5. A IEEE 754 single precision number uses 1 bit for the sign, 8 bits for the exponent and 23 bits for the mantissa. What would be the range of values that could be represented with a hypothetical less-than-halfprecision number that used 1 bit for the sign, 3 bits for the exponent and 4 bits for the mantissa. Assume an exponential bias of 4 and that the exponent values of (000)2 and (111)2 are reserved.

(a) What exactly is the largest positive value that can be represented by less-than-half-precision number format described in the previous question? Express your answer in base 10

(b) How many significant base 2 digits can the less-than-half-precision number store?

(c) Show the contents of the 8 bits if 6 is stored as a less-than-halfprecision number?

(d) Given the following contents of a byte representing a less-than-halfprecision number, what number is this in base 10? 10101100 6. Describe how you could represent a set with a byte if U = {a, b, c, d, e, f, g, h} (i.e., there are up to eight distinct items that could be placed in the set).

7. (Optional Bonus): What is the largest value that is strictly less than 1 that can be represented by the less-than-half-precision number?