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Which of the given number has its IEEE-754 32-bit floating-point representation as (0 10000000 110 0000 0000 0000 0000 0000) 

Which of the given number has its IEEE-754 32-bit floating-point representation as (0 10000000 110 0000 0000 0000 0000 0000)  Correct Answer 3.5

Concept:

32-bit floating-point representation of a binary number in IEEE- 754 is

Sign (1 bit)

Exponent (8 bit)

Mantissa bit (23 bits)


Calculation:

Binary number is

0 0110010 01101100000000000000000

Here, sign bit is 0. So, number is positive.

0

10000000

110 0000 0000 0000 0000 0000


Exponent bits = E = 10000000 = 128 (in decimal)

Mantissa bits M = 110 0000 0000 0000 0000 0000

In IEEE-754 format, 32-bit (single precision)

(-1)s × 1.M × 2E – 127

= (-1)0 × 1. 11 × 2128 – 127

= (1. 11)2 × 2

= (11.1)2 = 2 + 1 + 0.5 = 3.5

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