Express the decimal value 10.25 IEEE single precision format?

Question

Please show the working

Answer 1

First Convert 10.25 to binary format in this way

(10.25)₁₀=(1010.01)₂

For IEEE 754 format we have to normalize the number (decimal point following a leading 1): 1.01001*2³

Now, the leading 1 here is omitted while storing as it is implied as long as exponent is non zero (normalized representation)

here for Single precision Biased exponent= E'=E+127 (127 is bias)

                                                               E'=130=(10000010)₂

So for 32 bits: 

Sign bit(1 bit)

exponent bits(8bits)

mantissa(23bits)

0(for +ve sign)

10000010

01001000000000000000000

convert it into hexadecimal format:41240000

Comments

sign bit should be 0 na?

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yep... corrected!! :)