Nostr notes by Ken Shirriff

Basically, but it's a bit tricky because it uses a radix-4 ...

2026-10-29T20:42:09Z

In reply to nevent1q…zt4v
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Basically, but it's a bit tricky because it uses a radix-4 Booth multiplier.

It's a carry-skip adder: ...

2026-10-19T00:17:08Z

In reply to nevent1q…20qy
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It's a carry-skip adder: https://www.righto.com/2026/06/intel-8087-adder-reverse-engineered.html

Good thing I mentioned Kahan in my thread :-)

2026-10-18T18:17:48Z

In reply to nevent1q…2fcn
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Good thing I mentioned Kahan in my thread :-)

For more on the 8087's circuitry and the microcode, see my ...

2026-10-18T17:12:18Z

In reply to nevent1q…8w6n
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For more on the 8087's circuitry and the microcode, see my latest article: https://www.righto.com/2026/10/8087-addition-subtraction-microcode.html
Credits: I've been working on this with the members of the "Opcode Collective", especially Smartest Blob and
gloriouscow (npub1dhl…ud8y)

Although the 8087 chip was complicated, it became popular because ...

2026-10-18T17:11:19Z

In reply to nevent1q…9ezh
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Although the 8087 chip was complicated, it became popular because it made floating-point operations 100 times faster on the IBM PC and other systems. Its math became the standard (IEEE 754) used by all modern computers, so every time you do math, thank the 8087 chip :-)

The 8087 chip's microcode implemented infinity and other ...

2026-10-18T17:09:27Z

In reply to nevent1q…ymmm
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The 8087 chip's microcode implemented infinity and other special cases in complicated code. This flowchart shows part of the code. Don't worry, you're not expected to understand this "spaghetti" code :-) The point is that there's a lot going on.

The 8087 chip went beyond regular numbers, supporting special ...

2026-10-18T17:08:59Z

In reply to nevent1q…dhc0
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The 8087 chip went beyond regular numbers, supporting special values such as infinities, positive and negative 0, Not-A-Number. Computer scientist W. Kahan made sure special values were handled in mathematically sensible ways, so the chip had pages of special-case rules to follow.

Subtracting two floating-point numbers, say 8-7.5, takes a few ...

2026-10-18T17:08:06Z

In reply to nevent1q…dz7k
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Subtracting two floating-point numbers, say 8-7.5, takes a few steps. Floating-point numbers are stored as a power of 2 times a binary number. The numbers are shifted so the exponents align, and then subtracted in binary. To get rid of zeros at the front, the result is shifted (normalized).

With a microscope, I zoomed in on the tiny silicon die and ...

2026-10-18T17:07:38Z

In reply to nevent1q…qcyw
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With a microscope, I zoomed in on the tiny silicon die and identified the circuitry. The ROM holds the software (microcode) that controls the chip. The adder is the heart of the chip, while the shifter aligns numbers, sliding them back and forth.

Have you ever thought about how your computer adds and subtracts? ...

2026-10-18T17:06:34Z

Have you ever thought about how your computer adds and subtracts? It takes a lot of hardware to handle floating-point numbers like 12.34. I opened up Intel's 8087 math coprocessor chip from 1980 to see how it works...

The oscillator would typically be an external quartz crystal, ...

2026-10-10T18:53:45Z

In reply to nevent1q…6v7w
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The oscillator would typically be an external quartz crystal, which also has the advantage of making the filter frequency extremely accurate.

Yes, and also quantization, so you need a Nyquist filter. But you ...

2026-10-10T17:51:53Z

In reply to nevent1q…dkff
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Yes, and also quantization, so you need a Nyquist filter. But you can adjust the "resistance" by changing the frequency, so it's easy to sweep the filter for e.g. a spectrum analyzer.

For more photos of the ML10 chip and an explanation of how it ...

2026-10-10T17:50:04Z

In reply to nevent1q…m542
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For more photos of the ML10 chip and an explanation of how it works (it uses a "state variable filter"), see my latest article:
https://www.righto.com/2026/10/ML10-switched-capacitor-filter.html
Thanks to [@CuriousMarc](https://mastodon.social/@CuriousMarc ) for providing the chip.

The heart of most analog circuits is the operational amplifier, ...

