how to take twos complement of a byte in c++

Question

I am looking at some c++ code and I see:

 byte b = someByteValue;
 // take twos complement
 byte TwosComplement = -b;

Is this code taking t

Answer 1

On a two's complement machine negation computes the two's complement, yes.

On the Unisys something-something, hopefully now dead and buried (but was still extant a few years ago), no for a signed type.

C and C++ supports two's complement, one's complement and sign-and-magnitude representation of signed integers, and only with two's complement does negation do a two's complement.

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With byte as an unsigned type negation plus conversion to byte produces the two's complement bitpattern, regardless of integer representation, because conversion to unsigned as well as unsigned arithmetic is modulo 2ⁿ where n is the number of value representation bits.

That is, the resulting value after assigning or initializing with -x is 2ⁿ - x which is the two's complement of x.

This does not mean that the negation itself necessarily computes the two's complement bitpattern. To understand this, note that with byte defined as unsigned char, and with sizeof(int) > 1, the byte value is promoted to int before the negation, i.e. the negation operation is done with a signed type. But converting the resulting negative value to unsigned byte, creates the two's complement bitpattern by definition and the C++ guarantee of modulo arithmetic and conversion to unsigned type.

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The usefulness of 2's complement form follows from 2ⁿ - x = 1 + ((2ⁿ - 1) - x), where the last parenthesis is an all-ones bitpattern minus x, i.e. a simple bitwise inversion of x.