Question

In: Electrical Engineering

Show the IEEE 32-bit representation for 2.09375 and 17.1875

Show the IEEE 32-bit representation for 2.09375 and 17.1875

Solutions

Expert Solution

So, now we have binary of 2.09375 = 10.00011

we can write it as

1.000011 x 21

Since the sign is positive so sign bit will be 0.

E = 21

We add 127 to bias exponent

E will be 127 + 2 = 129 = 1000 0001

Mantissa will be decimal part.

sign Exponent Mantissa

0 1 0 0 0 0 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

For 17.1875

17.1875 in binary is

10001.0011

It can be written as

1.00010011 x 24

So, E = 16 + 127 = 143 ( after adding 127 as bias)

143 in binary = 10001111

Sign is 0

Mantissa is decimal part = 00010011

IEEE Format

0 1 0 0 0 1 1 1 1 0 0 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Manojponduru answered 1 year ago
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