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 number and it turns out that 3 is a special case. Let's take a closer look at multiplication... 1/N - ThreadSky

righto.com • 45 days ago

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 number and it turns out that 3 is a special case. Let's take a closer look at multiplication... 1/N

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daverooney.dev•45 days ago

That's really cool! Thanks for doing these threads and please keep it up!

righto.com•45 days ago

Multiplying binary numbers is like grade-school long division, except you multiply by 0 or 1 at each step. You add up the terms at the end, so 64-bit numbers would add 64 terms. Too much adding! The Pentium instead multiplies in base-8 so there are 1/3 the number of terms to add. Faster but tricky.

righto.com•45 days ago

Multiplying in base 8 means each term gets multiplied by 0 through 7. Multiplying by 2 or 4 is easy, just shift the number. A trick for ×7: multiply by 8 and subtract 1×. (This is Booth's algorithm.) For ×6, multiply by 8 and subtract 2×. But what about ×3? It needs a special circuit. 3/N

righto.com•45 days ago

To multiply by 3 in binary, you can add the number to 2 times the number (a quick shift). Unfortunately, adding two 64-bit numbers is slow because of carries. (Just like 999999+1: you need to keep doing carry-the-one.)
To make this addition fast, the Pentium uses complicated adder circuitry. 4/N

righto.com•45 days ago

The Pentium's adder uses a combination of techniques: carry-lookahead, carry-save addition, and Kogge-Stone. I won't go into details here but essentially all the carry bits are computed in parallel, so then the addition can happen in parallel. The photo shows one of the 8-bit addition blocks. 5/N

righto.com•45 days ago

Diving way into the circuitry, the adder uses an "XNOR gate" as part of adding two bits. Here's that circuit under the microscope. I removed two layers of metal to make it visible. 16 transistors are formed by doped silicon regions crossed by polysilicon wires. Metal wiring connects the transistors.

righto.com•45 days ago

An unusual feature of the Pentium is that it is constructed from BiCMOS. Most computers use a type of circuitry called CMOS. However, the Pentium also includes bipolar transistors, faster at the time.
The ×3 circuit uses some bipolar (NPN) transistors, huge compared to the skinny MOS transistors.

misterlambe.bsky.social•35 days ago

Hooray you're on Bluesky now. Excellent news.

nekomay.bsky.social•45 days ago

Very cool breakdown of an interesting feature!

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