Binary Multiplication Calculator
Multiply two binary numbers and see the product in both binary and decimal. Enter each value as a string of 0s and 1s and this calculator converts them to decimal, multiplies, then converts the product back to base-2.
Formula
product = (A₂ as decimal × B₂ as decimal), converted back to base-2
- Each binary number is converted to decimal, multiplied, and the product is converted back to binary.
- Binary multiplication works like decimal long multiplication, but each partial product is either the other number (when the bit is 1) or zero (when the bit is 0).
- Inputs must contain only the digits 0 and 1. A leading '0b' prefix is accepted and ignored.
- The decimal product is shown alongside the binary result so you can verify it against ordinary arithmetic.
- Multiplying by 10₂ (decimal 2) shifts every bit one place left — the binary version of multiplying by ten in decimal.
101 × 11
Inputs
- Binary A: 101
- Binary B: 11
101₂ = 5 and 11₂ = 3. 5 × 3 = 15, which is 1111₂ in binary.
Frequently asked questions
How does binary multiplication work?
It mirrors decimal long multiplication: for each bit of the second number you either copy the first number (bit = 1) or write zeros (bit = 0), shift left by the bit position, then add the partial products.
What does multiplying by 10₂ do?
Multiplying by 10₂ (decimal 2) shifts every bit one position to the left, just as multiplying by 10 shifts decimal digits left.
Can the numbers be different lengths?
Yes. Any two valid binary strings can be multiplied; the calculator handles the conversion and shifting automatically.
Why show the decimal product?
The decimal value makes it easy to check the binary result and relate it to familiar arithmetic.
Can I enter a '0b' prefix?
Yes. A leading 0b is stripped automatically, so 0b101 and 101 are treated the same.