Question

Write down the binary representation of the decimal number 126.5assuming the IEEE 754 double precision format. (Show your steps)

Answer 1

Answer 2

IEEE 754 Double Precision Representation of 126.5

1. Convert 126.5 to Binary

• 126 → 1111110

• 0.5 → .1

• Combined: 1111110.1

2. Normalize

• Scientific notation: 1.1111101 × 2⁶

3. Encode Components

• Sign bit (positive): 0

• Exponent (bias=1023): 6 + 1023 = 1029 → 10000000101 (11 bits)

• Mantissa (drop leading 1): 1111101000... (52 bits, padded with zeros)

• 
  

Final 64-bit Binary:

0   10000000101   1111101000000000000000000000000000000000000000000000

Hex: 405FD00000000000