Question

Given the following pair of decimal numbers:
A = 2.6125 x 101 and B = 4.150390625 x 10-1

1. a) Compute the binary representation of both A and B using the IEEE-754 single precision floating- point format.

2. b) Compute A+B in binary using the IEEE-754 single precision floating-point format.

Answer 1

A = 2.6125 x 10^1 = 26.125

B = 4.150390625 x 10^-1 = 0.4150390625

a) Compute the binary representation of both A and B using the IEEE-754 single precision floating- point format.

A = 26.125 = 11010.001

=> 1.1010001 x 2^4

biased exponent - 127+4 = 131 = 10000011

Normalised mantisa = 1010001

The IEEE 754 Single precision

0 01010001 10000011000000000000000

B = 0.4150390625 = 0.0110101001

=> 1.10101001 x 2^-2

biased exponent - 127-2 = 125 = 1111101

Normalised mantisa = 10101001

The IEEE 754 Single precision

0 10101001 11111010000000000000000

b) Compute A+B in binary using the IEEE-754 single precision floating-point format.

A+B = 26.5400390625 = 11010.1000101001

=> 1.10101000101001 x 2^4

biased exponent - 127+4 = 131 = 10000011

Normalised mantisa = 1010001

The IEEE 754 Single precision

0 10101000 10000011000000000000000