Wrap to w bits

A machine that stores whole numbers in w bits keeps only the lowest w bits of a result, and reads them as two’s complement: the top place (place w - 1) is worth minus 2 to the power w - 1. Return the number it ends up with for the whole number x.

wrap(200, 8)        # -56: 11001000 is -128 + 72
wrap(127, 8)        # 127
wrap(261, 8)        # 5: only the lowest 8 bits stay
wrap(-129, 8)       # 127
wrap(2 ** 31, 32)   # -2147483648

x may be negative. Python’s bit operators treat a negative number as two’s complement with endless 1s on the left (lesson 1), so masks work on it directly.

Limits

• w is from 1 to 200. x can be any whole number, including very large and negative ones.