Binary multiplication is simpler than decimal: each partial product is either a copy of the first number or zero. Hardware multipliers add shifted copies in exactly this way.
How to use the Binary Multiplication Calculator
- Binary factor 1
- Binary factor 2
- Representation
Everything is calculated in your browser, so results appear instantly and nothing you type is sent to a server.
How it works
Enter two binary numbers. One partial product row is written for each bit of the second number, shifted left by its position, and the rows are added.
Formula
0 × 0 = 0, 0 × 1 = 0, 1 × 1 = 1; product = sum of shifted copies of A for each 1-bit of B
Worked example
Inputs — Binary factor 1: 1011; Binary factor 2: 101; Representation: Automatic (fit the numbers).
Results — Product (binary) = 11 0111; Product (decimal) = 55; Factor 1 in decimal = 11; Factor 2 in decimal = 5; Partial products = 1011
0000·
1011··
────────
110111.
Key terms
- Partial product
- One row of a long multiplication.
Frequently asked questions
What is 1011 × 101?
110111 (11 × 5 = 55).
How many bits does a product need?
Up to the sum of the bit lengths of the factors.
Why is binary multiplication easy?
Each digit is 0 or 1, so every partial product is 0 or a shifted copy.
How do I multiply by 2 in binary?
Append a 0 (shift left).