Multiplying two unsigned binary numbers is similar to multiplying decimal numbers, but it's simpler because you only deal with 0s and 1s. Here’s a breakdown of the process:
Steps for Binary Multiplication
- Write the numbers: Align the multiplicand and multiplier properly, one above the other. This is Step 1 from the provided reference.
- Multiply by each digit of the multiplier: For each digit (bit) in the multiplier, multiply it by the entire multiplicand.
- If the multiplier bit is 1, the result is the multiplicand itself. This is derived from Step 2 in the reference, where the least significant bit (LSB) is multiplied.
- If the multiplier bit is 0, the result is all zeros.
- Shift the partial products: After multiplying by each digit of the multiplier, shift each partial product to the left by the appropriate number of places. The rightmost partial product is not shifted. The next partial product is shifted one position to the left, the third partial product two positions to the left, and so on. This aligns the partial products based on the place value of the multiplier bit.
- Add the partial products: Add all the shifted partial products together. Use the rules of binary addition (0+0=0, 0+1=1, 1+0=1, 1+1=10 – carry the 1).
Example
Let's multiply (11101)2 by (1001)2, which are used in the provided references.
| Step | Action | Result |
|---|---|---|
| 1 | Write down the multiplicand and multiplier | |
| Multiplicand: | 11101 | |
| Multiplier: | 1001 | |
| 2 | Multiply by the LSB of the Multiplier (1): | 11101 |
| 3 | Multiply by the next bit (0): | 00000 |
| 4 | Multiply by the next bit (0): | 00000 |
| 5 | Multiply by the MSB (1): | 11101 |
| 6 | Shift and Add: | |
| 11101 | ||
| 00000 | ||
| 00000 | ||
| 11101 | ||
| Sum: | 11110101 |
Therefore, (11101)2 * (1001)2 = (11110101)2.
Key Considerations
- Understanding Place Values: Remember that in binary, each position represents a power of 2 (from right to left: 20, 21, 22, etc.).
- Binary Addition: Familiarize yourself with the rules of binary addition, especially the carry-over.
- Practice: The best way to master binary multiplication is through practice.
