Question

Hi, I need help with this question.

What will be the smallest positive normalized number and the largest positive denormalized number that can be represented using the IEEE 754 single-precision floating-point binary format? Write both the IEEE 754 binary representations and the true binary values for both numbers.

Answer 1

Smallest normalized number

Sign: *

Actual Exponent: −126

Exp (biased): 1

Exponent field: 0000 0001

Fraction field: 000 0000 0000 0000 0000 0000

Value: ±2−126 ≈ ±1.18×10−38

Largest denormalized number

Sign: *

Actual Exponent: −126

Exp (biased): 0

Exponent field: 0000 0000

Fraction field: 111 1111 1111 1111 1111 1111

Value: ±(1−2−23) × 2−126 ≈ ±1.18×10−38