1
$\begingroup$

I'm a junior student in Electronic Engineering.

Recently, I learned about Gödel's incompleteness theorem. One of the concepts related to this theorem is Gödel numbering, which shows that every logical operation can be converted into an arithmetic operation.

This leads me to think that an Instruction Set Architecture (ISA) might not need to include specific logical operation instructions, as these operations could theoretically be performed using arithmetic operations instead.

I assume that the reason for including direct logical operation instructions is that they are much faster than performing logical operations through arithmetic operations, but I'm not entirely sure.

$\endgroup$
3
  • 3
    $\begingroup$ The reason for including anything in an instruction set is performance. mov is Turing-complete. $\endgroup$ Commented Jun 5 at 15:40
  • $\begingroup$ @NaïmFavier Thank you! your link about mov is quite interesting! $\endgroup$
    – MS Keane
    Commented Jun 5 at 15:56
  • $\begingroup$ Try implementing a function unsigned int bit_and (unsigned int x, unsigned int y). The best I can come up with (and it is not trivial) is O(n) for n bit numbers, while addition can be implemented in O(log n) n-bit bit operations. So there is a massive difference in performance. $\endgroup$
    – gnasher729
    Commented Jun 6 at 12:22

1 Answer 1

-1
$\begingroup$

Imo in digital electronics arithmetic operations are made of logical operations. And how do you build a digital circuit which performs a arithmetic operation without being a subset of a logical operation?

$\endgroup$
3
  • $\begingroup$ I do not even understand a digital circuit which performs [an] arithmetic operation without being a subset of a logical operation - how can a circuit be part of an operation? How does this answer Why include both if one can be expressed in terms of the other?? $\endgroup$
    – greybeard
    Commented Jun 23 at 5:55
  • $\begingroup$ @greybeard you can easily build a circuit made of transistors which would return the negation of a input signal.It is not easy to build a circuit made of transistors which would return the sum of 2 bits(2 input signals) without having already made a circuit which performs a logical operation.In digital electronics the arithmetic operations are made of logical operations , not vice versa. $\endgroup$ Commented Jun 26 at 4:08
  • $\begingroup$ Implementation of operations isn't ISA. $\endgroup$
    – greybeard
    Commented Jun 26 at 5:25

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.