Boolean gates. Part 2
-
Roughly speaking adding two 32 bit numbers requires 32 Boolean gates. Why do you need millions of transistors? I know there is also substraction, division, multiplying, comparison etc. Some operations probably require way more Boolean gates than the number of bits the numbers involved in the operation are made of. Also my guess is there is a comparison based mathematical operation type selector that directs the bits to the correct area on the processor pill. Still it’s difficult to imagine where millions of transistors go. If I think about it more I get it, this is just Alu. There is also non mathematical stuff that needs to be taken care of as well.
-
Roughly speaking adding two 32 bit numbers requires 32 Boolean gates. Why do you need millions of transistors? I know there is also substraction, division, multiplying, comparison etc. Some operations probably require way more Boolean gates than the number of bits the numbers involved in the operation are made of. Also my guess is there is a comparison based mathematical operation type selector that directs the bits to the correct area on the processor pill. Still it’s difficult to imagine where millions of transistors go. If I think about it more I get it, this is just Alu. There is also non mathematical stuff that needs to be taken care of as well.
Calin Negru wrote:
If I think about it more I get it, this is just Alu. There is also non mathematical stuff that needs to be taken care of as well.
Not to mention the floating point stuff, memory cache, multiple cores, and so on, and so on... The distance between a modern day CPU and a schoolbook design is larger than the distance between a Ford T and a Formula 1 car.
Mircea
-
Calin Negru wrote:
If I think about it more I get it, this is just Alu. There is also non mathematical stuff that needs to be taken care of as well.
Not to mention the floating point stuff, memory cache, multiple cores, and so on, and so on... The distance between a modern day CPU and a schoolbook design is larger than the distance between a Ford T and a Formula 1 car.
Mircea
Indeed, and all the peripheral systems, ADC, Timers, UARTs, I2C, SPI, DMA, PWM, DAC, to name but a few.
"the debugger doesn't tell me anything because this code compiles just fine" - random QA comment "Facebook is where you tell lies to your friends. Twitter is where you tell the truth to strangers." - chriselst "I don't drink any more... then again, I don't drink any less." - Mike Mullikins uncle
-
Roughly speaking adding two 32 bit numbers requires 32 Boolean gates. Why do you need millions of transistors? I know there is also substraction, division, multiplying, comparison etc. Some operations probably require way more Boolean gates than the number of bits the numbers involved in the operation are made of. Also my guess is there is a comparison based mathematical operation type selector that directs the bits to the correct area on the processor pill. Still it’s difficult to imagine where millions of transistors go. If I think about it more I get it, this is just Alu. There is also non mathematical stuff that needs to be taken care of as well.
-
Roughly speaking adding two 32 bit numbers requires 32 Boolean gates. Why do you need millions of transistors? I know there is also substraction, division, multiplying, comparison etc. Some operations probably require way more Boolean gates than the number of bits the numbers involved in the operation are made of. Also my guess is there is a comparison based mathematical operation type selector that directs the bits to the correct area on the processor pill. Still it’s difficult to imagine where millions of transistors go. If I think about it more I get it, this is just Alu. There is also non mathematical stuff that needs to be taken care of as well.
Well, a little more than 32 (unless you count a full adder as one gate? but I wouldn't). Especially if you use any type of [fast adder](https://en.wikipedia.org/wiki/Carry-lookahead\_adder) which is often mandatory to hit frequency targets. Subtraction doesn't cost much extra, you can reuse your adder by turning it into an adder-subtractor. Comparisons don't cost extra, comparison is subtraction. [Multipliers](https://en.wikipedia.org/wiki/Dadda\_multiplier) are bigger. So it costs a few more gates than you estimated, but also there are far more transistors: billions, these days. (Scalar) ALUs are not a big part of a modern high-performance CPU, even after accounting for there being a handful of them (I mean multiple per core, of course there are usually multiple cores too). Here's a fun article showing how big various parts of a CPU actually are, keep in mind it's showing a super obsolete Pentium 4: [Intel’s Netburst: Failure is a Foundation for Success – Chips and Cheese](https://chipsandcheese.com/2022/06/17/intels-netburst-failure-is-a-foundation-for-success/)
-
Roughly speaking adding two 32 bit numbers requires 32 Boolean gates. Why do you need millions of transistors? I know there is also substraction, division, multiplying, comparison etc. Some operations probably require way more Boolean gates than the number of bits the numbers involved in the operation are made of. Also my guess is there is a comparison based mathematical operation type selector that directs the bits to the correct area on the processor pill. Still it’s difficult to imagine where millions of transistors go. If I think about it more I get it, this is just Alu. There is also non mathematical stuff that needs to be taken care of as well.