2026-10-10T17:49:28Z

In reply to nevent1q…cgxz
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The heart of most analog circuits is the operational amplifier, or op-amp. Op-amps are very flexible; in this chip, they integrate signals. The op-amp is interesting under the microscope; its transistors have various sizes and patterns.

The switched capacitor is a bit bizarre. By opening and closing ...

2026-10-10T17:48:53Z

In reply to nevent1q…5gpm
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The switched capacitor is a bit bizarre. By opening and closing the switches at high frequency, charge moves in and out of the capacitor at a controlled rate, just like a resistor. Why replace a resistor with a complicated circuit? Because resistors are large and very inaccurate on chips.

Here's a close-up of one of the electronic switches. It uses ...

2026-10-10T17:48:10Z

In reply to nevent1q…r9f2
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Here's a close-up of one of the electronic switches. It uses four transistors and acts as a toggle switch. To prevent interference, the transistors are surrounded by two isolation rings. For the second photo, I removed the metal layer with acid to reveal the polysilicon and silicon underneath.

The chip contains two filters; the top and bottom filters are ...

2026-10-10T17:46:43Z

In reply to nevent1q…ce97
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The chip contains two filters; the top and bottom filters are mirror images. The chip contains 72 tiny capacitors, the pink squares in the middle. Above the capacitors are electronic switches, which switch the capacitors in and out of the circuit at high speed.

Under the microscope, a tiny map of Florida is visible. Harris, ...

2026-10-10T17:46:03Z

In reply to nevent1q…gcpa
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Under the microscope, a tiny map of Florida is visible. Harris, the manufacturer, was in Melbourne, Florida; the stylized H is the logo. The chip has various initials, presumably the names of the designers of the chip.

At first, we couldn't identify this mystery chip from Harris. ...

2026-10-10T17:45:32Z

In reply to nevent1q…95u6
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At first, we couldn't identify this mystery chip from Harris. Since it had a ceramic package, I could easily open it by tapping it along the seam with a chisel, popping the lid off and revealing the tiny silicon die inside.

I opened up a mystery chip; it turned out to be a "switched ...

2026-10-10T17:44:57Z

I opened up a mystery chip; it turned out to be a "switched capacitor filter" from 1984. Filters are important circuits, for example, adjusting the bass or treble in an audio signal. This chip, the MF10, was popular because it combined two filters into an easy-to-use chip. Let's take a closer look…

It's nice to know that my stuff from 34 (!) years ago still ...

2026-10-10T04:40:34Z

In reply to nevent1q…y7za
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It's nice to know that my stuff from 34 (!) years ago still turns up :-)

It turns out that you can do better than a Taylor series, because ...

2026-09-26T17:30:17Z

In reply to nevent1q…vqx3
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It turns out that you can do better than a Taylor series, because a Taylor series is optimized for a single point. You can use the "Remez algoirthm" to get a minimax function that is optimized over the whole interval.
I looked at the Pentium's formulas here: https://www.righto.com/2025/01/pentium-floating-point-ROM.html

Analog computers aren't appreciated nowadays, but at the ...

2026-09-26T17:18:46Z

In reply to nevent1q…kfgr
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Analog computers aren't appreciated nowadays, but at the time, they were usually faster than digital computers, responding instantaneously in real time.
As you mention, accuracy was a problem. If you want, say, 0.1% accuracy, you need expensive high-precision resistors and capacitors. But digital computers can give you as much accuracy as you want, just use more bits, built with cheap components.

Credits: I've been working on this with the members of the ...

2026-09-26T17:07:54Z

In reply to nevent1q…y3su
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Credits: I've been working on this with the members of the "Opcode Collective", especially Smartest Blob and gloriouscow (npub1dhl…ud8y), who used ML to convert ROM images to microcode data and extensively analyzed the contents.
Photo of the CORDIC II computer from "The Birth of CORDIC", by Jack Volder, the creator of CORDIC: https://web.archive.org/web/20160304064804if_/http://late-dpedago.urv.cat/site_media/papers/fulltext_2.pdf

For details on how the 8087 calculates tangents by using the ...

2026-09-26T17:05:29Z

In reply to nevent1q…5ya4
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For details on how the 8087 calculates tangents by using the CORDIC algorithm combined with polynomials, see my latest article:
https://www.righto.com/2026/09/8087-tangent-cordic.html

The 8087 chip implements its algorithms in microcode, specialized ...

