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I’m in a computer systems course and have been struggling, in part, with Two’s Complement. I want to understand it but everything I’ve read hasn’t brought the picture together for me. What I’m hoping for is a clear and concise definition that is easily understood by a programmer. Two’s complement is a clever way of storing integers so that common math problems are very simple to implement.
To understand, you have to think of the numbers in binary. That’s as far as we can go in positives. This is because 0000 is used for zero. This can be consider as Number Line of computers.
Doing this, the first bit gets the role of the “sign” bit, as it can be used to distinguish between positive and negative decimal values. 0, you can say discern the decimal value is positive. Probably the best part of two’s complement is how it simplifies math. The most significant bit is overflow, so the result is actually 0000. Another advantage besides easy addition and subtraction is that 2s complement only has one zero. That’s a real pain in the behind.