Binary Multiplication Calculator
Type two binary numbers and the product appears instantly as you type — no Calculate button; the result updates on every keystroke, in every base. The shift-and-add method is explained below.
Multiply Binary Numbers
Full binary calculator (all operations) → · Binary addition calculator →
How to multiply binary numbers
- Write the two numbers, one above the other, right-aligned.
- Go through the bottom number bit by bit, right to left. Where the bit is 1, write down a copy of the top number. Where it is 0, skip the row — multiplying by 0 contributes nothing.
- Shift each row left by its bit position. The row for the second bit starts one place further left, the third bit two places, and so on. Shifting left is what "times 2, times 4…" looks like in binary.
- Add all the rows with ordinary binary addition. The total is the product.
Binary multiplication rules
| Column | Result |
|---|---|
| 0 × 0 | 0 |
| 0 × 1 | 0 |
| 1 × 0 | 0 |
| 1 × 1 | 1 |
That is the whole times table. Everything beyond it is shifting and adding.
Worked example: 101₂ × 11₂ = 1111₂
| Step | Multiplier bit | Partial product |
|---|---|---|
| 1 | 1 (rightmost) | 101 |
| 2 | 1 (next bit, shifted one place left) | 1010 |
| Add | — | 101 + 1010 = 1111 |
Check in decimal: 101₂ is 5 and 11₂ is 3; 5 × 3 = 15, and 1111₂ is 15.
Common mistake: forgetting the shift
The most common binary multiplication error is adding the partial products without shifting them. If you added 101 + 101 for 101 × 11 you would get 1010 (10) instead of 1111 (15) — the second row must start one place further left, because that bit means "times 2". A quick decimal check (5 × 3 = 15) catches it immediately; the calculator above shows the decimal value next to every result for exactly that reason.
Frequently asked questions
How do I multiply binary numbers?
The same long multiplication you learned in decimal, but simpler: each digit of the second number is 0 or 1, so every partial product is either nothing or a copy of the first number, shifted left. Write one partial product per 1 bit, shift each by its bit position, then add them all with binary addition. The calculator above multiplies live as you type.
What is 101 × 11 in binary?
101 × 11 = 1111 in binary. Partial products: 101 × 1 = 101, and 101 × 1 shifted one place = 1010. Adding: 101 + 1010 = 1111. In decimal: 5 × 3 = 15, and 1111 is 15.
What are the binary multiplication rules?
For single bits there are only two rules that matter: 0 × anything = 0, and 1 × 1 = 1. Everything else in binary multiplication is shifting and adding — there is no times table to memorize beyond that.
Why does shifting left multiply by 2?
Each position in binary is worth twice the one before it, so moving every bit one place left doubles the value — exactly like appending a 0 in decimal multiplies by 10. 101 (5) shifted left is 1010 (10).
How do I multiply binary numbers in Python?
Use int(a, 2) * int(b, 2), then bin(result)[2:]. Example: bin(int("101", 2) * int("11", 2))[2:] gives "1111".