Learn and practice Restoring & Non-Restoring Division algorithms with step-by-step visualization
Understanding the fundamental concepts of binary division algorithms
Binary division is the process of dividing two binary numbers to find the quotient and remainder. Unlike decimal division, binary division uses only 0s and 1s, making it fundamental to computer arithmetic and digital logic design.
In restoring division, we subtract the divisor from the partial remainder. If the result is negative, we restore the original value by adding the divisor back. This method is straightforward but requires an extra addition step.
Non-restoring division eliminates the restoration step. If the partial remainder is negative, we continue with the negative value and add the divisor in the next iteration. This method is more efficient but slightly more complex.
Both algorithms follow similar steps: initialize registers, perform subtraction/addition based on remainder sign, shift operations, and repeat until all bits are processed. The key difference is in handling negative remainders.
Where:
• Dividend (Q): The number being divided
• Divisor (M): The number dividing the dividend
• Quotient: The result of division
• Remainder: The leftover value after division
Steps:
1. Initialize A = 0, Q = dividend, M = divisor
2. For each bit: Subtract M from A
3. If result ≥ 0: Set quotient bit to 1
4. If result < 0: Set quotient bit to 0 and restore A
5. Shift A and Q left
Steps:
1. Initialize A = 0, Q = dividend, M = divisor
2. For each bit: Check sign of A
3. If A ≥ 0: Subtract M, set quotient bit to 1
4. If A < 0: Add M, set quotient bit to 0
5. Shift A and Q left
Flowchart showing the step-by-step process of Restoring Division algorithm with proper initialization, shift operations, subtraction/restoration logic, and counter management
Flowchart showing the step-by-step process of Non-Restoring Division algorithm with proper initialization, shift operations, addition/subtraction logic based on A's sign, and counter management
| Aspect | Restoring Division | Non-Restoring Division |
|---|---|---|
| Complexity | Simple to understand | More complex logic |
| Speed | Slower (extra addition) | Faster (no restoration) |
| Hardware | More hardware needed | Less hardware needed |
| Error Handling | Easy to debug | Harder to debug |
| Applications | Educational purposes | High-performance systems |
| Step | Operation | A (Accumulator) | Q (Dividend) | M (Divisor) | Quotient | Action | Explanation |
|---|
Simple Division
Medium Division
Large Division
Power of 2 Division