Most computers choose a particular word length (measured in bits) for representing integers. Many current-generation processors have a word length of 64 bits.

a. How many different values can be encoded in a word of 64 bits if all values are to be positive integers (that is, unsigned representation, not two's-complement)? Express your answer as a power of two.

2^_____

b. Suppose we now use 128-bit words, but use twos-complement representation to allow for negative integers. How many distinct values can be encoded? Express your answer again as a power of two.

2^_____

c. What is the binary representation of the most negative number (i.e., the negative number with the largest magnitude) that can be represented? (Enter exactly 16 bits)

d. If you took the binary representation of this most negative number, and simply applied the method to compute its negative (i.e., flip all bits and add a '1'), what 16-bit binary value would you obtain? (Enter exactly 16 bits)