Nostr notes by Ken Shirriff

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...

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…

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...

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...

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.

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

2026-06-07T17:26:34Z

In reply to nevent1q…9q80
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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 did this work with the Opcode Collective, especially Smartest ...

2026-05-30T17:48:19Z

In reply to nevent1q…zy3l
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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…rf02
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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…4mgy
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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…a3e8
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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

For more on the Spacelab computer, see my latest article: ...

2026-05-23T16:54:05Z

In reply to nevent1q…zvej
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For more on the Spacelab computer, see my latest article: https://www.righto.com/2026/05/reverse-engineering-spacelab-computer.html

Around 1991, the Spacelabe computers were upgraded, replacing the ...

2026-05-23T16:53:26Z

In reply to nevent1q…2v05
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Around 1991, the Spacelabe computers were upgraded, replacing the French Mitra 125 MS computers with more powerful IBM-made AP-101SL computers. The new computers still used simple ICs, but the "flat-pack" ICs were packed more densely. They also used semiconductor memory instead of magnetic core.

This circuit board had a few bugs, which were fixed on the back ...

2026-05-23T16:52:04Z

In reply to nevent1q…es24
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This circuit board had a few bugs, which were fixed on the back with yellow "bodge" wires.

The boards need a lot of chips because a chip didn't do much ...

2026-05-23T16:51:10Z

In reply to nevent1q…htry
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The boards need a lot of chips because a chip didn't do much back then. Even the ALU chips had just 170 transistors. Multiplexers (mux) select which inputs to add, registers hold temporary values, and logic gates (NAND, inverters) tie things together.

The Arithmetic/Logic Unit (ALU) is the heart of a computer, ...

2026-05-23T16:50:20Z

In reply to nevent1q…4guq
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The Arithmetic/Logic Unit (ALU) is the heart of a computer, performing arithmetic. The ALU is a tiny part of a modern processor, but it occupied three circuit boards in the Spacelab computer. The larger chips are '181 ALU chips, each adding four bits; 8 chips let you add 32 bits.

The Space Shuttle could hold a flying laboratory called Spacelab ...

2026-05-23T16:49:16Z

The Space Shuttle could hold a flying laboratory called Spacelab in its cargo bay. Three French-made computers ran Spacelab. I opened up a Spacelab computer and found that instead of a microprocessor, it is built from a multitude of simple chips. Let's take a closer look at the computer...

In the 1960s, the B-52 bomber could navigate by the stars. ...

2026-04-18T16:42:04Z

In the 1960s, the B-52 bomber could navigate by the stars. Celestial navigation requires spherical trigonometry, so an analog Angle Computer solved these equations electromechanically. Let's look inside...

In 1967, IBM introduced the System/4 Pi line of aerospace ...

2026-03-29T16:53:11Z

In 1967, IBM introduced the System/4 Pi line of aerospace computers, packing mainframe performance into a compact box. 4 Pi computers powered everything from military aircraft to the Space Shuttle to sonar systems on submarines. Thread...

The 8086's microcode specifies what ALU operation to perform ...

2026-01-23T17:35:57Z

In reply to nevent1q…shqa
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The 8086's microcode specifies what ALU operation to perform along with which temporary register to use. The control circuitry holds this information in latches. A PLA (Programmable Logic Array) decodes the instruction into dozens of control signals. The Lookup Table (LUT) PLA generates six signals that configure the ALU to perform the desired operation.

The arithmetic/logic unit (ALU) in the Intel 8086 processor ...

2026-01-23T17:31:57Z

The arithmetic/logic unit (ALU) in the Intel 8086 processor (1978) is more complicated than you might expect, performing 28 different operations from addition and logical AND to shifts and BCD adjustment. A special control circuit reconfigures the ALU for each operation. Let's look closer...

If you're interested in obscure details of the microcode in ...

2025-12-30T19:51:11Z

If you're interested in obscure details of the microcode in the Intel 8087 floating-point chip, I have a new blog post...
https://www.righto.com/2025/12/8087-microcode-conditions.html

In 1980, Intel announced the 8087 Math Coprocessor, a chip that ...

2025-12-09T18:33:38Z

In 1980, Intel announced the 8087 Math Coprocessor, a chip that made floating-point 100 times faster. I opened up the chip, took photos of the silicon structures, and analyzed its circuitry. It's a very complex chip for its time. Let's take a look inside...

