Question

Assuming single precision IEEE 754 format, what decimal number is represent by the following 32-bit binary word?

1 10000000 01100000000000000000000

Answer 1

Decimal number: -2.75

Explanation:

The first bit in 110000000 01100000000000000000000 represents sign bit (0 means positive, 1 means negative)

Next 8 bits 1 10000000 01100000000000000000000 are the exponent bits. which means the multiplier is 2.

next 23 bits 1 10000000 01100000000000000000000 (1.0+ (0.5 *0 + 0.25*1 + 0.125 *1 + 0.0625 * 0 +......)) represents the mantissa which makes it 1.375.