2026-09-26T17:05:06Z

In reply to nevent1q…9wu9
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The 8087 chip implements its algorithms in microcode, specialized low-level code inside the chip. By examining the microcode ROM under a microscope, the Opcode Collective extracted the bits and I reverse-engineered the algorithm.

CORDIC became popular, especially in scientific calculators. The ...

2026-09-26T17:04:21Z

In reply to nevent1q…f6lu
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CORDIC became popular, especially in scientific calculators. The 8087 chip uses CORDIC, but goes further, also using a polynomial ratio to get more accuracy. The simple function 3x/(3-x^2) (blue) is surprisingly close to the tangent (red), better than a Taylor series (green).

Usually, rotating a vector by an angle requires complicated math. ...

2026-09-26T17:03:52Z

In reply to nevent1q…89ya
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Usually, rotating a vector by an angle requires complicated math. But for some special angles, the calculation requires just shifts and adds, easy to do in hardware. The CORDIC algorithm breaks down an angle into special angles (using a table), does quick vector rotations, producing the trig answer.

Back in 1956, the Mach-2 B-58 Hustler had an analog navigation ...

2026-09-26T17:03:35Z

In reply to nevent1q…p72t
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Back in 1956, the Mach-2 B-58 Hustler had an analog navigation computer. It wasn't accurate enough, so they built a digital replacement. Sines and cosines are easy in analog, but required a new digital algorithm. They invented the CORDIC algorithm and built the 134-pound CORDIC computer.

How do computers calculate complicated trig functions such as ...

2026-09-26T17:02:02Z

How do computers calculate complicated trig functions such as tangent? I took a look at Intel's 8087 floating-point chip under the microscope to find out. The chip combines two techniques to evaluate the tan function quickly and accurately: polynomials and an algorithm called CORDIC...

It's complicated. The 8087 more-or-less watches the ...

2026-09-13T15:13:11Z

In reply to nevent1q…j087
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It's complicated. The 8087 more-or-less watches the instruction stream and grabs instructions to execute. The 8086 runs in parallel until it executes a WAIT instruction to sync up. The 8086 and 8087 have independent registers. So how does the 8087 access memory if the address is in an 8086 register? The trick is that the 8086 does a fake access to the memory location and the 8087 grabs the address off the bus.

Credits: I've been working on this with the members of the ...

2026-09-12T16:31:04Z

In reply to nevent1q…f2hv
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Credits: I've been working on this with the members of the "Opcode Collective", especially Smartest Blob and gloriouscow (npub1dhl…ud8y), who converted the ROM images to microcode data and extensively analyzed the contents.
7/7

The 8087's microcode is too complicated and low-level to ...

2026-09-12T16:30:34Z

In reply to nevent1q…t5cq
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The 8087's microcode is too complicated and low-level to explain here. For details, see my latest article:
https://www.righto.com/2026/09/8087-microcode-reverse-engineering-fscale.html

I can now explain the microcode for an instruction called FSCALE ...

2026-09-12T16:30:02Z

In reply to nevent1q…fgwz
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I can now explain the microcode for an instruction called FSCALE that scales a number by a power of 2. It sounds simple, but the 8087 has an appalling number of special cases: positive and negative 0, two infinities, four rounding modes, three number sizes, six exceptions... so the code is complex.

Knowing the contents of the 8087's microcode is just the ...

2026-09-12T16:29:28Z

In reply to nevent1q…fgwz
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Knowing the contents of the 8087's microcode is just the first step; we've been working for months to assign meaning to the 0s and 1s. I've been reverse-engineering the circuitry in the 8087, units such as an adder, shifter, and registers, to understand what the microcode is doing.

Zooming in on the microcode storage ROM, you can see the ...

2026-09-12T16:28:40Z

In reply to nevent1q…y0ay
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Zooming in on the microcode storage ROM, you can see the individual transistors, the pinkish blobs. The 8087 is very unusual, using four transistor sizes, giving it double density: 2 bits per transistor. The Opcode Collective examined all 13184 transistors, revealing the 0s and 1s of the microcode.

Under a microscope, you can see the circuitry of the 8087. The ...

2026-09-12T16:27:01Z

In reply to nevent1q…pket
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Under a microscope, you can see the circuitry of the 8087. The 8087 performs its calculations using low-level software called microcode, stored in the large ROM in the middle. Along with the "Opcode Collective", I'm trying to understand the algorithms in the microcode, from addition to arctangents.

In 1980, Intel introduced the 8087 floating-point coprocessor ...

2026-09-12T16:25:43Z

In 1980, Intel introduced the 8087 floating-point coprocessor chip. Plugging this chip into your IBM PC made math 100 times faster, good for CAD and spreadsheets. I opened up the chip to reverse-engineer exactly how it does complicated calculations. Let's take a look inside...

Ouch! I've seen many damaged core planes, since they are so ...

2026-08-31T01:32:08Z

In reply to nevent1q…4pwy
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Ouch! I've seen many damaged core planes, since they are so delicate.

In brief, it's easy to magnetize a core one direction or the ...

2026-08-31T01:31:21Z

In reply to nevent1q…lehz
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In brief, it's easy to magnetize a core one direction or the other (by passing the current in one direction or the other). But it's hard to demagnetize a core, or anything else for that matter.

I got to see the famous moth in person at the Smithsonian... ...

2026-08-30T19:21:25Z

In reply to nevent1q…kcmr
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I got to see the famous moth in person at the Smithsonian...

Nice photo! You must have worked hard to get it to come out so ...

2026-08-30T17:56:44Z

In reply to nevent1q…6s6m
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Nice photo! You must have worked hard to get it to come out so clearly.

Credits: thanks to Steve Jurvetson for letting me disassemble the ...

2026-08-30T17:56:06Z

In reply to nevent1q…pqj5
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Credits: thanks to Steve Jurvetson for letting me disassemble the computer. Core close-up photo from [@CuriousMarc](https://mastodon.social/@CuriousMarc ). Core diagram from Digital Computer Components and Circuits, 1957.

For more on the Spacelab computer and its core memory system, see ...

2026-08-30T17:55:35Z

In reply to nevent1q…0z5a
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For more on the Spacelab computer and its core memory system, see my latest article: https://www.righto.com/2026/08/spacelab-core-memory.html

This photo shows the computer with one of its logic boards ...

2026-08-30T17:54:57Z

In reply to nevent1q…2n63
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This photo shows the computer with one of its logic boards removed. The core memory occupies the right third of the computer. The round military-style connectors on the front of the computer connected to other systems on Spacelab. CIMSA was the manufacturer.

The core memory stack has two driver boards that generate the ...

2026-08-30T17:54:31Z

In reply to nevent1q…qa9k
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The core memory stack has two driver boards that generate the high-current pulses through the X and Y wires. The boards are crammed with integrated circuits that were specially designed for core memory systems.

Core memories usually have an "inhibit" wire for writing ...

2026-08-30T17:52:55Z

In reply to nevent1q…qcz6
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Core memories usually have an "inhibit" wire for writing data back. The core memory board uses a more complicated "2½D" design, which eliminates the inhibit wire. Three wires—X, Y, and sense—go through each core. The sense wires cross each other in the middle; this reduces the noise they pick up.

The core memory is arranged with 16 horizontal lines of cores to ...

2026-08-30T17:51:56Z

In reply to nevent1q…0ja5
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The core memory is arranged with 16 horizontal lines of cores to store each of the 18 bits in a word. This photo shows how the tiny wires from the core plane are soldered to the much larger traces on the circuit board.

The back side of each core memory board is crammed with chips. 18 ...

2026-08-30T17:47:46Z

In reply to nevent1q…86ze
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The back side of each core memory board is crammed with chips. 18 sense amplifier chips (yellow) provide 18 bits of output (16 bits+parity+storage protection). A multitude of diode modules are connected to the core plane's vertical wires (red) and horizontal wires (green).

Spacelab used three French-built minicomputers, model Mitra 125 ...

2026-08-30T17:46:48Z

In reply to nevent1q…9u2a
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Spacelab used three French-built minicomputers, model Mitra 125 MS. This photo shows the core memory stack in front of the computer. (The computer looks empty because I removed the circuit boards for analysis.) The computer is surprisingly heavy; it has a lot of metal for conduction cooling.

Each tiny ring can be magnetized clockwise or counterclockwise to ...

2026-08-30T17:46:09Z

In reply to nevent1q…5scy
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Each tiny ring can be magnetized clockwise or counterclockwise to store a 0 or 1. Putting a current through an X wire and a Y wire in the grid magnetizes the core where the two wires cross. Special magnetic materials ensure that the other cores are unaffected. The sense wire reads out the data.

Magnetic core memory uses tiny ferrite rings, one for each bit of ...

2026-08-30T17:45:29Z

In reply to nevent1q…5scy
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Magnetic core memory uses tiny ferrite rings, one for each bit of storage. The rings are arranged in a grid, with tiny copper wires threaded vertically and horizontally to select a core. To read a value, the green "sense" wire snakes through all the cores. Each ring is 32 mils (0.8mm) in diameter.

Before semiconductor RAM, most computers used magnetic core ...

2026-08-30T17:43:56Z

Before semiconductor RAM, most computers used magnetic core memory. This is the 128 KB core stack from the computer on Spacelab, the Space Shuttle's experimental laboratory. Let's take a closer look...

Yes, the RSS feed for my blog is ...

2026-08-03T19:28:29Z

In reply to nevent1q…2v7v
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Yes, the RSS feed for my blog is https://www.righto.com/feeds/posts/default

Nice! I have an MS7A module too, and wrote about it here: ...

2026-07-31T20:27:03Z

In reply to nevent1q…chql
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Nice! I have an MS7A module too, and wrote about it here: https://www.righto.com/2026/06/ibm-604-thyraton-tube-module.html

Yes, the tube is based on a regular tube (the 6J6), but IBM ...

2026-07-31T20:20:25Z

In reply to nevent1q…zdae
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Yes, the tube is based on a regular tube (the 6J6), but IBM redesigned it for more reliability. They changed the grid and plate to avoid shorts from tiny conductive particles and split the shared cathode into two separate cathodes. (Source: "IBM's Early Computers", p66)

I might be able to identify your tube module. Does it have a ...

2026-07-31T18:33:33Z

In reply to nevent1q…ksug
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I might be able to identify your tube module. Does it have a label on the handle, like TH-1? How many pins does the base of the module have? 9 or 10?

Diversity was limited to the hairstyles.

2026-07-31T17:13:55Z

In reply to nevent1q…zqhs
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Diversity was limited to the hairstyles.

To IBM's credit, they advertised this system as equivalent to ...

2026-07-31T16:47:34Z

In reply to nevent1q…zjpu
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To IBM's credit, they advertised this system as equivalent to 150 extra engineers, not as a replacement for 150 existing engineers.

Credits: thanks to Robert Garner for the tube module and ...

2026-07-31T16:42:55Z

In reply to nevent1q…9p2f
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Credits: thanks to Robert Garner for the tube module and CuriousMarc (npub1vgw…46mg) for electronics support.

IBM 604 image from Ed Thelen: https://ed-thelen.org/comp-hist/IBM-604.html
Vacuum tube diagram from IBM 604 manual: https://bitsavers.org/pdf/ibm/604/227-7609-0_604_CE_man_1958.pdf#page=27
IBM ad from Wikimedia:

For more information on the tube module, including circuit ...

2026-07-31T16:41:02Z

In reply to nevent1q…rwcp
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For more information on the tube module, including circuit diagrams, see my latest article: https://www.righto.com/2026/07/ibm-604-trigger-tube-module.html

The IBM 604 calculator used about 1300 tubes and rented for $550 ...

2026-07-31T16:40:36Z

In reply to nevent1q…eh3j
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The IBM 604 calculator used about 1300 tubes and rented for $550 a month. It was a very popular system with over 5600 units produced. IBM advertised it as equivalent to 150 engineers.

I've powered up the trigger module in this video. It is ...

2026-07-31T16:39:34Z

In reply to nevent1q…f8cj
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I've powered up the trigger module in this video. It is switched on or off by two inputs and remembers its state until switched again. I push two buttons to turn it on or off, and its state is displayed by two vintage neon bulbs. This may seem trivial, but the trigger (now called a flip-flop) is a key component of computers.

The tube module uses a "dual triode" tube, two amplifiers ...

2026-07-31T16:38:27Z

In reply to nevent1q…d3c3
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The tube module uses a "dual triode" tube, two amplifiers in one glass tube. In the first photo, the two vertical dark rectangles are the two plates. The second photo shows the tube powered up, with the heaters glowing orange at the top and bottom.

