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There are few interesting things to notice about 2's complement numbers. First, all negative numbers will have a 1 in the first bit, just like sign-magnitude form. Thus it is immediately obvious if the number is negative or not. Second, some negatives are easy to spot. -1 is always all 1s, no matter how many bits long the numbers are. If we were working with a new 64-bit SPARC II chip, we would know that -1 is
1111111111111111111111111111111111111111111111111111111111111111
without even trying to convert!
-2 is easy, too, since it is all 1s except for a final 0. -2 in 8 bits is 11111110, in 12 bits it is 111111111110. -4 is all 1s except for the final two 0s. In fact, there is an easy to spot pattern. -1 is always all 1s, which would normally be the largest unsigned binary number for n bits. From this point, the negative numbers count down or backwards. |