Aspire Faculty ID #16717 · Topic: CUET 2023 · Just now
CUET 2023

Given the following binary number in 32-bit (single precision) IEEE-754 format: $0011\ 1110\ 0110\ 1101\ 0000\ 0000\ 0000\ 0000$ The decimal value closest to this floating-point number is

Solution

Sign bit = $0$ (positive)

Exponent = $01111100_2=124$
Bias $=127 \Rightarrow E=124-127=-3$

Mantissa $\approx 1.1101101_2 \approx 1.82$

Value $\approx 1.82\times2^{-3}\approx0.227$

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