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# ~10 = -11?

siddharth sekhar
Ranch Hand
Posts: 34
hello friends

can any one explain me why 10 complement is -11 in java and not 5

thank you

Henry Wong
author
Sheriff
Posts: 23295
125
siddharth sekhar wrote:
can any one explain me why 10 complement is -11 in java and not 5

Can you explain to us why the complement of 10 should be 5? I don't see how you got to that assumption.

Anyway to answer your question. Integers (whole numbers) are stored in Twos complement format. And a complement (meaning ones complement) of a number is simply reversing the bits. And when you reverse the bits of 10 in twos complement, that is what you get.

http://en.wikipedia.org/wiki/Two's_complement

Henry

Campbell Ritchie
Marshal
Posts: 56541
172
What the ~ operator does is to return the one's complement of the number. It only works for integers. Two's complement is defined by subtraction, but there are other formulae which give the same results.
If you work out the two's complement of i in n bits, it is 2ⁿ − i: for 10 as an int that is
0b1_0000_0000_0000_0000_0000_0000_0000_0000 −
0b0000_0000_0000_0000_0000_0000_0000_1010
0b1111_1111_1111_1111_1111_1111_1111_0110

The one's complement is obtained by inverting every bit. It can be calculated from 2ⁿ − 1 − i: for 10 as an int that is
0b1111_1111_1111_1111_1111_1111_1111_1111 −
0b0000_0000_0000_0000_0000_0000_0000_1010
0b1111_1111_1111_1111_1111_1111_1111_0101 which means −11 QED

You can try it for any number: you will see there is an extra − 1 in the formula: so when you take the one's complement of 10 you get −11.
Notice that the formulae for complement arithmetic give different results depending how many bits you have, so you should always say, “Two's complement of 12345 in 32 bits” or similar. There is also ten's complement but you don't use that in computing.