3 ms·

awesome article! especially love deep dives like this into subjects where i have only rudimentary understanding. i see that the 4-phase logic is time-based. ar

awesome article! especially love deep dives like this into subjects where i have only rudimentary understanding. i see that the 4-phase logic is time-based. are there similar logic systems that are voltage-based, so instead of a high and low, you had very high, high, low, and very low? (i'm thinking a decimal computer would be neat but maybe too difficult given the relative benefits.)

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kens 6y ago
Ignoring analog computers, it's much much easier to build a binary circuit than a multi-level circuit. However, I know of two systems with 4-level logic. One is von Neumann's IAS machine (1952) and copies (ILLIAC, JOHNNIAC, MANIAC, etc). For addition, it used an analog vacuum tube circuit to add the voltages from the two input bits and carry, so you ended up with something like 0V, 20V, 40V, or 60V. Then a threshold circuit converted this to the binary sum and carry bit outputs. Another example of 4-level logic is the Intel 8087, the math coprocessor chip used in the IBM PC. The microcode for math computations was too big to fit on the chip, so Intel used a 4-level ROM, with four transistor sizes for each storage location. So each "bit" gave you four different voltages. Comparators converted the four voltages into two bits. The result was twice the ROM density, allowing the microcode to fit. (In actuality, it was less than twice the density because of the additional circuitry.) Finally, flash memory uses multiple voltage levels to store up to 4 bits per cell. As far as decimal computers, there were lots of decimal computers in the 1950s and 1960s for business use. However, they used BCD (binary-coded decimal) or timed pulses, rather than 10 voltage levels.
- clairity 6y ago
  neat, and thanks for the historical context! i didn't realize 4-level logic had been used in mass-market chips like the 8087.
exmadscientist 6y ago
You do see multi-level signalling in some communication interfaces, such as MIPI-C (3-level) or PAM4. But it's usually a massive headache not worth bothering with.

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kens 6y ago

Ignoring analog computers, it's much much easier to build a binary circuit than a multi-level circuit. However, I know of two systems with 4-level logic. One is von Neumann's IAS machine (1952) and copies (ILLIAC, JOHNNIAC, MANIAC, etc). For addition, it used an analog vacuum tube circuit to add the voltages from the two input bits and carry, so you ended up with something like 0V, 20V, 40V, or 60V. Then a threshold circuit converted this to the binary sum and carry bit outputs. Another example of 4-level logic is the Intel 8087, the math coprocessor chip used in the IBM PC. The microcode for math computations was too big to fit on the chip, so Intel used a 4-level ROM, with four transistor sizes for each storage location. So each "bit" gave you four different voltages. Comparators converted the four voltages into two bits. The result was twice the ROM density, allowing the microcode to fit. (In actuality, it was less than twice the density because of the additional circuitry.) Finally, flash memory uses multiple voltage levels to store up to 4 bits per cell. As far as decimal computers, there were lots of decimal computers in the 1950s and 1960s for business use. However, they used BCD (binary-coded decimal) or timed pulses, rather than 10 voltage levels.

clairity 6y ago
neat, and thanks for the historical context! i didn't realize 4-level logic had been used in mass-market chips like the 8087.

exmadscientist 6y ago

You do see multi-level signalling in some communication interfaces, such as MIPI-C (3-level) or PAM4. But it's usually a massive headache not worth bothering with.