Master the efficient way to multiply signed binary numbers with our interactive calculator
Booth's algorithm is a multiplication algorithm for signed binary numbers that reduces the number of additions required by recoding the multiplier. It's particularly efficient for numbers with consecutive 1s or 0s.
The algorithm examines pairs of bits in the multiplier and performs operations based on the pattern: 00 (no operation), 01 (add), 10 (subtract), 11 (no operation).
For numbers with consecutive 1s, Booth's algorithm can reduce multiple additions to just one addition and one subtraction, making it much faster than traditional multiplication.
Set accumulator (A) to 0, load multiplier (Q), and set Q₋₁ to 0
Look at Q₀ and Q₋₁ to determine the operation
Add, subtract, or do nothing based on bit pattern
Arithmetic right shift of A and Q
Continue until all bits are processed
| Q₀ | Q₋₁ | Action | Explanation |
|---|---|---|---|
| 0 | 0 | No operation | String of 0s - just shift |
| 0 | 1 | Add M to A | End of 1s string - add multiplicand |
| 1 | 0 | Subtract M from A | Start of 1s string - subtract multiplicand |
| 1 | 1 | No operation | Middle of 1s string - just shift |
Flowchart showing the step-by-step process of Booth's multiplication algorithm with proper initialization, decision logic, and arithmetic operations
Enter two decimal numbers and see Booth's algorithm in action
| Step | Q₀ | Q₋₁ | Action | A (Accumulator) | Q (Multiplier) | Q₋₁ | Explanation |
|---|
Positive × Positive
Positive × Negative
Negative × Positive
Negative × Negative