PIEBALD pulls his copy of Code by Charles Petzold off the shelf behind him. Chapter Twelve describes implementing A Binary Adding Machine from simple logic gates. His descriptions of logic gates use relays rather than transistors. I haven't counted, but it looks like a simple 32-bit adder built according to his diagrams might require a bit more than a hundred relays? I can't comprehend a full modern ALU though.
-
Well, a little more than 32 (unless you count a full adder as one gate? but I wouldn't). Especially if you use any type of [fast adder](https://en.wikipedia.org/wiki/Carry-lookahead\_adder) which is often mandatory to hit frequency targets. Subtraction doesn't cost much extra, you can reuse your adder by turning it into an adder-subtractor. Comparisons don't cost extra, comparison is subtraction. [Multipliers](https://en.wikipedia.org/wiki/Dadda\_multiplier) are bigger. So it costs a few more gates than you estimated, but also there are far more transistors: billions, these days. (Scalar) ALUs are not a big part of a modern high-performance CPU, even after accounting for there being a handful of them (I mean multiple per core, of course there are usually multiple cores too). Here's a fun article showing how big various parts of a CPU actually are, keep in mind it's showing a super obsolete Pentium 4: [Intel’s Netburst: Failure is a Foundation for Success – Chips and Cheese](https://chipsandcheese.com/2022/06/17/intels-netburst-failure-is-a-foundation-for-success/)
Thank you guys for sharing > harold “fast adder” That must be a recent improvement ( I have no clue, just a wild guess ) I’m just starting to understand what is probably the classical model. > tronderen “real estate” I like to think in somewhat similar terms
-
Thank you guys for sharing > harold “fast adder” That must be a recent improvement ( I have no clue, just a wild guess ) I’m just starting to understand what is probably the classical model. > tronderen “real estate” I like to think in somewhat similar terms
Not that recent. The 8008 used carry lookahead for example. And several 74181 (a 4-bit ALU chip which you can use multiple of in a group to build a wider ALU) could be combined with the 74182 (lookahead carry generator) to build an ALU with carry lookahead. These things are ancient (70's era tech). That does not mean that carry lookahead addition was always used everywhere, some chips were really trying to save on transistors and didn't use it. But anything modern, probably has some sort of fast adder. Ripple carry adders do not scale well (imagine a 64-bit ripple carry adder, yikes) and transistors are significantly cheaper than a dime a dozen.
-
Roughly speaking adding two 32 bit numbers requires 32 Boolean gates. Why do you need millions of transistors? I know there is also substraction, division, multiplying, comparison etc. Some operations probably require way more Boolean gates than the number of bits the numbers involved in the operation are made of. Also my guess is there is a comparison based mathematical operation type selector that directs the bits to the correct area on the processor pill. Still it’s difficult to imagine where millions of transistors go. If I think about it more I get it, this is just Alu. There is also non mathematical stuff that needs to be taken care of as well.
-
Not that recent. The 8008 used carry lookahead for example. And several 74181 (a 4-bit ALU chip which you can use multiple of in a group to build a wider ALU) could be combined with the 74182 (lookahead carry generator) to build an ALU with carry lookahead. These things are ancient (70's era tech). That does not mean that carry lookahead addition was always used everywhere, some chips were really trying to save on transistors and didn't use it. But anything modern, probably has some sort of fast adder. Ripple carry adders do not scale well (imagine a 64-bit ripple carry adder, yikes) and transistors are significantly cheaper than a dime a dozen.
If you take a look at multicore procesors that’s probably a lot more things going on and not suited as an entry level lesson. If you want to learn anything you need to strip down all the fancy things.
-
My (14 years old) son designed and implemented a 4-bit adder. For all but the LSB he used three XOR and two AND gates.
"In testa che avete, Signor di Ceprano?" -- Rigoletto
Interesting