Intel's 386 processor (1985) was critical to the success of ...

2025-11-22T16:51:46Z

Intel's 386 processor (1985) was critical to the success of Intel. With 285,000 transistors, it was too much for Intel's design process and the schedule started slipping. Intel pivoted to "standard cells", an automated technique for chip layout to get back on track. Let's look closer...

Last week, the vintage IBM 1401 computer at the Computer History ...

2025-06-20T02:57:39Z

Last week, the vintage IBM 1401 computer at the Computer History Museum started behaving strangely: it wouldn't halt. More specifically, if you had two HALT instructions in a row, it would halt for the first, but when you continued, it crashed mysteriously. Here's how we fixed it.... 1/N

Credits: thanks to Richard for providing the FDAI. I worked on ...

2025-06-14T15:49:01Z

In reply to nevent1q…zkxu
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Credits: thanks to Richard for providing the FDAI. I worked on this with nprofile1qy2hwumn8ghj7un9d3shjtnddaehgu3wwp6kyqpqu45ptd4rfrspczx8s8gw6wytd9kt5wkhgecj7w22z7chgsgzcp3se4padw (nprofile…padw), nprofile1qy2hwumn8ghj7un9d3shjtnddaehgu3wwp6kyqpqpfrfxd768sn93znqxkwyu8mvnqnugncvrjcz5q6gt765a9y6xtzscypt8z (nprofile…pt8z), and Mike Stewart.
Simulator photo from "Introduction to Shuttle Mission Simulation": https://ia804505.us.archive.org/8/items/intro-to-sms/intro%20to%20sms.pdf#page=22

For more details on the FDAI, including the servo loops and ...

2025-06-14T15:46:07Z

In reply to nevent1q…ehme
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For more details on the FDAI, including the servo loops and electronic amplifiers (powered by germanium transistors), see my blog post: https://www.righto.com/2025/06/inside-apollo-fdai.html

The FDAI instrument that we examined was built in 1968, before ...

2025-06-14T15:45:49Z

In reply to nevent1q…78rz
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The FDAI instrument that we examined was built in 1968, before the Moon landing, and was then repurposed for a Space Shuttle simulator. The red arrow in this photo shows an FDAI in a Shuttle simulator. When the Shuttle (and simulators) moved to digital screens, the old instruments were scrapped.

Why don't the wires get tangled when the ball spins? There ...

2025-06-14T15:45:08Z

In reply to nevent1q…0vmq
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Why don't the wires get tangled when the ball spins? There are two slip rings that provide electrical contact as the ball rotates around the roll and pitch axes. This closeup shows how stationary brushes contact metal rings on the rotating shaft, allowing 23 connections.

Here's a video of the FDAI in motion. I removed the ...

2025-06-14T15:44:14Z

In reply to nevent1q…6cnm
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Here's a video of the FDAI in motion. I removed the hemispheres so you can see what happens inside the ball.

Removing the hollow hemispheres from the ball shows the ...

2025-06-14T15:41:44Z

In reply to nevent1q…tucz
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Removing the hollow hemispheres from the ball shows the complicated mechanism inside the ball, including the pitch and yaw motors. The pitch motor causes the entire mechanism to rotate, while the yaw motor spins the hemispheres.

Hopefully this orange will clarify how the FDAI's mechanism ...

2025-06-14T15:41:13Z

In reply to nevent1q…05lf
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Hopefully this orange will clarify how the FDAI's mechanism works :-). Rotating my hand would rotate the ball around the roll axis (red). The ball can pivot forward or back for the pitch axis (yellow). If you imagine a hollow hemisphere sitting on top, spinning the hemisphere is the yaw axis (green). 3/N

How does the FDAI's ball rotate on three axes without coming ...

2025-06-14T15:40:13Z

In reply to nevent1q…gaen
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How does the FDAI's ball rotate on three axes without coming loose? The trick is that the ball mechanism rotates on two axes, but is covered by a hollow shell that rotates on the third (yaw) axis. The motors for pitch and yaw axes are inside the ball, while the roll motor is outside. 2/N

When landing on the Moon, the astronauts watched an instrument ...

2025-06-14T15:39:28Z

When landing on the Moon, the astronauts watched an instrument called the FDAI that showed the spacecraft's orientation. The ball inside the Flight Director/Attitude Indicator rotated in three axes as the Lunar Module rotated. Let's look inside and see how it works. 1/N

In the Apollo space program, the FDAI (Flight Director Attitude ...

