Question

If the IEEE Standard 754 representation of a floating point number is given as 01101110110011010100000000000000, determine the binary value represented by this 32-bit number

Answer 1

1. Identify the elements that make up the binary representation of the number:

First bit (the leftmost) indicates the sign,
1 = negative, 0 = positive.

The next 8 bits contain the exponent:
1101 1101

The last 23 bits contain the mantissa:
100 1101 0100 0000 0000 0000

2. Convert the exponent from binary (base 2) to decimal (base 10):

The exponent is allways a positive integer.

1101 1101₍₂₎ =

1 × 2⁷ + 1 × 2⁶ + 0 × 2⁵ + 1 × 2⁴ + 1 × 2³ + 1 × 2² + 0 × 2¹ + 1 × 2⁰ =

128 + 64 + 0 + 16 + 8 + 4 + 0 + 1 = 221₍₁₀₎

3. Adjust the exponent:

Exponent adjusted = 221 - 127 = 94

4. put all the values into expression

(sign) (1 . Mantissa) × 2^{(Exponent adjusted)} =

(0) (1 . 100 1101 0100 0000 0000 0000) × 2⁹⁴

011001101010000000000000000000000000000000000000000000000000000000000000000000000000000000000000

if you have any doubt, feel free to ask in the comments.