 403's timing is based off the rotating shafts that drive the machine, rather than clock time. Each revolution of the shaft corresponds to a "card cycle", the reading and processing of one card. The fundamental timing unit is a rotation of 18°: this is the time between reading successive card holes, moving a typebar by one character, and rotation of a counter by one count. At 150 cards per minute, these values work out to approximately 400 milliseconds per card and 20 milliseconds per 18° step, remarkably fast for mechanical operations.

Reading cards

To understand the accounting machine, one must first understand how punched cards hold data. Punched cards hold 80 characters of data; each character is represented by the hole pattern in a column. The card below shows how numbers and the alphabet are punched; each character is printed at the top of the card with the corresponding punches in the column below. A digit is simply represented by a hole in the corresponding row, 0 through 9. (Note that numbers are stored in decimal, not binary.) To support alphanumeric data, two "zone" rows were added above the digit rows.10 A letter is represented by putting two holes in a column: a zone punch and a digit punch.11

An 80-column IBM punched card. Each column encodes a character (printed at top) by punching holes in the column. For a digit, a hole is punched in the row with the same number. A letter is encoded by adding a "zone punch" in one of the top three rows.

You might expect the accounting machine to read cards a column at a time, so one character gets processed at a time. But instead, cards are read "sideways", starting at the bottom. All 80 columns are read in parallel, one row at a time, starting with row 9 and ending with row 0 and then the zone rows. The accounting machine uses sets of 80 wire brushes to read a card, one for each column. If there is a hole, the brush makes contact with the energized metal roller underneath the card, completing a circuit and generating a pulse. Thus, each column will have a pulse corresponding to its hole, with the 9 pulse first, followed by 8 and so forth, ending with 0. Thus, each character is encoded serially, and each plugboard wire carries one of these serial signals, but all columns are processed in parallel.

Printing

Typebars in an IBM 402 accounting machine. Courtesy Columbia University Computing History.

The accounting machine's printing mechanism consists of 88 typebars;12 each vertical bar holds all the characters that can be printed. The typebars move vertically to line up the proper characters and then hammers13 hit the typebars into an inked ribbon to print the selected characters. Thus, the characters in a line of text are printed simultaneously.

The wires in the plugboard control what gets printed by stopping each rising typebar at the right time to select the desired character. The motion of the typebars is carefully timed to match the reading of a card, so the "3" row (for instance) of a card is read at the same time that the "3" on the typebar moves into position. If the brush's hub is wired to a column's print hub, this signal energizes a print magnet, releasing a "stop pawl" which meshes with a tooth on the typebar, stopping it with the "3" character in position to print. If a "2" is read instead, the brush reads the hole one time unit later; the typebar will have risen one more position, causing a "2" to be printed.

The printing mechanism consists of a complex arrangement of mechanical parts: cams, pawls, slides, springs and clutches, in combination with electromagnets to activate these parts at the right time. The mechanism can print 100 lines per minute, so the parts are flying around rapidly and require exact timing. The typebars move one position for every 18° rotation of the driveshaft, keeping them synchronized with card reading.

Counters

The heart of the accounting machine is the electromechanical counters that sum the values. Each digit in a counter is represented by a wheel that rotates to perform addition. The position of the wheel indicates the digit. For instance, to add 27 to a counter, the tens digit wheel is rotated two positions and the unit wheel is rotated seven positions. Thus, to add the value in a card field, the wheels must rotate an amount corresponding to the number punched in the card. The wheel starts rotating when a hole is read, rotates one position as each additional row is read, and stops reading at row 0. Since row 9 is read first and row 0 is last, the result is the counter rotates the number of positions indicated by the hole.

An electromechanical counter from the IBM 403 accounting machine performs addition on two digits by rotating the counter wheels.

The photo above shows a two-digit counter unit. The counter wheels are at the left. The start and stop coils cause the counter to start and stop rotating at the correct times by activating lever arms that control a clutch under the wheel. Carry is implemented by cams underneath the wheel that close electrical contacts. On the back of the board are the electrical contacts that read out the value stored in the counter; these are wired to the connector on the right.

Diagram of the electromechanical counter, indicating the key components. From the IBM 403 Field Manual.

The plugboard specifies which card columns are added to which counter digits. To add a field's value to a counter, a column's read brush is wired to the counter through the plugboard, so the card controls how much the counter rotates. This signal activates the counter's start coil, engaging the counter's clutch and starting the counter's rotation. At the 0 position, the stop coil disengages the clutch, stopping the counter. For instance, if the brush read a 7 from the card, the counter will rotate through seven positions before stopping, adding 7 to its value. If the brush read a 1, the counter will rotate by just one position. The reason this works is the synchronization between card movement and counter rotation; an 18° rotation corresponds to the card moving by one row as well as one count on the counter wheel. (A counter wheel has 20 positions spaced 18° apart. Counting by 10 rotates the wheel halfway.) Subtraction is performed by adding the complement.14

A carry from one position to the next is handled by a complex mechanism. You might expect that when one wheel rolls over from 9 to 0, it increments the higher wheel like an odometer, but that would be slow for multi-digit counters. (Keep in mind that the counters can add 150 numbers per minute, so they are spinning rapidly.) Instead, the counters use a mechanism similar to carry lookahead. If a wheel is at 9, an electrical contact closes, allowing a lower-order carry to be passed through to the higher wheel. If a wheel passes from 9 to 0, it closes a different electrical contact, generating a carry. After the "regular" addition, any necessary carries are generated in parallel and added in a single time step. Thus, something like 99999999+1 isn't delayed by a ripple carry; instead all digits get a carry in parallel.

