twos-complement

Why is ~3 equal to -4 in Python?

I'm getting started in Python programming. I'm reading a basic tutorial, but this point is not very clear to me. I would appreciate any help you can give me. ...

Python - Applying Two's Complement to a String

Hello, I am trying to add the Two's Complement to a Binary number represented with a string. Assuming the string has already been flipped, how would I go about "adding" 1 to the last character, and replacing the other characters in the string as needed? Example: 100010 is flipped to 011101, and is represented as a string. How would you...

Two's complement proof

Is it possible to prove by induction that the two's complement of any string of 0's will always result in 0, for all sequences of length n? I'm trying to do this using the value formula, i.e. value = -a_n-1 x 2^(n-1) + summation{i=0 to n} (a_i x 2^i), where n = number of bits in string ...

Wrapping my head around hardware representations of numbers: a hypothetical two's complement question

This is a super naive question (I know), but I think that it will make for a good jumping off point into considering how the basic instruction set of a CPU actually gets carried out: In a two's complement system, you cannot invert the sign of the most negative number that your implementation can represent. The theoretical reason for thi...