Example Representations

• Find floating point for 5.125

  • 5.125 = 5 + 0.125 = 5 + 1/8 = 5 + 1*2-3
    = 1012 + .0012 = 101.001
  • Normalize: 101.0012*20 ---> 1.01001*22
  • Thus 5.125 = (-1)0*1+.0100 1000 0... * 2129
    

• In reverse, what floating point number is

  • (-1)1*(1.0111 000 0...)*2130
  • In binary scientific notation it is -1.0111*23
  • Reducing the exponent to 0 yields -1011.12
  • = -(1110 + 2-1) = -(1110 + 1/2) = -11.510

01000000101001000000000000000000

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