Relays

The accounting machine is controlled by hundreds of relays, electromechanical switches that provide all the "control logic" for the system. The photo below shows the back of the accounting machine, filled with relays; more relays are on the end panel. To generate timing signals signals for the relays, switches were opened and closed by cams attached to the rotating shaft. Thus, everything in the system is timed from the rotating shaft.

The IBM 403 accounting machine is controlled by hundreds of relays, many of which are mounted in the back of the machine. Photo from the Field Engineering Manual, fig 81.

Conclusions

Punched card data processing is almost forgotten now, but it ruled data processing for almost a century. Even before computers existed, businesses used punched cards and tabulators for accounting. IBM's accounting machines were able to perform surprisingly complex tasks even though they were built from electromechanical components that seem primitive today. Accounting machines and plugboard programming remained popular into the 1960s, when businesses gradually switched to stored-program business computers such as the IBM 1401. Even so, IBM continued marketing accounting machines until 1976. Incredibly, one company in Texas still uses an IBM 402 accounting machine for their accounting today (details), illustrating the amazing longevity of punched card technology.

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Thanks to Carl Claunch (one of the Xerox Alto restoration co-conspirators) for providing the plugboard and documentation.

Notes and references

1. April 15 is traditionally tax day in the US, but if you don't have your taxes done yet, don't panic. In 2017, US tax day is April 18 due to the weekend and holiday. ↩

2. To support addition, tabulators used a module called an "accumulator" with rotating dials to hold decimal numbers. This accumulator gave its name to the accumulator register still used in microprocessors today. For example, Intel's x86 processors have a register called EAX, the EXtended Accumulator. ↩

3. The history of IBM's tabulating machines is described in IBM's Early Computers. Also see Columbia University's computing timeline. ↩

4. Another part of the unit record system is the card sorter, which rapidly sorts cards on a field, putting them in the proper order to be processed by an accounting machine. I discuss IBM card sorters in detail here. ↩

5. The 402 and 403 accounting machines were essentially the same except the 403 could print three-line addresses. In order to print three lines from one card, the 403 has three card reading stations instead of two. (That is, it read each card three times using three sets of 80 brushes). This feature is called MLP (multi-line printing) and is useful for printing addresses on invoices, for instance. An MLP card is indicated with a special punch: 8, 9 and (1, 2, 3 or 4) punched in a single column; the last digit controls the number of lines printed. ↩

6. I wouldn't be surprised if these accounting machines were technically Turing-complete due to their support for conditional operations, although it's unclear how to represent the tape. Perhaps storage could be implemented by punching a new deck of cards on each cycle through the machine. Of course this would be impractical for any real use. ↩

7. I suspect each card represents one employee pay stub and each field indicates a payroll deduction. However, there are alternative explanations for the plugboard. For instance, the id field could indicate a company division, and each card represents a subdivision. In this case, the accounting machine could be totaling the tax deductions for each division such as business expenses and depreciation. Or each card could represent one month. Since there are no variable names, it is speculation. ↩

8. The table below summarizes the program implemented by the plugboard, showing the mapping between input fields on the card and output fields on the printer.

   Card columns	Output columns	Subtotal counter	Total counter
   1-4	1-4	4C
   34-38	5-10	8D	4A/2D
   44-45	11-18	8A	8B
   61-66	19-26	6A	2C/4D
   67-71	27-32	6B	2A/4B
   28-33	35-40	6C	8C
   14-17		4D
   from switch		2B

   Columns 14-17 are summed but not printed. Presumably they are punched on the summary punch card. Columns 34-38 are only processed if the "setup change 1" switch is active. Counter 2B is controlled by the panel switch, adding either 2 or 5 each step. I can't figure out a reason for this; I assume the plugboard on the summary punch (which I don't have) does something useful with this value. ↩

9. The tax plugboard I'm examining was labeled with embossing tape which dates the labeling of the board to post 1958. The board could originally be older, or it could have been used into the 1960s. ↩

10. The row above "0" is called 11 or X, while the row above that is 12. For alphabetical characters, the "0" row is used as a zone instead of a digit. (This causes some complications in the accounting machine, such as a special mechanism to print a "numeric zero" versus a "zone zero".) ↩

11. This punch card code evolved into EBCDIC (Extended Binary Coded Decimal Interchange Code), the encoding used by IBM computers in place of ASCII. Many of the strange characteristic of EBCDIC, such as the alphabet not being entirely sequential, are due to its roots in punched cards. ↩

12. The accounting machine has typebars on the left that print alphanumerics and typebars on the right that just print digits. For alphanumeric printing, the digit signal moves the typebar in steps of four, while the zone signal moves the typebar 0 through 3 steps. Thus, an alphanumeric character can be printed. Typebars with special characters could also be installed, to print $, @, - or %. ↩

