Question

Represent (10.375)10 as single precision IEEE 754, show all the steps

Answer 1

Steps involved in converting (10.375)₁₀ to single precision IEEE 754 is.

Step1:

find binary value of 10.375

10.375 in binary is  1010.011

Step2:

Represent the above binary number as the following

= 1.010011 x 10³

Step3:

sign = 0 since it is positive

Step4:

Now calculate the biased exponent to get the biased exponent add 127 with the power of 10 from step.

biased exponent = 127 + 3 = 130

Step5:

Represent the biased exponent in binary

130 in binary is 10000010

Step6:

Normalised mantissa is the binary of the value after decimal point from step2.

Normalised mantissa = 010011

We will add 0's to the right of the normalised mantissa to get the decimal point.

Therefore the following is our representation in IEEE754 single precision

IEEE754 single precision is = 01000001001001100000000000000000

0 10000010 01001100000000000000000

Here

highlighted in red is sign

highlighted in blue is exponent

highlighted in green is mantissa

(If you still have any doubt regarding this quesion please comment I will definitely help)