Before transistors, vacuum tubes were widely used as switches and ...

2026-07-31T16:37:19Z

In reply to nevent1q…pcr0
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Before transistors, vacuum tubes were widely used as switches and amplifiers. A heater heats up the cathode, which emits electrons. They are attracted to the plate, causing current to flow. A negative voltage on the grid blocks the electrons, controlling the current flow.

This module was part of IBM's 604 Electronic Calculating ...

2026-07-31T16:36:42Z

In reply to nevent1q…3exx
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This module was part of IBM's 604 Electronic Calculating Punch. It read 100 punch cards a minute, performed calculations that were specified by a wiring panel, and punched the results on cards. In the lower left, you can see rows of tube modules with their handles sticking out.

This vacuum tube module was used in an IBM programmable ...

2026-07-31T16:36:03Z

This vacuum tube module was used in an IBM programmable calculator from 1948. This module, called a "trigger", stored one bit of information. Let's take a closer look and see the module operate.

Credits: IOP boards provided by Richard, 4 Pi board from ...

2026-06-28T16:30:48Z

In reply to nevent1q…7ezz
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Credits: IOP boards provided by Richard, 4 Pi board from Tube🌞 Time (npub1xvg…62t2).
Photo of the IOP and CPU courtesy of RR Auction. IOP documentation from Mike Stewart. Exploded diagram from https://ibiblio.org/apollo/Shuttle/IBM-74-A31-016%20-%20Space%20Shuttle%20Advanced%20System,%204%20Pi%20-%20Prototype%20Input,%20Output%20Processor%20(IOP).pdf#page=145

Want more photos? Or more info, such as how the I/O processor ...

2026-06-28T16:29:58Z

In reply to nevent1q…f8rc
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Want more photos? Or more info, such as how the I/O processor implements 25 virtual processors with two instruction sets on top of a single physical processor? See my latest article: https://www.righto.com/2026/06/space-shuttle-io-processor-boards.html

This diagram shows how the circuit boards (called pages) were ...

2026-06-28T16:29:31Z

In reply to nevent1q…50ge
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This diagram shows how the circuit boards (called pages) were plugged into the I/O Processor's aluminum-alloy case. For storage, the system used magnetic core memory, larger pages at the back. This system didn't use a microprocessor; it was built from 11 logic pages crammed with simple chips.

IBM had a series of aerospace computers called System/4 Pi. These ...

2026-06-28T16:29:01Z

In reply to nevent1q…swy6
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IBM had a series of aerospace computers called System/4 Pi. These computers all used standard-sized boards (top). Except that the I/O Processor's boards (bottom) were one inch wider. I guess they needed the extra space for more circuitry.

The second board is memory (PROM), holding microcode for the I/O ...

2026-06-28T16:27:42Z

In reply to nevent1q…tq6q
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The second board is memory (PROM), holding microcode for the I/O Processor, which is a (very strange) computer, independent of the CPU. Each gold-lidded chip holds 2K bits in tiny metal fuses. The chip is programmed by blowing the fuse for each 1 bit, literally burning the PROM.

First board is a network interface. Each side is identical and ...

2026-06-28T16:26:34Z

In reply to nevent1q…mhtr
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First board is a network interface. Each side is identical and supports two networks. The IBM hybrid module (right) contains tiny transistors, resistors, etc. to handle the analog stuff. The golden Motorola chips format bits to transmit and receive them. The other chips are mostly shift registers.

The Space Shuttle had five general-purpose computers that ...

2026-06-28T16:25:31Z

The Space Shuttle had five general-purpose computers that controlled, monitored, and navigated the Shuttle. Each computer consisted of two boxes: the CPU (right) and the I/O Processor (IOP, left). The IOP connected the computer to 24 high-speed networks. Let's look at two boards from the IOP... 1/N

Intel used parallel prefix adders later, such as Kogge-Stone in ...

2026-06-13T19:01:24Z

In reply to nevent1q…f7lh
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Intel used parallel prefix adders later, such as Kogge-Stone in the Pentium.

The big shifter for normalization is on the left.

For more info:
https://www.righto.com/2025/01/pentium-carry-lookahead-reverse-engineered.html
https://www.righto.com/2020/05/die-analysis-of-8087-math-coprocessors.html

For full details, see my latest article: ...

