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I want to know how Maths Co-Processors are made and how they work. I do understand that these are based upon electrical (yet chemical) switches, but how do they calculate things ?

I don't understand how switching something on and off not only make something tick but also make it do much more. I get it that it can turn on and off but how does it consider a certain given number and adds that with another number and give the result ?! That is just mind blowing to me.

I tried to look for answers but I couldn't find any. I also want to know about other (Main CPU) processor(s) but I am keeping that for another question.

Thank You !

Raj
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2 Answers2

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Both the CPU and that math coprocessor (now a part of the CPU) work in the same way --- using logic gates to implement the actual logic, using flip flops for registers, and using RAM for cache.

Mathematical operations are implemented as a combination of circuits (collections of logic gates) and tables (a type of memory). Their exact implementation depends on the processor, and can be quite complicated and hard to get right (see for example the Pentium FDIV debacle).

To know more, consult a textbook like The Elements of Computing Systems.

Yuval Filmus
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  • Thank You for your answer sir. I look forward to getting the book. Would you like to mention any more sources or resources to get the information ? And again, Thank You for your answer. – Raj Mar 20 '16 at 11:43
  • There are other, similar books which you can find (for example) by looking at the Amazon page of this one. – Yuval Filmus Mar 20 '16 at 11:47
  • Yes, sure. I will do so. I tried to search for (on Google, mostly) Maths Co-Processor etc. but I couldn't find much information and so I came here. And also, I will like to know ins-and-outs of Computers etc. So what books would you suggest as being best, according to you of course. – Raj Mar 20 '16 at 11:54
  • I haven't read any of them, but I'm sure Amazon has lots of reviews. Probably all popular books are excellent. – Yuval Filmus Mar 20 '16 at 12:01
  • I am on it Sir. Thank You once again. – Raj Mar 20 '16 at 12:07
  • Although, I still find it very much fascinating how on and off (switches) can govern most of what we do in Computers etc. And how do on and off even Calculate is what is beyond my understanding. I am eagerly waiting to read the book. Do you also know any good books that is regarding History Of Computers ? I will use that as a supplementary material to the Architectural books and I am looking for ones that could complement these too. – Raj Mar 20 '16 at 12:13
  • There are lots of books covering different aspects of history, but I don't know any of them specifically. You can easily find them by searching online. – Yuval Filmus Mar 20 '16 at 12:14
  • Yes; I have. And I will be posting some links as soon as I reach 10 Reputation points because until then, I am only allowed to post two links. – Raj Mar 20 '16 at 12:35
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    I don't want to clutter this question with answers, but the basic plan is: Understand how CPUs work at a high-level, understand enough digital logic to understand how basic arithmetic can be implemented, understand how FPUs represent floating-point numbers (paying special attention to rounding control), then finally start deep-diving into the details (e.g. Booth encoding, Wallace trees, the Goldschmidt algorithms). – Pseudonym Mar 21 '16 at 05:44
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I could have done this in comments, but I want to keep it more neat and so, I am doing this as an answer.

So here are some books that can be helpful and in fact are; very informative.

1. The Elements of Computing Systems By Noam Nisan, Shimon Schocken - (Suggested by Mr. Yuval)

http://www.amazon.com/The-Elements-Computing-Systems-Principles/dp/0262640686

2. Code By Charles Petzold

http://www.amazon.com/Code-Language-Computer-Hardware-Software/dp/0735611319

3. How Computers Work By Roger Young

http://www.amazon.com/How-Computers-Work-Processor-Edition/dp/1442113987/

4. Digital Design And Computer Architecture By David Harris -

http://www.amazon.com/Digital-Design-Computer-Architecture-Edition/dp/0123944244

5. Inside The Machine By Jon Stokes -

http://www.amazon.com/Inside-Machine-Introduction-Microprocessors-Architecture/dp/1593276680

6. How Computers Work By Ron White -

http://www.amazon.com/How-Computers-Work-Evolution-Technology/dp/078974984X/

There are many other books you can look for. These were suggestions on the Amazon page for 'The Elements Of Computing System' but 'Code' is a very famous and nice book. And so are the others but neither have I read all of them.

Other Helpful Books Are :-

And again, there are many other books one can find and if you do so, which is not mentioned in the list but you find it to be good, please do post the name of the book and the author at least.

Thank You !

Raj
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