GATE CSE 2021 Set 1 Q34: Decimal value of an IEEE 754 single-precision pattern

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

$S: 1 \qquad E: 10000001 \qquad F: 11110000000000000000000$

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 ________.

Try it: numerical answer: type the value

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Numerical answer. No negative marking.

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Answer: -7.75 (official GATE 2021 final answer key)

Concept used: A normalised value is $(-1)^S \times 1.F \times 2^{E - 127}$ .

First step: $E = 129$ , so the scale is $2^2$ ; the significand is $1.1111_2 = 1.9375$ .

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Source: official GATE 2021 Set 1 CS question paper and final answer key, organised by IIT Bombay. Question paper · Answer key