3. Fixed-point numbers

a) [10 marks] A fixed-point binary number system has 'm' whole bits and 'n' fractional bits. What is the range of numbers represented, assuming an unsigned format? Does every binary rational in this range have a finite decimal expansion? ___ (yes/no) Justify your answer.

b) [10 marks] A fixed-point binary number system has 4 whole bits and 12 fractional bits. Represent the decimal fractions 0.75, 0.3, and 1/20 in this format. Recipe: Deal with the integer part separately. Now, take the fractional part, multiply by 2, record the integer part as one digit of your answer, and repeat until the fractional part is 0, or you run out of binary digits. Practice on 0.6875 = 11/16 = (0000.101100000000)---or just (0.1011). Do not round. Show answers in hexadecimal.