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Inside the Intel 8087 chip: floating-point addition and subtraction

In 1980, Intel introduced the 8087, a chip that made floating-point operations much faster in the IBM PC and other systems. Although the 8087 supports advanced operations such as tangents, square roots, and logarithms, this article focuses on basic arithmetic operations: addition...

Inside a 1980s filter chip that uses switched capacitors

Sometimes it's easier to identify an IC with a microscope. While sorting a box of old ICs, CuriousMarc came across some Harris ICs labeled "F1-10-5", a mysterious part number that didn't show up in any databooks. Since unidentifiable ICs are useless, he gave me one to analyze. Co...

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

I hope you're not tired of the 8087, because I have another article about Intel's floating-point chip.1 In 1980, Intel introduced the 8087, making floating-point operations much faster in the IBM PC and other systems. In this article, I look at the algorithm behind the chip's tan...

Microcode in Intel's 8087 floating-point chip: the scale instruction

In the 1970s, floating-point arithmetic was a mess. Computer manufacturers had a dozen incompatible arithmetic standards. Moreover, floating-point systems were designed around hardware simplicity rather than mathematical rigor, leading to problems with numerical stability. This c...

Cores in space: The core memory module from a 1980 Spacelab computer

Spacelab was a reusable laboratory that could be carried in the Space Shuttle's cargo bay, providing lab space for astronauts and experiments.1 Because Spacelab was a European project, it used a French-built minicomputer, the Mitra 125 MS,2 rather than the Shuttle's main computer...

Energizing a vacuum-tube flip-flop module from a 1948 IBM system

In 1948, IBM introduced the 604 Electronic Calculating Punch. This machine was a programmable calculator, about the size of a double refrigerator. It was not quite a computer, but was programmed by plugging wires into a plugboard. This machine read numbers from a punch card, perf...

Examining circuit boards from the Space Shuttle's I/O Processor

The Space Shuttle's five1 general-purpose computers played a critical role in each flight: controlling the engines, monitoring thousands of sensors, displaying data to the astronauts, and navigating the Shuttle. Each computer consisted of two 60-pound aluminum-alloy boxes: the bo...

The adder at the heart of Intel's 8087 floating-point chip

In 1980, Intel released the Intel 8087 floating-point coprocessor, a chip that could make math up to 100 times faster. As well as arithmetic and square roots, the 8087 computed transcendental functions including tangent, exponentiation, and logarithms. But it all depended on a 69...

Powering up a module from the IBM 604: an electronic calculator from 1948

1948 was an interesting time for computing. For decades, businesses had used punch card equipment that added and sorted electromechanically. Now these electromechanical relays and counting wheels were being used to build room-filling general-purpose computers such as Harvard Mark...

Microcode inside the Intel 8087 floating-point chip: register exchange

In 1980, Intel introduced the 8087 floating-point chip, a co-processor that made floating-point operations up to 100 times faster. This chip was highly influential, and today most processors use the floating-point standard introduced by the 8087.

Reverse engineering circuitry in a Spacelab computer from 1980

Spacelab was a reusable laboratory that could be carried in the cargo bay of the Space Shuttle, providing lab space for astronauts and experiments. Spacelab was controlled by a French-built minicomputer, called the Mitra 125 MS. Unlike modern computers, this computer didn't conta...

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

Before GPS, how did aircraft navigate? One important technique was celestial navigation: navigating from the positions of the stars, planets, or the sun. While celestial navigation is accurate, cannot be jammed, and doesn't require any broadcast infrastructure, it is a difficult...

The rise and fall of IBM's 4 Pi aerospace computers: an illustrated history

The morning of April 12, 1981, 20 years to the day after Yuri Gagarin became the first person in space, the Space Shuttle thundered into the Florida sky. Commander Young and Pilot Crippen were at the controls as the Shuttle ascended on its first flight. But the launch, like much...

Instruction decoding in the Intel 8087 floating-point chip

But how does a PC decide if an instruction was a floating-point instruction for the 8087 or a regular instruction for the 8086 or 8088 CPU? And how does the 8087 chip interpret instructions to determine what they mean? It turns out that decoding an instruction inside the 8087 is...

Notes on the Intel 8086 processor's arithmetic-logic unit

In 1978, Intel introduced the 8086 processor, a revolutionary chip that led to the modern x86 architecture. Unlike modern 64-bit processors, however, the 8086 is a 16-bit chip. Its arithmetic/logic unit (ALU) operates on 16-bit values, performing arithmetic operations such as add...

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

In the 1980s, if you wanted your computer to do floating-point calculations faster, you could buy the Intel 8087 floating-point coprocessor chip. Plugging it into your IBM PC would make operations up to 100 times faster, a big boost for spreadsheets and other number-crunching app...

The stack circuitry of the Intel 8087 floating point chip, reverse-engineered

Early microprocessors were very slow when operating with floating-point numbers. But in 1980, Intel introduced the 8087 floating-point coprocessor, performing floating-point operations up to 100 times faster. This was a huge benefit for IBM PC applications such as AutoCAD, spread...

Unusual circuits in the Intel 386's standard cell logic

I've been studying the standard cell circuitry in the Intel 386 processor recently. The 386, introduced in 1985, was Intel's most complex processor at the time, containing 285,000 transistors. Intel's existing design techniques couldn't handle this complexity and the chip began t...

Solving the NYTimes Pips puzzle with a constraint solver

The New York Times recently introduced a new daily puzzle called Pips. You place a set of dominoes on a grid, satisfying various conditions. For instance, in the puzzle below, the pips (dots) in the purple squares must sum to 8, there must be fewer than 5 pips in the red square,...

A Navajo weaving of an integrated circuit: the 555 timer

The noted Diné (Navajo) weaver Marilou Schultz recently completed an intricate weaving composed of thick white lines on a black background, punctuated with reddish-orange diamonds. Although this striking rug may appear abstract, it shows the internal circuitry of a tiny silicon c...