Binary Division by Repeated Subtraction

  • Set quotient to zero
  • Repeat while dividend is greater than or equal to divisor
    • Subtract divisor from dividend
    • Add 1 to quotient
  • End of repeat block
  • quotient is correct, dividend is remainder
  • STOP

    Binary Division by Shift and Subtract

    Basically the reverse of the mutliply by shift and add.

     

     

  • Set quotient to 0
  • Align leftmost digits in dividend and divisor
  • Repeat
    • If that portion of the dividend above the divisor is greater than or equal to the divisor
      • Then subtract divisor from that portion of the dividend and
      • Concatentate 1 to the right hand end of the quotient
      • Else concatentate 0 to the right hand end of the quotient
    • Shift the divisor one place right
  • Until dividend is less than the divisor
  • quotient is correct, dividend is remainder
  • STOP

    Binary Multiply - Repeated Shift and Add

    Repeated shift and add - starting with a result of 0, shift the second multiplicand to correspond with each 1 in the first multiplicand and add to the result. Shifting each position left is equivalent to multiplying by 2, just as in decimal representation a shift left is equivalent to multiplying by 10.

  • Set result to 0
  • Repeat
    • Shift 2nd multiplicand left until rightmost digit is lined up with leftmost 1 in first multiplicand
    • Add 2nd multiplicand in that position to result
    • Remove that 1 from 1st multiplicand
  • Until 1st multiplicand is zero
  • Result is correct
  • STOP


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