2025-05-21T16:22:00Z

In the Apollo space program, the FDAI (Flight Director Attitude Indicator) showed the orientation of the spacecraft through a ball that rotates on three axes. The yellow needles and black pointers show error and movement rate. This FDAI was later modified for use in a Space Shuttle simulator.

@nprofile…4j76 I took this photo today, so there's no way ...

2025-05-18T01:04:26Z

In reply to nevent1q…s8zd
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nprofile1qy2hwumn8ghj7un9d3shjtnddaehgu3wwp6kyqpq33739jwjscp0laejsmjy6fgfcu88n9mpahpchefkaezf8r380cnq4f4j76 (nprofile…4j76) I took this photo today, so there's no way you could have seen it before. I'm not aware of any similar photos.

How thin is spider silk compared to the wiring on a chip? ...

2025-05-17T19:02:38Z

How thin is spider silk compared to the wiring on a chip? Here's a close-up of a spiderweb strand diagonally across an Intel 386 processor. The spiderweb is 4 µm thick, just a bit thinner than this 1985 chip's 5 µm metal wiring. Wiring in modern chips is 100 times thinner.

Tape drive repair at the Computer History Museum. I helped figure ...

2025-05-16T21:55:49Z

Tape drive repair at the Computer History Museum. I helped figure out why the tape drives wouldn't backspace. The problem turned out to be a bad germanium transistor on an inverter card. 1/5

Anyone use Intel's 386 processor from 1985, the first 32-bit ...

2025-05-10T16:24:11Z

Anyone use Intel's 386 processor from 1985, the first 32-bit x86? To improve performance, it preloaded instructions into a 16-byte prefetch queue (highlighted in red). Why does such a small queue take up so much of the chip? Let's look under the microscope at its complicated circuitry... 1/N

Zooming in on the 386 shows 30 registers. The registers are ...

2025-05-01T17:43:50Z

In reply to nevent1q…8cq8
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Zooming in on the 386 shows 30 registers. The registers are constructed from one-bit cells, creating the grid pattern in the image. However, the six different types of cells create visible changes in the texture. A "notch" is created by the 16-bit registers, half the width of the 32-bit registers.

Intel's 386 processor (1985) moved the x86 architecture to 32 ...

2025-05-01T17:42:53Z

Intel's 386 processor (1985) moved the x86 architecture to 32 bits, but it needed to be backward compatible with earlier 16 and 8-bit processors. As a result, it needed complicated circuitry for its internal registers: six different circuits for 30 registers. Let's look at the silicon circuits. 1/N

If you were following my recent repair of a vintage Commodore PET ...

2025-04-24T15:36:56Z

If you were following my recent repair of a vintage Commodore PET home computer, you may enjoy this video from nprofile1qy2hwumn8ghj7un9d3shjtnddaehgu3wwp6kyqpqu45ptd4rfrspczx8s8gw6wytd9kt5wkhgecj7w22z7chgsgzcp3se4padw (nprofile…padw)
https://youtu.be/nxilekpLp6g?si=FZYD7hcjmsCpyP2F

The Commodore PET, along with the Apple II and the Radio Shack ...

2025-04-13T16:16:17Z

The Commodore PET, along with the Apple II and the Radio Shack TRS-80, formed the "1977 Trinity" that made home computers popular. The PET was very quirky, combining a tiny keyboard, a cassette drive for storage, and a monitor in a trapezoidal case. I got one, but it didn't work. Let's fix it... 1/N

One of the classic videos inside Google was "I just want to ...

2025-04-03T19:40:10Z

One of the classic videos inside Google was "I just want to serve 5 terabytes of data", satirizing the complexity of doing anything at Google scale. The video features animated characters Panda Woman (trying to serve data) and Broccoli Man (presenting more and more obstacles). I was reminded of this video because I'm at the Phoenix airport and I'm sure that the synthesized announcement voice here is the same as Broccoli Man. I keep expecting an announcement of "Five terabytes is so little that I've forgotten how to count that low."

https://www.youtube.com/watch?v=3t6L-FlfeaI

If any of my followers want to read about the Pentium in German, ...

2025-04-02T03:43:04Z

If any of my followers want to read about the Pentium in German, one of my articles has been translated:
https://www.heise.de/hintergrund/Zahlen-bitte-Verrueckt-Fuer-X3-brauchte-der-Pentium-einen-eigenen-Schaltkreis-10323633.html

The Pentium processor, like many others, implements its ...

