To combine and extend what David and Ernest said...

If we just look at 16 bits 4 = 0000000000000100. The ~ does a one's complement operation, so ~4 = 1111111111111011. The - does a two's complement operation, which is the one's complement plus 1, so -4 = 1111111111111100. Since 5 = 0000000000000101, -5 = 1111111111111011, which is the same things as ~4.

Why use two's complement for negative numbers? Because it makes subtraction work. For instance let's try 5 + (-4): 0000000000000101 + 1111111111111100 = 0000000000000001 with a 1 bit that got carried off the left end. With the one's complement, the answer is off by one.

One other clever thing about two's complment is that -0 = 0, while ~0 != 0.

Ryan [ April 26, 2005: Message edited by: Ryan McGuire ]

David Harkness
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Too long outside of the classroom. Thanks guys for clarifying!