How to get the decimal value from the bit representation of a float value?(2)

For example: Float value is 54321.1

Bit representation on little endian machine: 1A315447

Actual Bit representation is : 4754311A

Bit representation: 01000111010101000011000100011010

Float interpretation: sign 1 bit, exponent 8 bits, fraction 23 bits.

         Sign    Exponent          fraction

           0     10001110     10101000011000100011010

Decimal

value              142         5517594/2^23

 

Use normal interpretation:

E = 142-(2^(8-1)-1)

(1 + 5517594/2^23)*(2^(142-(2^(8-1)-1)))

2^23 = 8388608;

142-(2^(8-1)-1) = 15;

(1 + 5517594/2^23) = 1. 6577484607696533203125

(2^(142-(2^(8-1)-1))) = 32768

 

(1 + 5517594/2^23)*(2^(142-(2^(8-1)-1))) = 1. 6577484607696533203125 * 32768= 54321.1015625

~54321.1

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