IEEE 754 floating-point standard

• Leading “1” bit of significand is implicit

• Exponent is “biased” to make sorting easier

  • all 0s is smallest exponent all 1s is largest
  • bias of 127 for single precision and 1023 for double precision
  • summary: (–1)sign ?????significand) ???2exponent – bias 

• Example:

  • decimal: -.75 = -3/4 = -3/22
  • binary: -.11 = -1.1 x 2-1
  • floating point: exponent = 126 = 01111110
  • IEEE single precision: 10111111010000000000000000000000

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