2026-06-13T16:26:30Z

In reply to nevent1q…708z
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For full details, see my latest article:
https://www.righto.com/2026/06/intel-8087-adder-reverse-engineered.html
A group of us, including gloriouscow (npub1dhl…ud8y) and Smartest Blob are reverse-engineering the 8087.

For those who like schematics, here's four bits of the adder, ...

2026-06-13T16:25:09Z

In reply to nevent1q…mdh6
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For those who like schematics, here's four bits of the adder, reverse-engineered. It's too complicated to explain here, but for those who care: "Manchester carry chain" computes carries, along with a "carry skip" circuit. "F" is the input from the fraction bus and "prop" is the "propagate" value.

The adder is part of a set of registers and shifters that make ...

2026-06-13T16:24:32Z

In reply to nevent1q…5uh9
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The adder is part of a set of registers and shifters that make multiplication, division, and square roots fast. The 8087 multiplies two bits at a time (twice as fast) thanks to the Multiply Decision Box and selector. The Quotient Register is for division. Square roots get bits from the Skip Shifter.

I dissolved the metal with acid so you can see the silicon ...

2026-06-13T16:23:47Z

In reply to nevent1q…dw9z
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I dissolved the metal with acid so you can see the silicon circuits in the 8087 chip. The pinkish regions are doped silicon. The thin lines are polysilicon wires on top of the silicon. When polysilicon crosses doped silicon, it forms transistors, the switches that make circuits work.

For performance, the adder is constructed in blocks of four bits. ...

2026-06-13T16:22:57Z

In reply to nevent1q…t3va
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For performance, the adder is constructed in blocks of four bits. Here's one block under the microscope. This shows the chip's single metal layer, the metal wiring on top of the silicon that connects things. Modern chips can have over 20 layers. The thick vertical wires on the side power the adder.

Intel introduced the 8087 floating-point chip in 1980 to make ...

2026-06-13T16:21:58Z

Intel introduced the 8087 floating-point chip in 1980 to make math faster. The chip does tangents, square roots, and so forth, but fundamentally everything is computed through additions and subtractions, performed by an adder at the heart of the chip. Let's look at the adder's circuitry... 1/N

The motivation for a thyratron over a triode is that it can ...

2026-06-07T19:06:21Z

In reply to nevent1q…r6g0
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The motivation for a thyratron over a triode is that it can handle larger currents. Yes, it's like a thyristor (which is short for thyratron transistor).

We got a nice glow from mercury-filled thyratrons:

Yes, the thyratron is very similar to an SCR (also known as a ...

2026-06-07T19:02:50Z

In reply to nevent1q…t69w
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Yes, the thyratron is very similar to an SCR (also known as a thyristor: thyratron transistor).

I've powered up one of those 8-tube modules before: ...

2026-06-07T19:00:50Z

In reply to nevent1q…hkw7
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I've powered up one of those 8-tube modules before: https://www.righto.com/2018/01/ibm-mainframe-tube-module-part-ii.html

The eight tubes have nothing to do with bytes (which didn't exist at the time). Eight tubes was just a convenient size for a module. They generally don't handle 8 bits, because circuits often need more than one tube. Some modules handle 5 bits, some 3, it depends.

For more on the IBM 604 and this thyratron tube module, see my ...

2026-06-07T17:29:42Z

In reply to nevent1q…hpej
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For more on the IBM 604 and this thyratron tube module, see my latest article: https://www.righto.com/2026/06/ibm-604-thyraton-tube-module.html

Pluggable tube modules were an important innovation. They made it ...

2026-06-07T17:29:23Z

In reply to nevent1q…awpq
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Pluggable tube modules were an important innovation. They made it easy to repair tube-based systems, they packaged components densely, and they paved the way for IBM's tube computers in the 1950s. IBM featured the modules in this 1952 ad from Time magazine: "Fingers you can count on". 4/N

The tube is not exactly a vacuum tube since it has a bit of xenon ...

2026-06-07T17:28:12Z

In reply to nevent1q…nkz5
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The tube is not exactly a vacuum tube since it has a bit of xenon gas inside. It is called a thyratron: when it turns on, the xenon ionizes, allowing a large current to flow through the tube. In the IBM 604, thyratron tubes provided high-current pulses to the electromagnets to punch holes in cards.

