GATE | GATE CS 2021 | Set 1 | Question 34

Consider the following representation of a number in IEEE 754 single-precision floating point format with a bias of 127.

S : 1     E : 10000001      F : 11110000000000000000000 

Here, S,E and F denote the sign, exponent, and fraction components of the floating point representation.

The decimal value corresponding to the above representation (rounded to 2 decimal places) is ____________.
(A) -7.75
(B) +7.75
(C) -5.57
(D) 5.75

Answer: (A)
Explanation: Given,
Sign bit = 1 → Number is negative.

Biased Exponent bits = 10000001 = 129 → E = 129-127 = 2

Mantissa bits = 11110000000000000000000

Number = – 1.111100..00 * 22 → -111.11

Hence, Number = -7.75 in decimal.
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