2025-03-31T17:41:27Z

The Pentium processor, like many others, implements its instructions in microcode. Each step of an instruction is described by a micro-instruction, stored in the chip in the microcode ROM.
This die photo shows the parts of the Pentium. Let's take a quick look at the microcode ROM...1/N

This reference card explains what keyset presses and mouse ...

2025-03-23T16:24:26Z

In reply to nevent1q…f4mr
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This reference card explains what keyset presses and mouse buttons generate each character. Memorize this chart and then you too can use the keyset. A much steeper learning curve than the mouse.

Here's the vintage keyset with my USB interface. I used an ...

2025-03-23T16:23:38Z

In reply to nevent1q…uzxx
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Here's the vintage keyset with my USB interface. I used an Arduino-like microcontroller (the Teensy) to make the keyset act like a standard USB keyboard. To get upper case and special characters, you click mouse buttons at the same time. Too much coordination for me!

Engelbart's daughter, Christina Engelbart, loaned me a ...

2025-03-23T16:22:49Z

In reply to nevent1q…kwum
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Engelbart's daughter, Christina Engelbart, loaned me a keyset, so I built a USB interface for it and plugged it into my laptop. I had a hard time using the keyset and I'm not surprised it didn't catch on. Supposedly it takes "only" a week to learn, too long for me.

https://www.youtube.com/watch?v=DpshKBKt_os

In 1994, Wired writer Steven Levy wrote a book "Insanely ...

2025-03-23T16:22:15Z

In reply to nevent1q…4dwm
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In 1994, Wired writer Steven Levy wrote a book "Insanely Great: The Life and Times of Macintosh, the Computer that Changed Everything". He discussed how Engelbart influenced the Mac, calling the 1968 demo "the mother of all demos". The name stuck, ensuring the fame of Engelbart's demo.

Engelbart's demo was later called "The Mother of All ...

2025-03-23T16:21:34Z

In reply to nevent1q…ry39
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Engelbart's demo was later called "The Mother of All Demos". But first, an Intel demo at Comdex got that name. In 1990, Iraq invaded Kuwait and Saddam Hussein promised "The Mother of All Battles" in the Gulf War. "The mother of all..." became a meme, applied to many things including Intel's demo.

In the 1970s, some members of Engelbart's team moved to Xerox ...

2025-03-23T16:20:19Z

In reply to nevent1q…ry39
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In the 1970s, some members of Engelbart's team moved to Xerox PARC. They put his concepts into the Xerox Alto, giving it a keyset, mouse, and graphical user interface. Steve Jobs toured PARC, taking the mouse and GUI ideas for the Apple Lisa and the Macintosh. But he left the keyset behind.

Engelbart's demo was like a PowerPoint presentation over ...

2025-03-23T16:19:35Z

In reply to nevent1q…xk2d
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Engelbart's demo was like a PowerPoint presentation over Zoom, projected onto a large screen. He collaborated with co-workers 30 miles away, talking with them, editing shared files, browsing the code online, and clicking links with the mouse (which he invented). Impressive for 1968!

In 1968, Douglas Engelbart revolutionized computing by showing ...

2025-03-23T16:19:00Z

In 1968, Douglas Engelbart revolutionized computing by showing the mouse, hypertext, and collaborative computing in "The Mother of All Demos". Most of his ideas are now part of everyday computing, but one device—the keyset—failed to catch on. Let's look at Engelbart's demo and the keyset. 1/N

Intel's Pentium processor (1993). Looking inside the chip , I ...

2025-03-02T18:29:59Z

Intel's Pentium processor (1993). Looking inside the chip , I found a large, complicated circuit just to multiply by 3 (lower right). Why? The Pentium uses a fast technique to multiply 64-bit numbers and it turns out that 3 is a special case. Let's take a closer look at multiplication... 1/N

What is the origin of the word "mainframe"? Digging ...

2025-02-01T18:56:05Z

What is the origin of the word "mainframe"? Digging through archives, I traced it back to 1953. The IBM 701 computer was built from "frames": power frames, a storage frame, a drum frame, and the main frame. This 1953 drawing from the Installation Manual shows the dimensions of the "main frame". 1/n

Intel's Pentium processor (1993) was a complex chip for its ...

