IEEE 754 Floating-Point Rep

Convention to represent floating point numbers

Contains:

• sign
  • 0 for positive, 1 for negative
• exponent
  • If exponent is 2, need to do the following for (32-bit):
    • 2 + 127 = 129
    • Store 129 (as binary) in excess-127
• mantissa
  • is normalised, with an implicit leading bit 1
  • e.g. $110.12$ becomes $1.1012\ast 2^2$
  • In the above example, only 1012 is stored in the mantissa field (since 1 is implicit!)

Two Formats

• Single Precision (32 bits)
  • 1-bit sign
  • 8-bit exponent (excess-127)
  • 23-bit mantissa
• Double Precision (64 bits)
  • 1-bit sign
  • 11-bit exponent (excess 1023)
  • 52-bit mantissa

After getting the 32/64-bit representation, we may convert to hexadecimal to improve readability.