@kenshirriff@oldbytes.space

Ken Shirriff @kenshirriff@oldbytes.space

· 3w ago

Replying to

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.

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Ken Shirriff @kenshirriff@oldbytes.space

· 3w ago

Replying to

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.

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Ken Shirriff @kenshirriff@oldbytes.space

· 1w ago

Replying to

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.

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Ken Shirriff @kenshirriff@oldbytes.space

· 1w ago

Replying to

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.

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Ken Shirriff @kenshirriff@oldbytes.space

· 1w ago

Boosted by @joe@f.duriansoftware.com

Replying to

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

righto.com

Reverse-engineering the vintage Intel 8087's tangent algorithm: more than CORDIC

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Ken Shirriff @kenshirriff@oldbytes.space

· 2mo ago

Replying to

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.

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Ken Shirriff @kenshirriff@oldbytes.space

· 1w ago

Replying to

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).

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Ken Shirriff @kenshirriff@oldbytes.space

· 2mo ago

Replying to

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.

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Ken Shirriff @kenshirriff@oldbytes.space

· 2mo ago

Replying to

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.

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Ken Shirriff @kenshirriff@oldbytes.space

· 2mo ago

Replying to

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.

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Ken Shirriff @kenshirriff@oldbytes.space

· 1w ago

Replying to

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.

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Ken Shirriff @kenshirriff@oldbytes.space

· 2mo ago

Replying to

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

righto.com

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Ken Shirriff @kenshirriff@oldbytes.space

· 2mo ago

Replying to

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.

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Ken Shirriff @kenshirriff@oldbytes.space

· 2mo ago

Replying to

Credits: thanks to Robert Garner for the tube module and @CuriousMarc@mastodon.social 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: https://commons.wikimedia.org/wiki/File:IBM_150_Extra_Engineers_1951.jpg

ed-thelen.org

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Ken Shirriff @kenshirriff@oldbytes.space

· 5mo ago

Replying to

For more on the electromechanical Angle Computer, see my article: https://www.righto.com/2026/04/B-52-star-tracker-angle-computer.html

righto.com

The electromechanical angle computer inside the B-52 bomber's star tracker

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Ken Shirriff @kenshirriff@oldbytes.space

· 6mo ago

Replying to

I forgot to explain the 4 Pi name. IBM's System/360 mainframes got their name because they supported a full 360º circle of applications, from business to scientific. The 4 Pi aerospace computers, however, were designed for the 3-D world, a "sphere" of applications. While a circle has 360º, a sphere has 4π steradians of solid angle.

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Ken Shirriff @kenshirriff@oldbytes.space

· 3mo ago

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

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Ken Shirriff @kenshirriff@oldbytes.space

· 5mo ago

Replying to

The "Astro Tracker" was the heart of the celestial navigation system. The 4-inch clear bubble stuck out from the top of the aircraft to view the stars. Inside, a telescope and photomultiplier tube tracked a star, steered by motors and prisms.

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Ken Shirriff @kenshirriff@oldbytes.space

· 5mo ago

Replying to

The back of the Angle Computer has devices called synchros that read out the star's position relative to the aircraft. At the bottom, motors drive the mechanism.

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Ken Shirriff @kenshirriff@oldbytes.space

· 5mo ago

Replying to

This close-up of the Angle Computer shows the complexity of the gears inside. The thicker brass-colored cylinders are differential gears that add two signals using rotations.

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Ken Shirriff @kenshirriff@oldbytes.space

· 5mo ago

Replying to

Inside the Angle Computer, a star pointer corresponds to the position of the star on the celestial sphere. Gears move the pointer to match the star's coordinates (called the declination and Local Hour Angle).

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Ken Shirriff @kenshirriff@oldbytes.space

· 6mo ago

Replying to

In 1991, the Space Shuttle upgraded its computer to the AP-101S, replacing two 60-pound boxes with one box. Since there were five computers on the Shuttle, this change freed up 300 pounds for additional cargo. The CPU was implemented in three boards full of chips, one below. These boards were much larger than the earlier 4 Pi boards.

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Ken Shirriff @kenshirriff@oldbytes.space

· 6mo ago

Replying to

There were many more models of System/4 Pi computers, including refrigerator-sized computers used on submarines; see my article for details: https://www.righto.com/2026/03/ibm-4-pi-computer-history.html

righto.com

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Ken Shirriff @kenshirriff@oldbytes.space

· 9mo ago

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

righto.com

Conditions in the Intel 8087 floating-point chip's microcode

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Ken Shirriff @kenshirriff@oldbytes.space

· 6mo ago

Replying to

IBM's 4 Pi computers were built from simple TTL integrated circuits and used magnetic core memory for storage. "Flat-pack" integrated circuits on multi-layer circuit boards provided dense logic. The board below was round to fit inside a tactical missile, but most of the computers used standardized rectangular boards called "pages".

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Ken Shirriff @kenshirriff@oldbytes.space

· 6mo ago

Replying to

The Space Shuttle used a more advanced System/4 Pi computer called the AP-101B. A separate computer, the I/O Processor, provided 24 data buses to all parts of the Shuttle. These boxes still used individual TTL chips and magnetic core memory.

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Ken Shirriff @kenshirriff@oldbytes.space

· 7mo ago

Replying to

Instruction decoding in the 8087 has many more complications: hardcoded instructions handled by the "Bus Interface Unit", instructions that load a constant from the constant ROM, and handling the instruction queue. For more details, see my latest blog post: https://www.righto.com/2026/02/8087-instruction-decoding.html

righto.com

Instruction decoding in the Intel 8087 floating-point chip

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Ken Shirriff @kenshirriff@oldbytes.space

· 7mo ago

Replying to

The microcode inside the 8087 chip uses conditional jumps for many purposes. Some conditions examine the instruction, so the microcode can act differently for different instructions. Here's the PLA that stores target addresses for microcode jumps. Target 0 is special: it does a three-way branch depending if the instruction is multiplication, division, or addition/subtraction.

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Ken Shirriff @kenshirriff@oldbytes.space

· 7mo ago

Replying to

Like many processors, the 8087 uses a "Programmable Logic Array" (PLA) to decode the bit patterns in instructions. A PLA consists of grids of transistors, with some of the transistors missing. The pattern of transistors controls the PLA's function. The grid is a dense and flexible way of implementing this logic.

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Ken Shirriff @kenshirriff@oldbytes.space

· 2mo ago

Replying to

@VE2UWY@mastodon.radio 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)

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Ken Shirriff @kenshirriff@oldbytes.space

· 5mo ago

Replying to

@vk2bea They say that the accuracy was within 0.1 degree.

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Ken Shirriff @kenshirriff@oldbytes.space

· 8mo ago

Replying to

For details on the Algorithms of Love event tonight, see the Computer History Museum page. It also has a link to watch the event live on YouTube. https://computerhistory.org/events/algorithms-of-love/

CHM

Algorithms of Love

Watch the program live on YouTube here! Online dating is a fast growing $9+ billion industry, and that’s just humans seeking humans! Dating AIs are already generating billions and growing at 25% a year. Join us for a conversation that will investigate how computers have changed how we live and love today and what changes might […]

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Ken Shirriff @kenshirriff@oldbytes.space

· 5mo ago

Replying to

@dnaunton The SR-71 used a different system, the NAS-14V2 astroinertial navigation system. Nortronics built the SR-71 system and Kollsman built the B-52 system. The B-52 system is said to have also been used in the Hound Dog cruise missile. A very detailed document on the SR-71 star tracker is here: https://audiopub.co.kr/wp-content/uploads/2021/10/NAS-14V2-ANS-System.pdf

audiopub.co.kr

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Ken Shirriff @kenshirriff@oldbytes.space

· 3mo ago

Replying to

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.

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Ken Shirriff @kenshirriff@oldbytes.space

· 5mo ago

Replying to

@numodular Although this unit looks like a gyroscope, it is not at all a gyroscope. There is nothing spinning.

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Ken Shirriff @kenshirriff@oldbytes.space

· 13mo ago

Replying to

@OscarCunningham@mathstodon.xyz @divbyzero@mathstodon.xyz @andrewt@mathstodon.xyz That QR code is the coolest thing. Nice how the black parts show the underlying structure, including the alternating squares of the timing pattern, while the colored parts have the data

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Ken Shirriff @kenshirriff@oldbytes.space

· 7mo ago

Replying to

@raymaccarthy The 8087 doesn't help with 16-bit integer math.

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Ken Shirriff @kenshirriff@oldbytes.space

· 7mo ago

Replying to

@Sonic2k Early calculator chips are pretty weird. They operate in decimal and are serial, so they operate on one bit at a time with a one-bit ALU. So all the data is constantly in motion.

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Ken Shirriff @kenshirriff@oldbytes.space

· 14mo ago

Replying to

@azonenberg From the application note, I think the main issue is if the VCO locks onto a sideband, then you get distorted audio. It's better to replace this with white noise so the user knows that the tuning is off.

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Ken Shirriff @kenshirriff@oldbytes.space

· 14mo ago

Replying to

@StumpyTheMutt That must have been frustrating! I read that this chip was very sensitive to the board layout so something subtle might have thrown it off.

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Ken Shirriff @kenshirriff@oldbytes.space

· 6mo ago

Replying to

@urwumpe Fair enough :-)

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Ken Shirriff @kenshirriff@oldbytes.space

· 14mo ago

Replying to

@murtaugh @futurebird Yikes!

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