2025-01-21T17:07:53Z

Intel's Pentium processor (1993) was a complex chip for its time, with 3 layers of metal wiring over the silicon. I removed the layers, one at a time, so we can take a look at each layer... 1/n

For more details on how a carry-lookahead adder works, see my ...

2025-01-18T18:38:26Z

In reply to nevent1q…d7n7
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For more details on how a carry-lookahead adder works, see my blog post: https://www.righto.com/2025/01/pentium-carry-lookahead-reverse-engineered.html

Another closeup of the adder. For this photo, I removed the top ...

2025-01-18T18:38:07Z

In reply to nevent1q…85ua
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Another closeup of the adder. For this photo, I removed the top two metal layers and left the bottom metal layer. At the top, the partial sum circuit is repeated 8 times. At the bottom, XOR is repeated 8 times. In the middle, the carry lookahead circuitry is a jumble since each bit is different. 4/n

By tracing out the circuitry of the adder, I created a schematic. ...

2025-01-18T18:37:38Z

In reply to nevent1q…pan6
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By tracing out the circuitry of the adder, I created a schematic. It takes a lot of logic gates to build a carry-lookahead adder, but it is faster than a regular adder. It figures out all the carries in parallel, using a tricky technique of merging "generate" and "propagate" signals. 3/n

Here's a closeup of the adder and associated circuitry. The ...

2025-01-18T18:36:51Z

In reply to nevent1q…hqnp
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Here's a closeup of the adder and associated circuitry. The 8-bit adder is marked in red. The circuitry below helps test the chip; the Pentium includes a lot of circuitry just for testing. In this photo, I removed all 3 metal layers, showing the polysilicon and doped silicon forming transistors. 2/n

Adding on a computer is trickier than you'd expect. The ...

2025-01-18T18:35:50Z

Adding on a computer is trickier than you'd expect. The Pentium processor (1993) used a variety of circuits for addition. I reverse-engineered an adder in the floating point unit and found that it is a "Kogge-Stone carry-lookahead adder", using some tricks to make it faster. Let's look inside. 1/n

Intel's Pentium processor (1993) can compute sines, ...

2025-01-05T18:03:09Z

Intel's Pentium processor (1993) can compute sines, logarithms, and other special functions. To do this, it has a ROM with 304 floating-point constants. I reverse-engineered this ROM and extracted the constants. You can see pi in the ROM, binary 11.001001..., encoded in the transistor pattern. 1/n

My previous Mastodon thread has more photos and details on the ...

2024-12-28T19:03:45Z

In reply to nevent1q…m6f6
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My previous Mastodon thread has more photos and details on the Pentium FDIV bug:
https://oldbytes.space/@kenshirriff/113606898880486330

I wrote a blog post that describes the Pentium division bug and ...

2024-12-28T19:03:07Z

In reply to nevent1q…2jx6
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I wrote a blog post that describes the Pentium division bug and its circuitry in great detail:
https://www.righto.com/2024/12/this-die-photo-of-pentium-shows.html

The division algorithm uses a lookup table, stored in a circuit ...

2024-12-28T19:02:39Z

In reply to nevent1q…48sd
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The division algorithm uses a lookup table, stored in a circuit called a PLA. Unfortunately, Intel missed 16 entries in the table. One in 9 billion divisions hit a missing entry, yielding the wrong result. 2/N

In 1994, a math professor discovered that Intel's Pentium ...

2024-12-28T19:01:57Z

In 1994, a math professor discovered that Intel's Pentium chip sometimes gave the wrong answer when dividing. Fixing this "FDIV" bug cost Intel $475 million. I analyzed the Pentium chip and found the bug. 1/N

A vintage Intel video on the 386 processor, feat. Pat Gelsinger ...

2024-12-21T04:33:46Z

A vintage Intel video on the 386 processor, feat. Pat Gelsinger and Gene Hill, just dropped on YouTube.
https://youtu.be/LQcLhBZY12g
Thanks to the Computer History Museum for digitizing this.

I hope to have a blog post with more details on the Pentium FDIV ...

2024-12-06T17:13:54Z

In reply to nevent1q…9h0w
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I hope to have a blog post with more details on the Pentium FDIV bug soon. Until then, you can read about the Pentium Navajo rug: https://oldbytes.space/@kenshirriff/113063183366751314
9/9

Intel said the FDIV bug was unimportant, but the public ...