13. You might expect that to print each line, all the hammers hit the typebars, but it's more complex than that. First, each hammer has a mechanical "hammerlock" control, which can enable the hammer, disable the hammer, or put the hammerlocked hammers under program control. Thus, part of the line may be printed or suppressed based on the data. In addition, the hammers also have mechanical "hammersplit" levers which when raised cause leading zeros in a field to be suppressed. This allows the value "000123" to be printed as "   123" for instance. ↩

14. Subtraction uses 9's complement addition. That is, subtracting a digit n is done by adding 9-n. This is accomplished mechanically by starting the counter's rotation at position 9 and stopping when a hole is read. For example, if the hole is at position 7, the counter will increment by two positions. There are a few complications with 9's-complement subtraction. The answer is off by one, but an "end-around carry" adds 1 to yield the correct result. Negative numbers require special handling to be printed properly using the "net balance method" or the "balance selection" method; see the 403 manual if you care about the details. The numeric typebars include a "CR" symbol, which indicates negative numbers as a "credit". On a punch card, negative numbers are typically indicated with an X-punch (i.e. a zone punch in row 11) over the value. ↩

15. IBM's accounting machine manuals are available on Bitsavers. The operation of the IBM accounting machines is discussed in detail in: IBM 402, 403 and 419 Accounting Machines: Manual of Operation. For a thorough discussion of how the machine works internally, see IBM 402, 403, 419 Field Engineering Manual of Instruction. For an overview of how plugboard wiring for IBM's works, see IBM Functional Wiring Principles. ↩

Inside the vintage 74181 ALU chip: how it works and why it's so strange

The 74181 ALU (arithmetic/logic unit) chip powered many of the minicomputers of the 1970s: it provided fast 4-bit arithmetic and logic functions, and could be combined to handle larger words, making it a key part of many CPUs. But if you look at the chip more closely, there are a few mysteries. It implements addition, subtraction, and the Boolean functions you'd expect, but why does it provide several bizarre functions such as "A plus (A and not B)"? And if you look at the circuit diagram (below), why does it look like a random pile of gates rather than being built from standard full adder circuits. In this article, I explain that the 74181's set of functions isn't arbitrary but has a logical explanation. And I show how the 74181 implements carry lookahead for high speed, resulting in its complex gate structure.

Schematic of the 74LS181 ALU chip, from the datasheet. The internal structure of the chip is surprisingly complex and difficult to understand at first.

The 74181 chip is important because of its key role in minicomputer history. Before the microprocessor era, minicomputers built their processors from boards of individual chips. A key part of the processor was the arithmetic/logic unit (ALU), which performed arithmetic operations (addition, subtraction) and logical operations (AND, OR, XOR). Early minicomputers built ALUs out of a large number of simple gates. But in March 1970, Texas Instruments introduced the 74181 Arithmetic / Logic Unit (ALU) chip, which put a full 4-bit ALU on one fast TTL chip. This chip provided 32 arithmetic and logic functions, as well as carry lookahead for high performance. Using the 74181 chip simplified the design of a minicomputer processor and made it more compact, so it was used in many minicomputers. Computers using the 74181 ranged from the popular PDP-11 and Xerox Alto minicomputers to the powerful VAX-11/780 "superminicomputer". The 74181 is still used today in retro hacker projects.1

The 74181 implements a 4-bit ALU providing 16 logic functions and 16 arithmetic functions, as the datasheet (below) shows. As well as the expected addition, subtraction, and Boolean operations, there are some bizarre functions such as "(A + B) PLUS AB".

The datasheet for the 74181 ALU chip shows a strange variety of operations.

So how is the 74181 implemented and why does it include such strange operations? Is there any reason behind the 74181's operations, or did they just randomly throw things in? And why are the logic functions and arithmetic functions in any particular row apparently unrelated? I investigated the chip to find out.

The 16 Boolean logic functions

There's actually a system behind the 74181's set of functions: the logic functions are the 16 possible Boolean functions f(A,B). Why are there 16 possible functions? If you have a Boolean function f(A,B) on one-bit inputs, there are 4 rows in the truth table. Each row can output 0 or 1. So there are 2^4 = 16 possible functions. Extend these to 4 bits, and these are exactly the 16 logic functions of the 74181, from trivial 0 and 1 to expected logic like A AND B to contrived operations like NOT A AND B. These 16 functions are selected by the S0-S3 select inputs.

Arithmetic functions

The 74181's arithmetic operations are a combination of addition, subtraction, logic operations, and strange combinations such as "A PLUS AB PLUS 1". It turns out that there is a rational system behind the operation set: they are simply the 16 logic functions added to A along with the carry-in.2 That is, the arithmetic functions are: A PLUS f(A,B) PLUS carry-in. For example, If f(A,B)=B, you get simple addition: A PLUS B PLUS carry-in. If f(A,B) = NOT B, you get A PLUS NOT B PLUS carry-in, which in two's-complement logic turns into subtraction: A MINUS B MINUS 1 PLUS carry-in.

