Adding two numbers without using the addition operator

Question

In c ~ is 1's complement operator. This is equivalent to: ~a = -b + 1 So, a - ~b -1 = a-(-b + 1) + 1 = a + b – 1 + 1 = a + b

Can anyone explains this to me?

This will only make sense after you understand two's complement numbers. — user3386109
– user3386109, Commented Mar 29, 2014 at 18:50
The steps taken by that derivation are a bit odd. a - ~b -1 = a-(-b + 1) + 1 is valid (and equals a + b), but it doesn't really make sense as a step. It looks sort of like it's substituting ~b = -b + 1 (which is incorrect) and sort of accidentally fixing it by changing the subtraction at the end to an addition. Very weird. — user555045
– user555045, Commented Mar 29, 2014 at 19:07

old_timer · Accepted Answer · 2014-03-29 18:58:42Z

4

From elementary school math we know

a = -(-a);

From twos complement we know that

-a = (~a) + 1  (invert and add one)

so we know that

a + b 
= a - (-b)      elementary math
= a - (~b + 1)  twos complement
= a - (~b) - 1   distribute the negative (elementary math)

answered Mar 29, 2014 at 18:58

old_timer

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Deduplicator · Accepted Answer · 2014-03-29 19:01:34Z

0

You are right that ~ is always 1's complement (aka bitwise not) in c. Where you are going wrong is this: C does not guarantee 2's complement for numbers. So all your calculations depend on using a major flavor of C.

answered Mar 29, 2014 at 19:01

Deduplicator

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