From floating-point binary

Assume 10 bits for the mantissa and 6 bits for the exponent. The number is in normalised form.

Convert floating-point binary to denary:

Enter decimal number (e.g. -12.5)

To convert floating-point binary to denary, use the formula: mantissa × 2exponent

Steps:

  1. Check if mantissa starts with 0 (positive) or 1 (negative in two's complement)
  2. Convert mantissa to decimal (treat as 0.1xxxxx...)
  3. Convert exponent to decimal (may be in two's complement)
  4. Calculate: mantissa × 2exponent

Example: Mantissa 0110100000, Exponent 000011

Mantissa: 0.1101 = 0.8125
Exponent: 3
Result: 0.8125 × 2³ = 6.5

In floating-point binary representation, numbers are stored using a mantissa and exponent:

  • Mantissa (10 bits): Represents the significant digits in normalised form (0.1xxxxx...)
  • Exponent (6 bits): Represents the power of 2 to multiply the mantissa by

To convert from floating-point binary to denary:

  1. Check if the mantissa is in two's complement (negative number)
  2. Convert the mantissa to decimal (treating it as 0.1xxxxx...)
  3. Convert the exponent to decimal (may be in two's complement if negative)
  4. Calculate: mantissa × 2^exponent
  5. Apply the sign if the original number was negative

References:

  • Wikibooks Computer Science A level (floating-point): AQA OCR
  • Wikibooks Computer Science A level (normalisation): AQA

Further reading: