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    Upvotes16Top Answeredited Oct 7, 2010 at 1:53

    Using two's complement to represent negative values has the benefit that subtraction and addition are the same. In your case, you can think of 12 - 7 as 12 + (-7). Hence you only need to find the two's complement representation of -7 and add it to +12:

    12 001100
    -7 111001 -- to get this, invert all bits of 7 (000111) and add 1
    ----------
    5 1000101

    Then discard the carry (indicates overflow), and you have your result: 000101 which equals to 5 as expected.

    For your example of -15 + 2, simply follow the same procedure to get the two's complement repr...

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