GATE 2021 CS – Question 34

Digital Logic · Number Representation and Arithmetic · 1 mark · Numerical answer

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 ______.

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Correct answer: -7.75

Explanation

Exponent = 129 - 127 = 2. Mantissa = 1.1111 (binary) = 1.9375. Value = -1.9375 x 4 = -7.75.