2024-12-06T17:10:23Z

In reply to nevent1q…sr4m
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Intel said the FDIV bug was unimportant, but the public disagreed. Newspapers and TV discussed the bug. Intel claimed the bug would happen every 27,000 years; IBM said every 24 days and stopped selling Pentiums. Intel gave in and replaced Pentiums at a cost of $475 million. 8/9

You'd expect that Intel fixed the problem by adding the 5 ...

2024-12-06T17:08:01Z

In reply to nevent1q…zym2
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You'd expect that Intel fixed the problem by adding the 5 missing entries. Instead, they filled *all* the unused entries with 2's. This made the table easier to store in a PLA, shrinking it by 1/3. The fixed PLA has lots of unused rows at the bottom. 7/9

Intel claimed the bug was due to an error in a script to download ...

2024-12-06T17:05:52Z

In reply to nevent1q…x0qh
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Intel claimed the bug was due to an error in a script to download the entries into the PLA. But due to the 16 missing entries, I think they made a mathematical error in constructing the table, misjudging the effect of a 7-bit adder. Here's the adder, just above the PLA. 6/9

Smart mathematicians figured out Pentium's division algorithm ...

2024-12-06T17:00:36Z

In reply to nevent1q…pnly
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Smart mathematicians figured out Pentium's division algorithm and the missing entries in 1995 by examining the pattern of errors. But I can confirm it in silicon. Moreover, I see 16 missing entries in the table, not just 5, but 11 of them don't cause errors due to luck. 5/9

I studied the transistor grids under a microscope and extracted ...

2024-12-06T17:00:01Z

In reply to nevent1q…uwep
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I studied the transistor grids under a microscope and extracted the pattern. From this, I reverse-engineered the lookup table for division. The photos show a small part of the grids. A transistor is formed by a polysilicon line crossing doped silicon. No crossing, no transistor. 4/9

The table is stored in a circuit called a PLA (Programmable Logic ...

2024-12-06T16:56:09Z

In reply to nevent1q…nt0a
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The table is stored in a circuit called a PLA (Programmable Logic Array). A PLA stores logic equations in two grids of transistors: the "AND plane" and the "OR plane". Logic equations are defined by putting a transistor (or not) at each grid point. This is much more compact than a ROM: 112 rows instead of 2048. 3/9

The Pentium uses a division algorithm called SRT. It generates ...

2024-12-06T16:52:25Z

In reply to nevent1q…8a4p
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The Pentium uses a division algorithm called SRT. It generates two bits at a time, making division twice as fast. SRT's secret is quotient digits can be negative: -2, -1, 0, 1, 2. A 2048-entry table gives the digit for a particular divisor and remainder. Unfortunately, 5 entries (red) were wrong. 2/9

Intel launched the Pentium processor in 1993. Unfortunately, ...

2024-12-06T16:48:26Z

Intel launched the Pentium processor in 1993. Unfortunately, dividing sometimes gave a slightly wrong answer, the famous FDIV bug. Replacing the faulty chips cost Intel $475 million. I reverse-engineered the circuitry and can explain the bug. 1/9

For more on antenna diodes in the Pentium, see my latest blog ...

2024-11-23T20:53:37Z

In reply to nevent1q…d0ns
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For more on antenna diodes in the Pentium, see my latest blog post:
https://www.righto.com/2024/11/antenna-diodes-in-pentium-processor.html

Here's a photo of the Pentium die with main functional blocks ...

2024-11-23T20:53:18Z

In reply to nevent1q…xz8l
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Here's a photo of the Pentium die with main functional blocks labeled. In this photo, the three layers of metal wiring almost completely hide the underlying silicon. 5/6

This closeup photo shows the three layers of wiring on the ...

2024-11-23T20:44:34Z

In reply to nevent1q…qqcc
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This closeup photo shows the three layers of wiring on the Pentium and the transistors underneath. The L-shaped hook towards the lower left is a connection to an antenna diode. 4/6

The solution is to add extra diodes to the circuitry, special ...

2024-11-23T20:40:35Z

In reply to nevent1q…67fs
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The solution is to add extra diodes to the circuitry, special devices that will drain away the dangerous charge.
These diodes are relatively rare, only needed when long wires on the chip are connected to a transistor gate on one end and the other end isn't connected yet. The long wire acts (metaphorically) as an antenna, so the protective diode is called an antenna diode. 3/6

The problem is that the chip manufacturing process uses plasma to ...

