Question

What are the mantissa and exponent values if 6.75 is represented in 8 bit binary floating point representation

Answer 1

Answer:

Mantissa is 1011 and exponent is 101

Explanation:

Step 1 : Convert the integer part of the decimal value into binary value => 6(10) = 110(2)

Step 2 : Convert the decimal part into binary value => 0.75×2 = 1.50; it generates 1 and continue with the remaining => 0.50 × 2=1.0; it generates 1 and nothing remains.

So 0.75(10)=0.11(2)

Step 3 : Add the exponent part => 6.75(10)=110.11(2)= 110.11(2)×2^0

Step 4 : Normalize the binary value => 110.11(2)×2^0 = 11.011(2)×2^1

11.011(2)×2^1 = 1.1011(2)×2^2

Step 5 : Get the mantissa

Mantissa = 1011

Step 6 : Get the exponent

Add 3 to the power value => 3+2=5 and binary value of 5 is 101

Thus, 101 is the exponent

Therefore , Mantissa=1011

Exponent=101