Other arithmetic functions take a bit more analysis. Suppose f(A,B) = NOT (A OR B). Then each bit of A PLUS f(A,B) will always be 1 except in the case where A is 0 and B is 1, so the result of the sum is A OR NOT B. Even though you're doing addition, the result is a logical function since no carry can be generated. The other strange arithmetic functions can be understood similarly.3

Thus, the 16 arithmetic functions of the 74181 are a consequence of combining addition with one of the 16 Boolean functions. Even though many of the functions are strange and probably useless, there's a reason for them. (The Boolean logic functions for arithmetic are in a different order than for logical operations, explaining why there's no obvious connection between the arithmetic and logical functions.)

Carry lookahead: how to do fast binary addition

The straightforward but slow way to build an adder is to use a simple one-bit full adders for each bit, with the carry out of one adder going into the next adder. The result is kind of like doing long addition by hand: in decimal if you add 9999 + 1, you have to carry the 1 from each column to the next, which is slow. This "ripple carry" makes addition a serial operation instead of a parallel operation, harming the processor's performance. To avoid this, the 74181 computes the carries first and then adds all four bits in parallel, avoiding the delay of ripple carry. This may seem impossible: how can you determine if there's a carry before you do the addition? The answer is carry lookahead.

Carry lookahead uses "Generate" and "Propagate" signals to determine if each bit position will always generate a carry or can potentially generate a carry. For instance, if you're adding 0+0+C (where C is the carry-in), there's no way to get a carry out from that addition, regardless of what C is. On the other hand, if you're adding 1+1+C, there will always be a carry out generated, regardless of C. This is called the Generate case. Finally, for 0+1+C (or 1+0+C), there will be a carry out if there is a carry in. This is called the Propagate case since if there is a carry-in, it is propagated to the carry out.4 Putting this all together, for each bit position you create a G (generate) signal if both bits are 1, and a P (propagate) signal unless both bits are 0.

The carry from each bit position can be computed from the P and G signals by determining which combinations can produce a carry. For instance, there will be a carry from bit 0 to bit 1 if P₀ is set (i.e. a carry is generated or propagated) and there is either a carry-in or a generated carry. So C₁ = P₀ AND (C_in OR G₀).

Higher-order carries have more cases and are progressively more complicated. For example, consider the carry in to bit 2. First, P₁ must be set for a carry out from bit 1. In addition, a carry either was generated by bit 1 or propagated from bit 0. Finally, the first carry must have come from somewhere: either carry-in, generated from bit 0 or generated from bit 1. Putting this all together produces the function used by the 74181: C₂ = P₁ AND (G₁ OR P₀) AND (C₀ OR G₀ OR G₁).

As you can see, the carry logic gets more complicated for higher-order bits, but the point is that each carry can be computed from G and P terms and the carry-in. Thus, the carries can be computed in parallel, before the addition takes place.5

Creating P and G with an arbitrary Boolean function

The previous section showed how the P (propagate) and G (generate) signals can be used when adding two values. The next step is to examine how P and G are created when adding an arbitrary Boolean function f(A, B), as in the 74181. The table below shows P and G when computing "A PLUS f(A,B)". For instance, when A=0 there can't be a Generate, and Propagate depends on the value of f. And when A=1, there must be a Propagate, while Generate depends on the value of f.

A	B	A PLUS f(a,b)	P	G
0	0	0+f(0,0)	f(0,0)	0
0	1	0+f(0,1)	f(0,1)	0
1	0	1+f(1,0)	1	f(1,0)
1	1	1+f(1,1)	1	f(1,1)

In the 74181, the four f values are supplied directly by the four Select (S pin) values, resulting in the following table:6

A	B	A PLUS f	P	G
0	0	0	S1	0
0	1	1	S0	0
1	0	1	1	S2
1	1	10	1	S3

The chip uses the logic block below (repeated four times) to compute P and G for each bit. It is straightforward to verify that it implements the table above. For instance, G will be set if A is 1, B is 1 and S3 is 1, or if A is 1, B is 0 and S2 is set.

This circuit computes the G (generate) and P (propagate) signals for each bit of the 74181 ALU chip's sum. The S0-S3 selection lines select which function is added to A.

Creating the arithmetic outputs

The addition outputs are generated from the internal carries (C0 through C3), combined with the P and G signals. For each bit, A PLUS f is the same as P ⊕ G, so adding in the carry gives us the full 4-bit sum. Thus, F0 = C0 ⊕ P0 ⊕ G0, and similarly for the other F outputs.7 On the schematic, each output bit has two XOR gates for this computation.

Creating the logic outputs

For the logic operations, the carries are disabled by forcing them all to 1. To select a logic operation, the M input is set to 1. M is fed into all the carry computation's AND-NOR gates, forcing the carries to 1. The output bit sum as as above, producing A ⊕ f ⊕ 1 = A ⊕ f. This expression yields all 16 Boolean functions, but in a scrambled order relative to the arithmetic functions.8

Interactive 74181 viewer

To see how the circuits of the 74181 work together, try the interactive schematic below.9 The chip's inputs are along the top and right; click on any of them to change the value. The A and B signals are the two 4-bit arguments. The S bits on the right select the operation. C is the carry-in (which is inverted). M is the mode, 1 for logic operations and 0 for arithmetic operations. The dynamic chart under the schematic describes what operation is being performed.

The P and G signals are generated by the top part of the circuitry, as described above. Below this, the carry lookahead logic creates the carry (C) signals by combining the P and G signals with the carry-in (Cn). Finally, the sum for each bit is generated (Σ) from the P and G signals7, then combined with each carry to generate the F outputs in parallel.10

Result and truth table for inputs entered above
Select :

	0000
A	0000
B	0001
F	1001

Ai	Bi	Pi	Gi	Fi
0	0	X	Y	F
0	1	X	Y	F
1	0	X	Y	F
1	1	X	Y	F

Die photo of the 74181 chip.

I opened up a 74181, took die photos, and reverse engineered its TTL circuitry. My earlier article discusses the circuitry in detail, but I'll include a die photo here since it's a pretty chip. (Click image for full size.) Around the edges you can see the thin bond wires that connect the pads on the die to the external pins. The shiny golden regions are the metal layer, providing the chip's internal wiring. Underneath the metal, the purplish silicon is doped to form the transistors and resistors of the TTL circuits. The die layout closely matches the simulator schematic above, with inputs at the top and outputs at the bottom.

Die photo of the 74181 ALU chip. The metal layer of the die is visible; the silicon (forming transistors and resistors) is hidden behind it.

Conclusion

While the 74181 appears at first to be a bunch of gates randomly thrown together to yield bizarre functions, studying it shows that there is a system to its function set: it provides all 16 Boolean logic functions, as well as addition to these functions. The circuitry is designed around carry lookahead, generating G and P signals, so the result can be produced in parallel without waiting for carry propagation. Modern processors continue to use carry lookahead, but in more complex forms optimized for long words and efficient chip layout.12

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Notes and references

1. Retro projects using the 74181 include the APOLLO181 CPU, Fourbit CPU, 4 Bit TTL CPU, Magic-1 (using the 74F381), TREX, Mark 1 FORTH and Big Mess o' Wires. ↩

2. The carry-in input and the carry-out output let you chain together multiple 74181 chips to add longer words. The simple solution is to ripple the carry from one chip to the next, and many minicomputers used this approach. A faster technique is to use a chip, the 74182 look-ahead carry generator, that performs carry lookahead across multiple 74181 chips, allowing them to all work in parallel. ↩

3. One thing to note is A PLUS A gives you left shift, but there's no way to do right shift on the 74181 without additional circuitry. ↩

4. To simplify the logic, the 74181 considers 1+1+C both a Propagate case and a Generate case. (Some carry lookahead systems consider 1+1+C to be a Propagate case but not a Generate case.) For the 74181's outputs, Propagate must be set for Generate to be meaningful. ↩

5. The carry-lookahead logic in the 74181 is almost identical to the earlier 74LS83 adder chip. The 74181's circuitry can be viewed as an extension of the 74LS83 to support 16 Boolean functions and to support logical functions by disabling the carry. ↩

6. The way the S0 and S1 values appear in the truth table seems backwards to me, but that's how the chip works. ↩

7. The bit sum Σ can be easily produced from the P and G signals. Some datasheets show each Σ signal generated as P XOR G, while other datasheets show Σ generated as NOT P AND G. Since the combination P=0, G=1 never arises, both generate the same results. I show XOR on the schematic as it is conceptually easier to understand, but examining the die shows the physical circuit uses the NOT/AND gates. ↩

8. The logic functions are defined in terms of Select inputs as follows:

   A	B	F
   0	0	S1
   0	0	S0
   0	0	S2
   0	0	S3

   Because the first two terms are inverted, the logic function for a particular select input doesn't match the arithmetic function. ↩

9. The schematic is based on a diagram by Poil on WikiMedia, CC By-SA 3.0, with circuitry and labeling changes. ↩

10. The 74181 chip has a few additional outputs. The A=B output is used with the subtraction operation to test the two inputs for equality. The Cn+4 output is the inverted carry out, supporting longer words. P and G are the carry propagate and generate outputs, used for carry lookahead with longer words.11 ↩

11. The P and G outputs in my schematic are reversed compared to the datasheet, for slightly complicated reasons. I'm describing the 74181 with active-high logic, where a high signal indicates 1, as you'd expect. However, the 74181 can also be used with active-low logic, where a low signal indicates a 1. The 74181 works fine with active-low logic except the meanings of some pins change, and the operations are shuffled around. The P and G labels on the datasheet are for active-low logic, so with active-high, they are reversed. ↩

12. One example of a modern carry lookahead adder is Kogge-Stone. See this presentation for more information on modern adders, or this thesis for extensive details. ↩

Analyzing the vintage 8008 processor from die photos: its unusual counters

The revolutionary Intel 8008 microprocessor is 45 years old today (March 13, 2017), so I figured it's time for a blog post on reverse-engineering its internal circuits. One of the interesting things about old computers is how they implemented things in unexpected ways, and the 8008 is no exception. Compared to modern architectures, one unusual feature of the 8008 is it had an on-chip stack for subroutine calls, rather than storing the stack in RAM. And instead of using normal binary counters for the stack, the 8008 saved a few gates by using shift-register counters that generated pseudo-random values. In this article, I reverse-engineer these circuits from die photos and explain how they work.

The image below shows the 8008's tiny silicon die, highly magnified. Around the outside of the die, you can see the 18 wires connecting the die to the chip's external pins. The 8008's circuitry is built from about 3500 tiny transistors (yellow) connected by a metal wiring layer (white). This article will focus on the stack circuits on the right side of the chip and how they interact with the data bus (blue).

