For an n-digit 2's complement binary number (n>1), what is the number of negative integers (as a function of n)?
So my solution is 2^n but I don't think it's correct.
For example let's say we have a 4-digit 2's complement binary number: 1000. The 1 in the most significant digit's place indicates the number is negative, so we can only rearrange the 3 digits after that to indicate the number of negative integers, which would be:
1000 1100 1110 1111 1101 1001 1011 1010
So 2^n = 2^4 = 8 different negative integers. But I'm confused because this solution doesn't work if the 0 is in the most significant digit's place (i.e. 0001), in which case there are zero negative integers.
Any help is appreciated,
thanks in advance.