Assume that our computer stores decimal numbers using 16 bits - 10 bits for a sign/magnitude mantissa and 6 bits for a sign/magnitude base-2 exponent. (The way we showed in class.) Show the internal representation of the following decimal quantities.

a. + 7.5

b. - 20.25

c. - 1/64

a) 7.5 = 111.1*2° = 0.1111*2^3

which can also be written as

(1/2+1/4+1/8+1/16) * 8

sign of mantissa:=0

Mantissa (9 bits) : 111100000

sign of exponent: 0

Exponent (5 bits) : 0011

the final for this is:011110000000011

b) - 20.25 = - 10100.01*2^0 = - 0.1010001*2^5

sign of mantissa: 1

Mantissa (9 bits) : 101000100

sign of exponent: 0

Exponent (5 bits) : 00101

the final for this is:1101000100000101

c) - 1/64 = -.000001*2^0 = - 0.1*2^{-5}

sign of mantissa: 1

Mantissa (9 bits) : 100000000

sign of exponent: 0

Exponent (5 bits) : 00101

the final for this is:1100000000100101