Binary Multiplication Calculator
Educational tool for multiplying binary numbers. Visualizes the bit-shift and add steps involved in CPU arithmetic. Supports large integers.
About
Binary multiplication is the cornerstone of arithmetic logic units (ALUs) in modern processors. Unlike decimal multiplication, which requires memorizing a 9x9 table, binary multiplication only involves 0s and 1s, making it a process of "shift and add." If the multiplier bit is 1, the multiplicand is copied and shifted; if 0, a row of zeros is recorded.
This tool is designed for computer science students and engineers to visualize this process. It supports arbitrary precision (BigInt), meaning you can multiply 64-bit or 128-bit integers without the rounding errors typical of standard floating-point calculators. It displays the step-by-step intermediate sums, mirroring the actual logic gates within a digital multiplier.
Formulas
The operation follows the distributive property using powers of 2:
A × B = n∑i=0 (A × bi × 2i)
Where bi is the i-th bit of the multiplier. Practically, for every bit in B that is 1, we left-shift A by the bit's position and add to the accumulator.
Reference Data
| Decimal | Binary | Hexadecimal | Power of 2 |
|---|---|---|---|
| 1 | 0001 | 0x1 | 20 |
| 2 | 0010 | 0x2 | 21 |
| 4 | 0100 | 0x4 | 22 |
| 8 | 1000 | 0x8 | 23 |
| 16 | 10000 | 0x10 | 24 |
| 255 | 11111111 | 0xFF | 28-1 |
| 65535 | 1111...1111 (16) | 0xFFFF | 216-1 |