The tube module acts as a high-current switch: I hooked it up to ...

2026-06-07T17:26:34Z

In reply to nevent1q…92f2
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The tube module acts as a high-current switch: I hooked it up to control a light bulb. The first button turns the module on with a small signal. The second button cuts the power to turn the module off. 2/N

The IBM 604 Electronic Calculating Punch was introduced in 1948. ...

2026-06-07T17:24:35Z

The IBM 604 Electronic Calculating Punch was introduced in 1948. Not quite a computer, it was a programmable calculator that became very popular due to its low price of $550/month, and over 5600 were produced. I have a vacuum tube module from this system, so I powered it up... 1/N

I think the 8087 replaced empty registers with NaN for the FXCH ...

2026-06-02T19:00:20Z

In reply to nevent1q…rcza
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I think the 8087 replaced empty registers with NaN for the FXCH exchange instruction for consistency. As you say, the empty value could have been swapped. But then the instruction is a special case compared to every other instruction that converted an empty value to NaN.

I did this work with the Opcode Collective, especially Smartest ...

2026-05-30T17:48:19Z

In reply to nevent1q…37h5
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I did this work with the Opcode Collective, especially Smartest Blob and Gloriouscow.
The full ROM image: https://8087.martypc.net/#dzi=tiles%2Ftiles.dzi
A description of the 8087 microcode: https://github.com/a-mcego/granite/blob/main/tools/8087mc/bin/8087.md

We are reverse-engineering the meaning of the 8087's ...

2026-05-30T17:47:35Z

In reply to nevent1q…8s43
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We are reverse-engineering the meaning of the 8087's microcode. For more details, see my latest article:
https://www.righto.com/2026/05/microcode-inside-intel-8087-floating.html

A close-up of the microcode ROM shows the individual bits. Unlike ...

2026-05-30T17:47:12Z

In reply to nevent1q…tkpe
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A close-up of the microcode ROM shows the individual bits. Unlike most ROMs, the 8087 uses four transistor sizes, letting it store two bits per transistor. This complex, semi-analog approach was necessary to fit all the data into the chip; the 8087 pushed the limits of 1980 technology. 3/n

A microscope reveals the complex circuitry of the 8087 chip. The ...

2026-05-30T17:46:40Z

In reply to nevent1q…rd5k
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A microscope reveals the complex circuitry of the 8087 chip. The microcode ROM in the center holds the micro-instructions. It executes these micro-instructions to add, subtract, compute square roots, arctangents, and so forth. 2/n

In the 1980s, if you wanted your IBM PC to be faster for ...

2026-05-30T17:44:23Z

In the 1980s, if you wanted your IBM PC to be faster for spreadsheets or CAD, you could buy the Intel 8087 floating-point chip. Internally, the chip runs special code called microcode. We opened the chip, extracted the microcode, and are figuring out how it works. 1/n

Well, I'll use Armour Etch and Whink, which are like the ...

2026-05-24T00:45:41Z

In reply to nevent1q…mj5q
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Well, I'll use Armour Etch and Whink, which are like the consumer-friendly versions of HF. I've found that N-doping vs P-doping are visible without even trying, so maybe implants could also be visible. Of course, the implant concentration might be too low to see. But I wouldn't completely rule out reading the 286 ROM without giving it a try.

Has anyone tried etching the 286 to see if the implant ROM can be ...

2026-05-24T00:23:38Z

In reply to nevent1q…ngnm
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Has anyone tried etching the 286 to see if the implant ROM can be made visible without too much trouble? I could give it a try once I get the 8087 analysis finished :-)

Yes, the chips are TTL, specifically 5400-series. But that's ...

2026-05-24T00:00:48Z

In reply to nevent1q…utma
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Yes, the chips are TTL, specifically 5400-series. But that's hard to see because the part numbers are mostly JM38510 military numbers. And 7714 is a date code (1977 week 14), not a part number.

This wire looks like it has always been yellow.

2026-05-23T23:54:03Z

In reply to nevent1q…mfmr
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This wire looks like it has always been yellow.

Those documents should be very interesting. Do the documents ...

2026-05-23T17:30:17Z

In reply to nevent1q…3m5d
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Those documents should be very interesting. Do the documents describe programming the Spacelab computers in assembly, HAL/S, or something else?