GATE 2017 CS (CS2) – Question 22

Digital Logic · Number Representation and Arithmetic · 1 mark · Multiple choice

A 32-bit IEEE-754 single-precision bit pattern is 00111110011011010000000000000000. Which decimal value is closest?

$1.45\times10^1$
$1.45\times10^{-1}$
$2.27\times10^{-1}$
$2.27\times10^1$

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Show answer and explanation

Correct answer: (C) $2.27\times10^{-1}$

Explanation

Split as sign 0, exponent 01111100=124, and fraction 1101101 followed by zeros. The unbiased exponent is −3 and the significand is $1+1/2+1/4+1/16+1/32+1/128=1.8515625$. The value is 1.8515625/8=0.2314453125, closest to 0.227, C.

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