In decimal, what is the most negative number that can be represented using a 12-bit two’s complement binary integer?
In an n-bit two's complement representation scheme, the amount of numbers we can represent is 2n - 1. In 12- bit, it's 1111 1111 1111, or 4095 in decimal. The largest positive number must not have a leading 1, as it would have to be negative, so the largest positive number we can represent is 2n-1 - 1, which is 0111 1111 1111 or 2047 in decimal. Subtracting these two numbers 2047 - 4095 gives us, all the negative numbers we can represent, and since the smallest negative number is -1, this also equals to the largest negative number. -2048.
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