System uses a 6-bit 2's complement signed integer representation. What is the range of decimal values it can represent?

-32 to + 31

Explanation:

6 bit 2s complement representation will be of the form b1b2b3b4b5b6 where each bit is either 0 or 1.

The largest positive number that can be represented using this scheme is 011111

Translating this to decimal this is 1*2^4 + 1^2^3 + 1^2^2 + 1^2^1 + 1^2^0

=16 + 8 + 4 + 2 + 1 = 31

The smallest negative number that can be represented using this scheme is 100000

Translating this to decimal = - 1 * 2^5 = - 32

So the range of decimal values that can be represented is - 32 to + 31.