The die of the Intel 8008 microprocessor, showing the stack and other important subcomponents.

For the 8008 processor's birthday, I'm using the date of its first public announcement, an article in Electronics on March 13, 1972 entitled "8-bit parallel processor offered on a single chip." This article described the 8008 as a complete central processing unit for use in "intelligent terminals" and stated that chips were available at $200 each.1

You might think that an intelligent terminal is a curiously specific application for the 8008 processor. There's an interesting story behind that, going back to the roots of the chip: the Datapoint 2200 "programmable terminal", introduced in June 1970. The popular Datapoint 2200 was essentially a desktop minicomputer with its processor consisting of a board full of simple TTL chips. The photo below shows the CPU board from the Datapoint 2200. The chips are gates, flip flops, decoders, and so forth, combined to build a processor, since microprocessors didn't exist at the time.

The processor board from the Datapoint 2200. The 8008 microprocessor was created to replace this board, but was never used by Datapoint. Photo courtesy of unknown source.

Processors typically use a stack to store addresses for subroutine calls, so they can "pop" the return address off the stack. This stack is usually stored in main memory. However, the Datapoint 2200 used slow shift-register memory2 instead of expensive RAM for its main storage, so implementing a stack in main memory would be slow and inconvenient. Instead, the Datapoint 2200's stack was stored in four i3101 RAM chips, providing a small stack of 16 entries. 3 4 The i3101 was Intel's very first product, and held just 64 bits. In the photo above, you can see the chips in their distinctive white packaging each with a large "i" for Intel. 5

To keep track of the top of the stack, the Datapoint 2200 used a 4-bit up/down counter chip to hold the stack pointer. The clever thing about this design is there's no separate program counter (PC) and stack; the PC is simply the value at the top of the stack. You don't need to explicitly push and pop the PC onto the stack; for a subroutine call you just update the counter and write the subroutine address to the stack.

The story of the 8008's origin is that Datapoint went to Intel and asked if Intel could build a chip that combined the stack memory and the stack pointer onto a single chip. Intel said not only could they do that, they could put the whole processor board onto a single chip! This was the start of Intel's 8008 project to duplicate the Datapoint 2200's processor board onto a chip, keeping the Datapoint 2200 instruction set and architecture.6 After various delays, Intel completed the 8008 microprocessor, but Datapoint rejected it. Intel decided to sell the 8008 as a general-purpose processor chip, sparking the microprocessor revolution. Intel improved the 8008 with the 8080 and then the 16-bit 8086, leading to the x86 architecture that dominates desktop and server computers today.

The consequence of the 8008's history is that it inherited its architecture and instruction set from the Datapoint 2200 intelligent terminal. One of these features was the fixed, internal stack. But the 8008's implementation of that stack is unusual.

Shift-register counter

The most unexpected part of the 8008's stack is how it keeps track of the current position. The straightforward way to implement the stack would be with a binary up/down counter to keep track of the current stack position (which is what the Datapoint 2200 did). But to save a few transistors, the 8008 uses a nonlinear feedback shift register instead of a counter. The result is the stack entries are accessed in a pseudo-random order! But since they are read and written in the same order, everything works out fine.

The shift register outputs are based on a de Bruijn sequence, a cyclic sequence in which every possible output occurs as a subsequence exactly once. The 8008's de Bruijn sequence is shown below. The first value (000) is underlined in red. Shifting to the blue position yields the second value (001). Proceeding around the circle clockwise yields all eight values in the sequence: 000, 001, 010, 101, 011, 111, 110, 100 and finally back to 000. Note that each value appears exactly once, but they are not in standard binary order.

8

This de Bruijn sequence contains all eight 3-bit values as subsequences. 000 and 001 are underlined. The Intel 8008's internal counters are built form this sequence.

At each step in the sequence, the last two bits are shifted to the left and a new bit is placed on the right. Counting down is the converse: the first two bits are shifted to the right and a new bit is placed one the left. This process can be implemented with a shift register, a circuit that allows a bit sequence to be shifted and an additional bit inserted.7

The diagram below shows how the 8008 implements the nonlinear feedback shift register counter. While it make look complex, it's a straightforward implementation of the de Bruijn sequence. The three latches in the middle form a shift register, with each latch holding one bit. To count up, each bit is shifted to the left and a new bit is added on the right (green arrows). To count down, each bit is shifted to the right and a new bit is added on the left (purple arrows). The logic gate on the left generate the "new" bit for counting down and the gates on the right generate the new bit for counting up.

The 8008 uses the above circuit for its internal stack counter. The refresh counter is based on this, but counts up only.

The logic gates may appear complex. However, one feature of PMOS logic is it's as simple to build an AND-OR-NOR gate as a plain NOR gate, just by wiring transistors in parallel or series. Designing the logic is also straightforward: for each triple of current bits, the de Bruijn sequence specifies the next bit. If you've studied digital logic, Karnaugh maps can be used to create the logic circuits to generate the desired next bit.

Inside the stack storage

The 8008 uses dynamic RAM (DRAM) to for its stack storage and its registers. The other 1970s microprocessors that I've examined use static latches, so the 8008 is a bit unusual in this regard. Since Intel was primarily a RAM company at the time, I assume they wanted to leverage their RAM skills and save transistors by using DRAM.

