 # Question & Answer: Decode the IEEE floating point binary 1 1000 0010 1011 0000 0000 0000 0000 000 as a mixed fraction…..

Decode the IEEE floating point binary 1 1000 0010 1011 0000 0000 0000 0000 000 as a mixed fraction

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Question & Answer: Decode the IEEE floating point binary 1 1000 0010 1011 0000 0000 0000 0000 000 as a mixed fraction…..
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The given IEEE floating point binary is equivalent to -13.5 which can be expressed as a mixed fraction -(13+1/2)

An IEEE floating point binary is a 32 bit representation of a binary fraction.

The MSB indicates whether the number is positive or negative. Here its negative as MSB=-1

The next 8 bits represnt the exponent =130

The bias in exponent is 127 so bias+p=130

so p=3

the remaining bits are the fraction part which is equivalent to 1/2+1/8+1/16=0.5+0.125+0.0625=0.6875

so our decimal number=(1+0.6875)*8=13.5

and as the number is negative. SO ANSWER IS -13.5=13 1/2