Ken Shirriff
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Ken Shirriff
@righto.com
5.9K followers 290 following 360 posts
Computer history. Reverse-engineering old chips. Restored Apollo Guidance Computer, Alto. Ex-Google, Sun, Msft. So-called boffin.
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For more, see my latest blog post:
www.righto.com/2026/01/note...
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,...
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January 23, 2026 at 6:07 PM
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The 8086 processor uses microcode to specify each step of an instruction. The circuitry below decodes the microcode and sends control signals to the ALU so it performs the desired arithmetic or logic operation. In this die photo, you can see the individual transistors in the circuitry.
A close-up of the ALU control circuitry in the 8086. In this die image, I removed the metal layer to show the underlying silicon and polysilicon. I've labeled the temporary register latch, the XI multiplexer, the operation PLA, the operation latch, the lookup table PLA and miscellaneous decoding circuitry.
January 23, 2026 at 6:07 PM
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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...
A die photo of the 8086 microprocessor. The image shows a tan square with complex patterns of beige and dark lines showing the circuitry. Thicker light lines distribute power across the chip while black bond wires are attached around the edges. Various regions with different patterns are labeled with their function including a large rectangular region in the lower right that holds the microcode and the 16-bit ALU in the lower left. The ALU Control circuit at the bottom is highlighted.
January 23, 2026 at 6:07 PM
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Intel announced the 8087 floating-point chip in 1980. Now I have a blog post that explains a small part of the microcode in this chip.
www.righto.com/2025/12/8087...
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 ...
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December 30, 2025 at 7:54 PM
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The 8087 was much more advanced than previous floating point. In particular, it was designed by Prof. Kahan, a floating-point expert, and was much more rigorous and accurate. It became the IEEE 754 standard, which almost all computers now use.
ieeemilestones.ethw.org/Milestone-Pr...
Milestone-Proposal:Intel 8087 Math Coprocessor
ieeemilestones.ethw.org
December 11, 2025 at 8:17 PM
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I looked at the AM9511 datasheet. It's similar to the 8087 in that they are both floating-point chips that do arithmetic as well as transcendental functions, and both use a stack. However, the 9511 uses 16/32-bit floats, while the 8087 uses much larger floats, up to 80 digits.
December 11, 2025 at 8:15 PM
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No, I haven't looked at that chip yet.
December 9, 2025 at 7:11 PM
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For more on the stack circuitry in the 8087, see my blog post: www.righto.com/2025/12/8087...
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 copro...
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December 9, 2025 at 6:38 PM
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Intel was hesitant to produce the 8087 chip, considering it complex, risky, and with an unknown market. Intel's Israel site took on the project; the die is marked "i/IL". The chip was a highly profitable success. Now, almost all computers use floating-point systems based on the 8087.
A close-up of the 8087 die. There are white horizontal and vertical lines of various widths, the chip's metal wiring. Text in metal is also visible: "8087", "i/IL", and a maskwork/copyright marking: "(m) (c) intel 1980".
December 9, 2025 at 6:38 PM
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This diagram, based on the 8087 patent, shows the implementation of the stack. You saw the registers (yellow) earlier. This photo shows the three-bit circuitry that controls the stack (purple, green, and blue). The schematic shows one bit in detail.
A block diagram from the patent. It shows the top-of-stack pointer (TOS) with controls to increment and decrement when pushing or popping values. A subtractor circuit computes offsets into the stack. A multiplexer selects either the top-of-stack or the offset value. A decoder selects one entry in the stack based on this value. The value in the stack is split across the fraction bus, exponent bus, and tag bus. The stack control circuitry on the die. It consists of complex silicon structures forming tan patterns. I've labeled regions of the circuitry. Circuitry blocks handle increment/decrement and latching of the three bits. Underneath, blocks compute the sum and multiplex the two values. There are irregular regions of deep blue at the right. These are not significant, just oxide that didn't get completely removed when I dissolved the metal layer with acid. A complicated schematic showing one bit of the stack register control. The left half is a flip-flop that can hold a bit or toggle the bit (for incrementing or decrementing). The right half is a multiplexer to select either the top-of-stack from the flip-flop or the sum. The summing circuitry is not shown, but uses a carry-lookahead adder.
