Question

Consider the following 32 bit binary representation of the value using IEEE 754 single precision floating point representation. Show the corresponding signed number in decimal.

01000001001010100000000000000000

Answer 1

10.625

Step-by-step explanation:

The given binary single precision floating point number in IEEE 754 format is:

01000001001010100000000000000000

Dividing it into respective components:

Here sign bit (1 bit): 0

Exponent ( 8 bit) : 10000010

Mantissa (23 bit) : 01010100000000000000000

The exponent corresponds to 1 (if we add 127 to the given binary value)

The mantissa corresponds to 1.0625 ( on appending 1)

So the overall number is 1.0625 * 10 ^1 = 10.625