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I have seen online these diagrams for 4-bit adders which feature 4 individual full adders chained together with the carry out from the previous feeding into the carry in to the next.. Likewise, to add 8 bits, they would require 8 full adders. Presumably, for a 64 bit computer, you would need 64 full adders.

I know there are many different types of adders which may potentially solve this problem, but I'm talking about the basic full adders you see in a school textbook - if you wanted to do 64-bit addition, would you need to have 64 full adders together?

I'm also curious how many adder circuits a typical modern desktop would have - I mean, I see videos featuring components like this (https://www.amazon.com/4-BIT-BINARY-FULL-ADDER-DIP-16/dp/B00E4WLIWE), and, as far as a I can tell, this is a single, 4-bit adder. So if you have a couple of cm for a single such device, a computer would only be able to have a few dozen or so, but is this typical, or would a computer have millions of adders?

In this case, are these circuits you can buy online only 'huge', so that they are practical to work with for human hobbyists using breadboards as opposed to, you know, robots who manufacture stuff for commercial products, who can happily create millions of adder circuits on probably the than the size of your fingernail?

If anyone could clear any of these points up for me, I'd appreciate it.

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    \$\begingroup\$ That's a DIP through-hole component from back in the days. There are no DIP components inside a modern 64 bit CPU... \$\endgroup\$
    – Lundin
    Aug 16 '21 at 11:51
  • \$\begingroup\$ robots who manufacture ... size of your fingernail? The small size is NOT because of "robots". It can be done without robots. The design of microprocessors doesn't need robots. Only in the manufacturing and testing robots might be involved but they're not essential. I suggest that you educate yourself on the subject more. \$\endgroup\$ Aug 16 '21 at 11:56
  • \$\begingroup\$ @Bimplerekkie, the 'bitness' of a cpu is debateable but a 64 bit cpu does not have to have 64 bit instructions. ARM Cortex M0/3/4/7 is 32bit but has 16 bit instructions and there plenty of others. AVR is an 8bit cpu but has 16 bit instructions and we won't discuss PIC :( As for the OP's question - generally you'd have 64 full adders if you wanted a cpu with a 64 ALU. Or you could have 64 bit registers but double pump a 32 bit ALU - it all comes down to what performance you want. Taken to the extreme you could have a 1 bit ALU like the old drum computers. \$\endgroup\$
    – Kartman
    Aug 16 '21 at 12:02
  • \$\begingroup\$ @Lundin got it. Thanks \$\endgroup\$ Aug 16 '21 at 12:06
  • \$\begingroup\$ A full adder requires something like a dozen transistors. Modern CPUs like you'd have in a desktop or laptop have in the order of 1 billion transistors in them. Some of those will be used for adding stuff up. \$\endgroup\$
    – Mat
    Aug 16 '21 at 12:07
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if you wanted to do 64-bit addition, would you need to have 64 full adders together?

Yes.

I'm also curious how many adder circuits a typical modern desktop would have

Broadly this is the number of "execution units", plus however many for the "vector units", plus a whole load more for the graphics card. Very roughly I'd say 10,000 to 1,000,000 individual "full adders".

In this case, are these circuits you can buy online only 'huge', so that they are practical to work with for human hobbyists using breadboards as opposed to, you know, robots who manufacture stuff for commercial products, who can happily create millions of adder circuits on probably the than the size of your fingernail?

Yes. This is the "integrated" in "integrated circuit"; they're made by a photolithographic process, so you can have a billion transistors per chip without having to assemble anything.

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  • \$\begingroup\$ Thanks for clearing things up! \$\endgroup\$ Aug 16 '21 at 12:10
  • \$\begingroup\$ They used to make computers out of separate chips like full adder chips. Back in those days (approximately 1980s?) they would've paid a lot more attention to minimizing the number of chips. \$\endgroup\$
    – user253751
    Aug 16 '21 at 12:11
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    \$\begingroup\$ I disagree. You can implement a 64-bit adder using a single 4-bit adder with additional registers and multiplexers. Used to do things like that all the time back in the days of SSI and MSI logic, when all you had to work with were 4-bit and 8-bit wide devices. \$\endgroup\$
    – SteveSh
    Aug 16 '21 at 12:17
  • \$\begingroup\$ The 1980's HP85 computer has an 8bit processor that has instructions to do 64bit operations -a 64 bit operation takes at least 8 cycles though. What the programmer sees isn't necessarily what happens under the hood. \$\endgroup\$
    – Kartman
    Aug 16 '21 at 12:21
  • \$\begingroup\$ Indeed, you can pipeline it, so I suppose it's not a hard necessity - but that would be a very questionable design decision in a modern system. \$\endgroup\$
    – pjc50
    Aug 16 '21 at 12:24

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