Question

c. Wh at is the decimal number that corresponds to the following IEEE 32-bit floating point number? 1100 0001 0010 1000 0000 0000 0000 0000 d. What is the decimal number that corresponds to the following IEEE 32-bit floating point number? o o1111111 00000000000000000000000

Answer 1

c. -10.5

11000001001010000000000000000000

sign bit = 1 (negative)

exponent = 1000 0010 = 130 - 127 (bias) = 3

2^3 = 8

mantissa = 01010000000000000000000 = 0.3125

(-1)^ (sign) * (2^(exp-127))*(1+mantissa) = -1 * 8 * 1.3125 = -10.5

d. 1.0

00111111100000000000000000000000

sign = 0 (positive)

exponent = 0111 1111 = 127 - 127(bias) = 0

2^0 = 1

mantissa = 00000000000000000000000 = 0

(-1)^ (sign) * (2^(exp-127))*(1+mantissa) = 1 * 1 * 1.0 = 1.0

Hope this helps. Do Upvote! :)