AUD-CMA-v1

🔢 Drag and Carry Multiplication Algorithm v1

AU in AUD-CMA-v1 stands for Ahmet Ulucay. The AU Drag and Carry Multiplication Algorithm (AUD-CMA-v1) introduces a novel method for digit-wise multiplication using structured positional padding, non-traditional base multipliers, and a unique carry rule. Its hybrid approach blends convolutional patterns with simplified mental math, making it distinct from known multiplication methods in both theory and application.

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🔢 Core Idea

Given an input number n and a multiplier b (like 222, 111, or 33), the algorithm follows these steps:

1. Multiply each digit of n by the scalar m, where b = m × 111...1 (length = k)
2. Pad the digit list with k - 1 zeros on both ends
3. Slide a window of size k over the padded array and sum each window
4. Apply Drag-and-Carry, keeping only single-digit values (except the leftmost value, which can be multi-digit)
5. Join the result to get the final answer

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📘 Example

Multiply: 547 × 222

• m = 2, k = 3
• Multiply digits: [5, 4, 7] × 2 → [10, 8, 14]
• Pad: [0, 0, 10, 8, 14, 0, 0]
• Slide window size 3 → Sums: [10, 18, 32, 22, 14]
• Apply Drag-and-Carry → [12, 1, 4, 3, 4]
• Final Result: 121434

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📂 Structure

Use Cases:

• Multiplication by numbers like 11, 111, 222...
• Mental arithmetic techniques
• Educational visualizations for elementary math
• Embedded low-power processors without complex multiplication logic