*This solution is for the book I am currently reading. All of my notes and solutions are available at Google Code.*

Here is my work for problem 2.33 (skipped publishing 2.31 & 2.32 as they were thought exercises):

We can represent a bit pattern of length w = 4 with a single hex digit. For a two's- complement interpretation of these digits, fill in the following table to determine the additive inverses of the digits shown x -t 4 x ------------------------------- Hex Decimal Decimal Hex ------------------------------- 0 0 0 0 ------------------------------- 5 5 -5 B ------------------------------- 8 -8 -8 8 ------------------------------- D -3 3 3 ------------------------------- F -1 1 1 ------------------------------- Work: 8 = 1000 = -8 D = 1101 = -8 + 4 + 1 = -3 -5 -8 + 2 + 1 = 1011 = B