math - How does the CPU do subtraction?

Question

I have some basic doubts, but every time I sit to try my hands at interview questions, these questions and my doubts pop up.

Say A = 5, B = -2. Assuming that A and B are 4-bytes, how does the CPU do the A + B addition?

I understand that A will have sign bit (MSB) as 0 to signify a positive value and B will have sign bit as 1 to signify a negative integer.

Now when in C++ program, I want to print A + B, does the addition module of the ALU (Arithmetic Logic Unit) first check for sign bit and then decide to do subtraction and then follow the procedure of subtraction. How subtraction is done will be my next question.

A = 5
B = 2

I want to do A - B. The computer will take 2's complement of B and add A + 2's complement of B and return this (after discarding the extra bit on left)?

A = 2
B = 5

to do A - B. How does the computer do in this case?

I understand that any if-then etc kind of conditional logic all will be done in hardware inside ALU. computing 2s complement etc,discarding extra bit all will be done in hardware inside ALU. How does this component of ALU look like?

Answer 1

The whole reason we use 2's-complement is that addition is the same whether the numbers are positive or negative - there are no special cases to consider, like there are with 1's-complement or signed-magnitude representations.

So to find A-B, we can just negate B and add; that is, we find A + (-B), and because we're using 2's-complement, we don't worry if (-B) is positive or negative, because the addition-algorithm works the same either way.