A binary floating-point number has seven bits for a biased exponent. The constant used for the bias is 64. 

a. List the biased representation of all exponents from -64 to +63.

b. Show that a 7-bit magnitude comparator can be used to compare the relative magnitude of the two exponents. 

c. Show that after the addition of two biased exponents it is necessary to subtract 64 in order to have a biased exponents sum. How would you subtract 64 by adding its 2's complement value? 

d. Show that after the subtraction of two biased exponents it is necessary to add 64 in order to have a biased exponent difference.