Each bit of storage in the 8008 uses a cell with three transistors and one capacitors, called a 3T1C cell, similar to the cell in Intel's i1103 DRAM chip. The diagram below shows a closeup of the 8008's stack storage, with six DRAM cells visible. Each row is one 14-bit address in the stack. Each row has a read enable and write enable control line coming from the left. Each column stores one of the 14 bits; the column sense line is used to read and write the selected bit.

Detail of the Intel 8008 microprocessor's die, showing six storage cells for the stack registers. Each bit is stored with a DRAM cell consisting of three transistors and a capacitor.

The transistors for the first cell are labeled T1, T2 and T3. The value is stored on the capacitor labeled C. (There is no separate physical capacitor; the capacitance of the wiring is sufficient to store the bit.)

To write a bit, the write line for the desired row is pulled low, turning on T1. The desired voltage (low or high) is fed onto the sense line, passes through T1, and is stored by the capacitor. To read the value, the appropriate read line is pulled low, turning on T3. If C has a low voltage, T2 is turned on. This connects the sense line to ground through T3 and T2. On the other hand, if C has a high voltage, T2 is turned off and the sense line is not grounded. Thus, the circuitry connected to the sense line can tell what bit value is stored on C.

The inconvenience with dynamic RAM is that values can only be stored temporarily. After a few hundred microseconds, the charge stored on capacitor C will leak away and the value will be lost. The solution is a refresh circuit that periodically reads each value and writes it back, before the bit fades away. (A similar refresh process is used by your computer's RAM.) The 8008's internal RAM is refreshed at least every 240 microseconds, ensuring that bits are not lost. (Static RAM, on the other hand, uses a larger, more complex circuit for each bit, but will preserve the bit as long as the circuit is powered up.)

In the 8008, the stack storage (and the registers) are refreshed by continuously stepping through each entry: reading it and writing it back. To accomplish this, a second 3-bit shift-register counter is used as a refresh counter, tracking the current position that is being refreshed. The circuit for this is the same as the stack counter, except it omits the logic to count down, as it only needs to count in one direction.9

Understanding the die photo

I'll briefly explain what you're looking at in the die photo above. The chip itself is made from a silicon wafer. Plain silicon is essentially an insulator, but by doping it with impurities, it becomes a semiconductor. The dark lines indicate the boundary between doped and undoped regions; the doped silicon in the first cell is indicated in red.

On top of the silicon is the polysilicon layer, which is the yellowish stripes. Polysilicon acts as a conductor and is used as internal wiring of the chip. More importantly, a transistor is created when polysilicon crosses doped silicon. A thin oxide layer separates the polysilicon from the silicon, forming the transistor's gate. A low voltage on the polysilicon gate causes the transistor to conduct, connecting the two sides (called source and drain) of the transistor. A high voltage on the gate turns the transistor off, disconnecting the two sides. Thus, the transistor acts as a switch, controlled by the gate.

The top layer of the chip is the metal layer, which is also used as wiring. For the photo above, I removed the metal layer with hydrochloric acid to make the underlying silicon more visible. The green, blue and gray lines indicate where the metal wiring was before being removed. Transistors T1 and T3 are connected to the sense line (blue), while transistor T2 is connected to ground (green). The read and write lines enter the circuit on the left as metal wiring, connected to polysilicon lines.

The interface between the stack and the data bus

To access memory, the address in the stack must be provided to external memory via the 8 data/address pins on the chip. These pins are connected to the stack (and other parts of the 8008) via the data bus. The die photo below shows the circuitry that interfaces the 14-bit stack storage to the 8-bit data bus.11 At the top of the photo are the metal control lines and three of the data bus lines. At the bottom are the sense lines, discussed earlier, from the stack storage. In between are the transistors (orange) that connect the data bus and the stack.

The control lines select the low (L) or high (H) half of the address. These activate the appropriate read or write transistors, connecting the appropriate stack columns to the data bus.

The stack /bus driver circuit provides the "glue" between the data bus and the stack DRAM storage.

The transistors to write an address to the data bus are much larger than typical transistors, appearing as vertical yellow bars in the die photo. The reason for this is the data bus passes through the whole chip. Due to the length of the bus, it has relatively high capacitance and larger, high-current transistors are required to drive a signal on the data bus.

Near the bottom of the photo are the inverter amplifiers. Each sense line is attached to an inverter that boosts the signal from the stack storage. During refresh, this boosted signal is written back, strengthening the bit stored on the capacitor.10

Conclusion

By examining die photos, it is possible to reverse-engineer the 8008 microprocessor. One unusual feature of the 8008 is that instead of using standard binary counters internally, it saves a few gates by using shift-register counters. Although these count in a pseudo-random order rather than sequentially, the 8008 still functions correctly. One counter is used for the on-chip address stack. The 8008 also uses DRAM internally for stack storage and register storage, requiring a second counter to refresh the DRAM. Since every transistor was precious at the dawn of the microprocessor age, the 8008 has these interesting design decisions that produced compact circuitry.

If you're interested in the 8008, my previous article has a detailed discussion of the architecture, more die photos and information on how to take them. This article explains the 8008's ALU.

