Show the IEEE 754 binary representation for the floatingpoin

Show the IEEE 754 binary representation for the floating-point number 20.5 (ten) in single and double precision in detailed way.

Solution

20.0 = 10100 x 2⁰, 0.5 = 0.1 x 2⁰ together 1.01001 x 2⁴

Single Precision:

The exponent is 127+4 = 131 = 128 + 3 = 10000011

The entire number is

0 1000 0011 0100 1000 0000 0000 0000 000

Double Precision:

The exponent is 1023+4 =1027=1024 + 3 =10000000011

The entire number is:

0 1000 0000 011 0100 1000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000