- #1

s3a

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## Homework Statement

Convert the decimal number 2000.90210 to a single-precision IEEE 754 hexadecimal.

## Homework Equations

(exponent field)_10 - 127_10 = exponent_10

The first bit is the sign bit.

The 2nd to 9th bits are the exponent bits.

The 10th to 32nd bits are the fraction field bits.

1.(fraction field)_2 x 2^(exponent_10) leads to the base 10 final answer

## The Attempt at a Solution

My attempt at the solution is attached as MyWork.jpg.

I was planning to convert it to the binary IEEE 754 32-bit single-precision representation since that's what I am familiar with and then convert it to hexadecimal however, it seems that when I do this, my binary version is far off from the decimal value I'm initially given.

I'm not sure but, this might be related to the fact that the binary fraction field is (at least, seemingly) irrational.

Any help in solving this problem would be greatly appreciated!