2024-11-23T20:34:28Z

In reply to nevent1q…4rgx
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The problem is that the chip manufacturing process uses plasma to etch away unwanted metal to produce wiring. However, long wires on the chip can pick up electrical charge from the plasma. This charge can damage the chip's transistors. In particular, each transistor has a thin layer of "gate oxide", just a few hundred atoms thick, that can easily be damaged. 2/6

I was studying the Pentium processor's die and I noticed ...

2024-11-23T20:30:28Z

I was studying the Pentium processor's die and I noticed strange connections that I didn't understand. These turned out to be "antenna diodes", special diodes that protect the chip from damage during manufacturing. Let's take a look... 1/6

The weaving of a Pentium is so accurate that I could label the ...

2024-09-01T16:15:32Z

In reply to nevent1q…5hha
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The weaving of a Pentium is so accurate that I could label the functional blocks of the processor. Amusingly, the gallery hung the weaving backward. The wrong side is facing outward, so the chip is mirrored. I had to flip the image to make this diagram. 2/6

I recently saw an amazing Navajo rug at the National Gallery of ...

2024-09-01T16:14:25Z

I recently saw an amazing Navajo rug at the National Gallery of Art. It looks abstract at first, but it is a detailed representation of the Intel Pentium processor. Called "Replica of a Chip", it was created in 1994 by Marilou Schultz, a Navajo/Diné weaver and math teacher. Intel commissioned the weaving as a gift to the American Indian Science & Engineering Society. 1/6

The Minuteman III missile (1970) is America's land-based ...

2024-08-19T18:21:40Z

The Minuteman III missile (1970) is America's land-based nuclear deterrent, with 400 missiles ready to launch. The missile used a complex guidance system with over 17,000 electronic and mechanical parts that cost $4.5 million in current dollars. Let's take a look at the guidance system and computer. 1/N

This pretty chip from 1981 helped connect an IBM mainframe to ...

2024-07-16T18:41:34Z

This pretty chip from 1981 helped connect an IBM mainframe to data-entry terminals. 1/14

Standard cells use a library of standardized blocks for gates and ...

2024-07-07T17:40:39Z

In reply to nevent1q…z2uh
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Standard cells use a library of standardized blocks for gates and other circuits. Software builds your circuit by snapping the blocks into rows and laying out the wiring between the circuits. Quick and error-free, but not as dense and efficient as manual circuit design. 3/21

The fingernail-sized Pentium chip under a microscope. Some parts, ...

2024-07-07T17:40:37Z

In reply to nevent1q…rprw
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The fingernail-sized Pentium chip under a microscope. Some parts, like the cache and datapath were highly optimized by hand. Less critical areas, outlined in red, were designed by software using standard cells. The rows of cells are visible as gray columns. 2/21

Intel's Pentium processor (1993) was a big jump in processor ...

2024-07-07T17:40:34Z

Intel's Pentium processor (1993) was a big jump in processor performance, starting a brand that lasted until 2023. But what's inside the Pentium chip? How did Intel organize its 3.3 million transistors? Let's take a look inside and see the chip's "standard cells". 1/21

To use the Montreal subway, you tap a paper ticket against the ...

2024-06-23T16:01:42Z

To use the Montreal subway, you tap a paper ticket against the turnstile and it opens. But how does it work? And how can the ticket be so cheap that it's disposable? I opened up the tiny NFC chip inside to find out more... 1/15

The mechanical construction of the computer is clever, allowing ...

2024-05-29T14:19:46Z

In reply to nevent1q…37m9
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The mechanical construction of the computer is clever, allowing the densely packed boards to unfold like a book. Each "page" consists of two boards mounted back-to-back. The metal frame provides conductive cooling as well as support. 2/17

I received a mysterious aerospace computer from the early 1970s, ...

2024-05-29T14:19:44Z

I received a mysterious aerospace computer from the early 1970s, probably for navigation. It is crammed full of flat-pack integrated circuits surrounding a core memory module. Let's take a look inside... 1/17

Punch cards used to be a key part of computing. The IBM 1402 Card ...

2024-04-25T17:34:39Z

Punch cards used to be a key part of computing. The IBM 1402 Card Reader/Punch (1959) could read or punch hundreds of cards a minute. But the punch at https://twitter.com/ComputerHistory stopped punching the first 16 columns. An explanation of the punch unit and how we fixed it... 1/9