December 9, 2025 at 6:38 PM
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Each bit is stored in a "static RAM" cell, consisting of two inverters in a loop. This circuit has two stable states, holding a 0 or a 1. The implementation is complicated: silicon with polysilicon lines on top to make transistors. Horizontal metal wires connect everything.
A diagram showing two inverters in a loop. On the left, the first inverter has a 0 and the second has a 1. On the right, the values are switched. Thus, the circuit can hold a 0 or a 1. A close-up of the silicon showing the circuitry for one storage cell. Each cell has two inverters. Each inverter has a transistor and a weak pull-up transistor. A transistor is formed when polysilicon crosses over doped silicon. The two inverters are connected to bit lines to read and write the cell. This connection is through two selection transistors, controlled by a vertical word line.
December 9, 2025 at 6:38 PM
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Unlike most processors, the 8087 organizes its registers into a "stack", pushing numbers onto the top of the stack and popping them off. Here's a close-up of the eight registers, organized in a grid of cells. Each register holds an 80-bit number, so the registers are very tall.
The registers in the 8087 chip form a tall, skinny rectangle. The storage cells are arranged in eight columns for the eight registers. At the top are two tag bits, then 16 bits for sign and exponent, and then 64 bits for the fraction part of the number. The image zooms in on an 8 by 8 block of storage cells. For this image, I removed the metal layer with acid, so you can see the silicon structures underneath. The silicon appears pinkish-tan.
December 9, 2025 at 6:38 PM
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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...
A photo of the 8087 die under a microscope. The die is rectangular, with complex patterns in purplish-brown. The patterns consist of rectangular regions, striped regions in the bottom half of the chip, and other more irregular regions. At the right, two regions are highlighted in red: the registers and the stack control circuitry. Around the edges of the die, you can see the hair-thin bond wires that connect the chip to its 40 external pins. The complex patterns on the die are formed by its metal wiring, as well as the polysilicon and silicon underneath. The bottom half of the chip is the "datapath", the circuitry that performs calculations on 80-bit floating point values. At the left of the datapath, a constant ROM holds important constants such as π. At the right are the eight registers that form the stack, along with the stack control circuitry. The chip's instructions are defined by the large rectangular microcode ROM in the middle.
December 9, 2025 at 6:38 PM
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Not yet...
November 22, 2025 at 7:14 PM
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My latest blog post describes the wayward transistor and two other curiosities in the 386 processor's standard cell logic, so read it for details.

www.righto.com/2025/11/unus...
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 pr...
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November 22, 2025 at 4:56 PM
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Standard cells sped up the design of the 386 and the chip was completed ahead of schedule. Pat Gelsinger was one of the key people behind the use of standard cells in the 386 processor. Decades later, he became CEO of Intel.
A standard-cell inverter as it appears on the die, along with a diagram explaining the layout. The die image has green lines of polysilicon over grayish rectangles of silicon that look a bit like Lego bricks. The diagram shows how the inverter is constructed from a PMOS transistor and an NMOS transistor
November 22, 2025 at 4:56 PM
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In standard cell logic, all the transistors are in orderly stripes. Except one that's out of place below, in the middle of the wiring region. What's going on? I think it's a bug fix. Instead of redoing all the circuitry, someone realized they could patch an extra transistor into an empty spot!
A close-up of two columns of standard cell logic. I dissolved the metal layers with acid for this photo, so you can see the silicon. Each transistor has a dark outline around it. The transistors are all in columns except for one lone transistor between the columns; it is marked with a red arrow. The photo also has a few large greenish regions. These are areas where I couldn't remove the oxide layer completely, so they can be ignored.
November 22, 2025 at 4:56 PM
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It's much easier to build circuits with standard cells. Instead of manually arranging each transistor, you feed a description of the logic into a computer. It places the cells into rows, and then routes the wires to connect the cells. In 1985, this took many hours on an IBM mainframe computer.
