Question

Determine the decimal representation for 87.32 using the IEEE 754 single-precision format.

Answer 1

The number given is: 87.32

The binary representation of 87 (in decimal) is: 1010111‬

The binary representation of 0.32 (in decimal) is: 0.01010001111

Therefore,
87.32 = 1010111.01010001111
= 1.01011101010001111 x 2^6

sign = 0

Single Precision:

biased exponent => 127+6 = 133
133 in binary = 10000101
Normalised mantissa =  01011101010001111 (binary digits after the decimal point written in the scientific form)

IEEE 754 Single precision is written in 32 bits where, sign is the first bit, next 8 bits are the exponent and the remaining 23 bits are that of mantissa:

Therefore 87.32 in IEEE 754 Single precision representation is:

0 10000101 01011101010001111000000 -Answer

In hexadecimal it is: 42AEA3C0

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