Definition of Two's complement in a simple language

Question

I have been searching online but can't find a simple definition of Two's complement without the use of algorithms and math so just to to confirm that:

Two's complement is basically reverting the sign of a number in binary so if I have 2 then turn it to -2 and if I got -2 then turn it to 2. Is that it?

Does this answer your question? [What is “2's Complement”?](https://stackoverflow.com/questions/1049722/what-is-2s-complement) — Sean Reid, Jan 22 '20 at 15:51
no its doesn't. Answer to my question is a simple yes/no. is my above definition correct? I don't want complex mathematical proves or anything like that. — Alec, Jan 22 '20 at 15:52

Petr Skocik · Answer 1 · 2020-01-22T16:24:46.227

Two's complement of a fixed-width binary number X is a binary number that you get by inverting X's binary digits and adding one, discarding possible overflow.

twos_compl(X){ return ~X+1; }

E.g., for 4-bit wide numbers:

X       ~X      ~X+1
0000    1111    0000
0001    1110    1111
0010    1101    1110
0011    1100    1101

If a computer architectures uses two's complement to represent mathematically negated signed numbers, i.e., if twos_compl(X) == -X, then certain math operations become easy to implement.

(In such a representation of a signed number the highest bit then means -pow(2,bit_index_from_the_right) rather than the usual (usual for unsigned numbers and for every other bit in a signed two's complement representation) +pow(2,bit_index_from_the_right).)

For example, addition (or subtraction) on an architecture that uses two's complement representation for negative numbers will use the same instruction as the corresponding unsigned addition (or subtraction respectively), and it will work regardless of the sign of the operands.

In C on a two's complement platform:

int sadd(int A, int B) { return A+B; }
unsigned uadd(unsigned A, unsigned B) { return A+B; }

will compile to the same instruction.

And by definition of two's complement, so will:

int neg(int A) { return -A; }

and

int neg2(int A) { return ~A+1; }

So to summarize, two's complement isn't necessarily mathematical negation—it is a transformation of the binary representation of a number that a computer architecture may interpret as negation and if it does, it simplifies math on that computer architecture.

I find this answer somewhat entertaining in how technically precise the language is in the face of the asker seeming to be looking for a very reduced simplified explanation — Klaycon, Jan 22 '20 at 16:23

Definition of Two's complement in a simple language

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