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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

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 silcon. When polysilicon crosses doped silicon, it forms a transistors, the switches that make circuits work.

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.

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.