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Notes and references

1. The first announcement of the 8008 microprocessor in Electronics is shown below (click for a larger version). The announcement called the chip a "parallel processor", a term that had a different meaning back then, indicating that the processor operated on all 8 bits at the same time. This was in contrast to serial processors (such as the Datapoint 2200) that handled one bit of the word at a time.)

   ↩

   The 8008 chip was announced in Electronics on March 13, 1972: "8-bit parallel processor offered on a single chip."

2. In 1970, RAM memory chips were extremely expensive: $99.50 for an i3101 chip with just 64 bits of storage. Shift-register memory was cheaper and denser, with 512 bits of storage in an Intel 1405 chip. The big disadvantage is the bits were circulated around and around inside the chip, with only one bit available at a time. Sequential access wasn't a problem, but if you wanted to read memory out of order, you might need to wait half a millisecond for the right bit to circle around. I wrote about shift-register memories in detail here, with detailed die photos. ↩

3. The i3101 memory was called the 3101 due to Intel's part numbering system at the time, described in Intel Technology Journal, Q1 2001. To summarize, the first digit indicate the product family: 1xxx is PMOS, 2xxx is NMOS, 3xxx is bipolar and so forth. The second digit indicates the product type: 1 is RAM, 2 is a controller, 3 is ROM, and so forth. The last two digits are sequence numbers typically starting with 01. Thus, the first bipolar RAM was the 3101.

   During development, the 8008 chip was called the 1201, following Intel's naming scheme: the 1 indicated the chip was built from PMOS technology, the 2 indicated a custom chip and the 01 was a serial number. Fortunately, when it came time to market microprocessors, Intel decided that marketing was more important than systematic numbering: Intel's 4-bit microprocessor became the 4004 and their 8-bit microprocessor the 8008. ↩

4. Intel introduced the i3101 chip in April 1969. The i3101 RAM chip was a static memory chip, rather than the dynamic RAM chips common today. It was also built from Schottky TTL technology, rather than MOS used in modern RAM chips. Other companies, such as National Semiconductor, Signetics and Fairchild, made 64-bit memory chips compatible with the Intel i3101. However, they typically used the standard 74xx numbering scheme, calling the chip the 7489. ↩

5. Although the Datapoint's stack could hold 16-bit values, the Datapoint 2200 only used 13 address bits, supporting a maximum of 8K of memory. The 8008 expanded the address range to 14 bits, supporting 16K of memory, which was a huge amount at that time. However, the 8008's internal stack was only 8 values, rather than the 16 of the Datapoint 2200. ↩

6. Texas Instruments heard that Intel was designing a processor for Datapoint and asked Datapoint if they could build a processor for Datapoint too. TI beat Intel to the finish, creating the TMC 1795 processor before Intel completed the 8008, largely because Intel put the 8008 on the back burner. After Datapoint rejected TI's microprocessor, TI tried to find a new customer for the chip. TI was unsuccessful, and the TMC 1795 was abandoned and mostly forgotten. I've written about the TI chip in more detail here. ↩

7. You may be familiar with linear-feedback shift registers (LFSRs), which can be used as pseudo-random number generators or noise generators. With N stages, a LFSR can generate 2^N-1 output values. The de Bruijn sequence is generated from a nonlinear-feedback shift register. Nonlinear-feedback shift registers are a generalization of LFSRs; by using more complex feedback circuitry than just XOR, a nonlinear feedback shift register can generate sequences of arbitrary length. In particular, it can generate a sequence of 2^N values, while a LFSR is limited to 2^N-1. ↩

8. Nonlinear feedback shift registers seem pretty obscure. The only other use I've seen is the TMS 0100 calculator chip, which generates an internal sequence of length 11. For information on the theory, see The Synthesis of Nonlinear Feedback Shift Registers and Counting with Nonlinear Binary Feedback Shift Registers. The book Shift Register Sequences goes into great detail on linear and nonlinear sequences; Section VII:5 is probably most relevant, describing how to make a shift register cycle of any length.

   The TMS 1000 microcontroller saves a few gates by using a LFSR for the program counter. Instead of incrementing, the PC goes through a pseudo-random sequence. The code is stored in the ROM in the same sequence; everything works out, but it seems like a strange way to implement a program counter. ↩

9. I was expecting the stack counter and refresh counter to have a regular layout on the chip, with a single shift register stage repeated three times. However, on the 8008 die, the transistors are arranged irregularly, scattered around where there was room. Presumably this made the layout more compact. ↩

10. Since the signal read from stack storage passes through an inverter before being written back, you might expect the bit to get flipped. The explanation is that transistor T2 in the storage cell inverts the value on C. Thus, the value read from a sense line is inverted compared to the value written on the sense line. The inverter amplifier provides a second inversion, restoring the original value. ↩

11. Each 8008 instruction takes multiple clock cycles to execute. An instruction is broken into one or more machine cycles; each machine cycle typically corresponds to one memory access for instruction or data. Each machine cycle consists of up to 5 states (T1 through T5). An address is transmitted to memory during state T1 and T2, and the memory location is read or written during T3. Each T state requires two clock cycles, so an 8008 instruction takes a minimum of 10 clock cycles. The Intel 8008 user's manual provides detailed timings. ↩