Restoring Division Algorithm for Unsigned Integers: A Step-by-Step Explanation

Learn about the restoring division algorithm, a method for performing division on unsigned integers. This guide provides a step-by-step explanation of the algorithm, detailing the process of repeatedly subtracting the divisor from the dividend to obtain the quotient and remainder.

Restoring Division Algorithm for Unsigned Integers

Understanding Restoring Division

Restoring division is a method for performing division on unsigned integers. It's a relatively simple algorithm that produces a quotient and a remainder. The algorithm works by repeatedly subtracting the divisor from the dividend and keeping track of the result.

The Restoring Division Algorithm

Let's assume:

  • N: Number of bits in the dividend
  • M: Divisor (loaded into register M)
  • Q: Dividend (loaded into register Q)
  • A: Remainder (initialized to 0)

The algorithm proceeds as follows:

  1. Initialization: Initialize the registers A (remainder) to 0, load the divisor into register M, and load the dividend into register Q.
  2. Shift Left: Shift the combined contents of registers A and Q one bit to the left.
  3. Subtract: Subtract the contents of register M from register A.
  4. Check MSB: Examine the most significant bit (MSB) of register A.
    • If MSB is 0: Set the least significant bit (LSB) of Q to 1.
    • If MSB is 1: Set the LSB of Q to 0 and restore the previous value of A (add M back to A).
  5. Decrement Counter: Decrement the counter N.
  6. Repeat: Repeat steps 2-5 until N = 0.
  7. Result: The quotient is in register Q, and the remainder is in register A.

Example: Restoring Division

(The example from the original text performing restoring division of 11 by 3, showing the step-by-step register values and operations, should be included here. The table from the original text should be recreated here in HTML.)

Conclusion

The restoring division algorithm is a straightforward method for performing integer division. While not the most efficient approach, its simplicity makes it easy to understand and implement.