Non-Restoring Division For Unsigned Integer

The non-restoring division is a division technique for unsigned binary values that simplifies the procedure by eliminating the restoring phase. The non-restoring division is simpler and more effective than restoring division since it just employs addition and subtraction operations instead of restoring division, which requires extra steps to restore the original result after a failed subtraction.

Flow Chart of Non-Restoring Division For Unsigned Integer

Steps Involved in the Non-Restoring Division Algorithm

• Step-1: First the registers are initialized with corresponding values (Q = Dividend, M = Divisor, A = 0, n = number of bits in dividend)
• Step-2: Check the sign bit of register A
• Step-3: If it is 1 shift left content of AQ and perform A = A+M, otherwise shift left AQ and perform A = A-M (means add 2's complement of M to A and store it to A)
• Step-4: Again the sign bit of register A
• Step-5: If sign bit is 1 Q[0] become 0 otherwise Q[0] become 1 (Q[0] means least significant bit of register Q)
• Step-6: Decrements value of N by 1
• Step-7: If N is not equal to zero go to Step 2 otherwise go to next step
• Step-8: If sign bit of A is 1 then perform A = A+M
• Step-9: Register Q contains quotient and A contains remainder.

Example

Let’s divide the binary number 1011 (which is 11 in decimal) by 0011 (which is 3 in decimal) using the Non-Restoring Division Algorithm.

Initialization:

• Dividend (Q) = 1011
• Divisor (M) = 0011
• Accumulator (A) = 0000
• Number of bits (n) = 4

Step-by-Step Solution

1. Initial Setup:

• Q = 1011
• M = 0011
• A = 0000
• n = 4

2. First Iteration:

• Shift Left AQ: A = 0000, Q = 1011 becomes A = 0000, Q = 0110
• Perform Operation: A = A - M = 0000 - 0011 = 1101 (2's complement of 0011)
• Sign Bit of A: 1
• Update Q[0]: 0
• Decrement N: N = 3

3. Second Iteration:

• Shift Left AQ: A = 1101, Q = 0110 becomes A = 1010, Q = 1100
• Perform Operation: A = A + M = 1010 + 0011 = 1101
• Sign Bit of A: 1
• Update Q[0]: 0
• Decrement N: N = 2

4. Third Iteration:

• Shift Left AQ: A = 1101, Q = 1100 becomes A = 1011, Q = 1000
• Perform Operation: A = A - M = 1011 - 0011 = 1000 (2's complement of 0011)
• Sign Bit of A: 1
• Update Q[0]: 0
• Decrement N: N = 1

5. Fourth Iteration:

• Shift Left AQ: A = 1000, Q = 1000 becomes A = 0001, Q = 0000
• Perform Operation: A = A + M = 0001 + 0011 = 0010
• Sign Bit of A: 0
• Update Q[0]: 1
• Decrement N: N = 0

6. Final Adjustment:

• Sign Bit of A: 0 (no additional adjustment needed)
• Final Result: Quotient (Q) = 0011 (3 in decimal)
• Remainder (A) = 0010 (2 in decimal)

Advantages

• Simplicity : The lack of a restoring phase makes the algorithm simpler than the restoring division approach.
• Fewer Operations : Because there are only two operations required—addition and subtraction—the total computing complexity is decreased.
• Speed : Because it doesn't need additional steps to restore the dividend, it executes more quickly than restoring division.

Disadvantages

• Complexity of Signed Number Handling : Signed binary numbers need extra procedures to be handled, which makes non-standard applications more complicated.
• Needs More Registers : In order to store intermediate values during calculation, more registers could be needed.

Conclusion

By skipping the restoring phase, the Non-Restoring Division Algorithm provides a more efficient method for dividing unsigned binary values. This simplification makes calculation quicker and more effective, but it also comes with significant drawbacks, especially when working with signed numbers. All things considered, it is a helpful technique in digital systems where simplicity and quickness are valued highly.