A close-up of two standard cells in the 386. The cells are outlined with green boxes. The photo looks like dark brown horizontal and vertical lines on a tan background, with large and small circles in the boxes. The photo is mostly incomprehensible because of the density of wiring in the 386, but what it shows is a layer of horizontal wiring and a layer of vertical wiring (the stripes between the dark lines). The larger circles connect the two metal layers, while the small dots connect the metal layer to the silicon or polysilicon underneath,
November 22, 2025 at 4:56 PM
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The previous photo shows the 386 processor under a microscope. I've highlighted the regions that use standard cells and the layout was automated. Simple logic blocks (the "standard cells") are arranged in rows, with wiring between the rows. This creates a distinctive striped pattern.
A close-up of standard cell logic in the 386 processor. The circuitry appears as four irregular dark bands, with horizontal and vertical connections in the regions between the dark bands.
November 22, 2025 at 4:56 PM
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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...
A die photo of the 386 processor. It is a square with complicated patterns on top. Under the microscope, the circuits appear in dark purple. Parts of the chip have been marked with boxes: these are standard cell circuits and have a distinctive striped appearance.
November 22, 2025 at 4:56 PM
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MiniZinc solver page: www.minizinc.org
Link to Pips: www.nytimes.com/games/pips
The article on HN that inspired me to investigate constraint solvers: buttondown.com/hillelwayne/...
Play Pips, our new dominoes game for all skill levels.
Every domino has a spot. Can you find where each belongs?
www.nytimes.com
October 18, 2025 at 4:20 PM
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If you're a programmer, I recommend looking at constraint solvers. This different paradigm will broaden your horizons. It's also much easier than I expected. See my blog for details: www.righto.com/2025/10/solv...
Solving the NYTimes Pips puzzle with a constraint solver
The New York Times recently introduced a new daily puzzle called Pips . The idea is to place a set of dominoes on a grid, satisfying variou...
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October 18, 2025 at 4:20 PM
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MiniZinc gave me a solution to the Pips puzzle in 100 milliseconds. Admittedly, this puzzle is rated "easy", but MiniZinc quickly solves hard puzzles too. Internally, MiniZinc uses complicated algorithms such as backjumping and constraint propagation, but I don't need to worry about that.
A Pips problem with the solution. It has numbers in the cells, corresponding to dominoes. A much larger Pips puzzle, a 6 by 6 grid in an octagonal shape. It has 12 dominoes and many constraints. The image shows the solution.
October 18, 2025 at 4:20 PM
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I used a constraint solver called MiniZinc. I wrote constraints for the problem: the conditions on the grid, the shape of the grid, and the values of the dominoes. A few more constraints defined how the problem works. I didn't need to write algorithms because MiniZinc solves automatically.
The same three-by-three grid of squares with four dominoes below it. Two squares are labeled with "8", indicating that the numbers in that region must sum to eight. Another square is labeled "<5", indicating that the number in that square must be less than 5. The three bottom squares are labeled with an equals sign, indicating that the three numbers must be the same. The upper-right square is missing so there are 8 squares in total, able to hold four dominoes. Code: constraint pips[1,1] + pips[2,1] == 8; constraint pips[2,3] < 5; constraint all_equal([pips[3,1], pips[3,2], pips[3,3]]); Code: grid = [| 1,1,0| 1,1,1| 1,1,1|]; Code: spots = [|5,1| 1,4| 4,2| 1,3|];
October 18, 2025 at 4:20 PM
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The New York Times recently introduced daily puzzles called Pips. You place the dominoes on the grid so the numbers satisfy the labels.

I solved Pips with cool software called a constraint solver. You give the constraints, e.g. "sum to 8", and it "magically" finds a solution. Let's look closer...
A three-by-three grid of squares with four dominoes below it. Two squares are labeled with "8", indicating that the numbers in that region must sum to eight. Another square is labeled "<5", indicating that the number in that square must be less than 5. The three bottom squares are labeled with an equals sign, indicating that the three numbers must be the same. The upper-right square is missing so there are 8 squares in total, able to hold four dominoes.
October 18, 2025 at 4:20 PM