Last Updated on March 2, 2026 | 1 : 41 pm by Anas Brittany
Use this binary multiplication calculator to multiply two binary (base-2) numbers. Enter two binary values and the calculator will return the product in binary and decimal. You can also display steps to learn how binary multiplication works using shifts and addition.
Binary Multiplication Calculator
What Is Binary Multiplication?
Binary multiplication is multiplying numbers written in base-2 (using only 0 and 1). It follows the same idea as regular multiplication, but because binary digits are only 0 or 1, each step becomes simpler.
When multiplying in binary, each “1” digit in the multiplier creates a shifted copy of the other number, and then all shifted copies are added together.
Binary Multiplication Rules
Binary multiplication uses these basic digit rules:
- 0 × 0 = 0
- 0 × 1 = 0
- 1 × 0 = 0
- 1 × 1 = 1
So the only time you produce a 1 is when both digits are 1.
Shift-and-Add Method
A practical way to understand binary multiplication is:
- Start with the rightmost bit of the second number (the multiplier).
- If the bit is 1, write down the first number shifted left by that bit position.
- If the bit is 0, skip that position.
- Add all partial products together.
This method is the foundation of how multiplication works in digital circuits and low-level computing.
Example: Binary Multiplication
Multiply:
A = 1011
B = 110
B has 1 bits in positions 1 and 2 (counting from 0 at the right):
- A << 1 = 10110
- A << 2 = 101100
Add them:
10110
+101100
=1000010
So 1011 × 110 = 1000010 (binary).
Frequently Asked Questions
Why does shifting left multiply by 2?
In binary, each shift left moves all bits to the next place value, which doubles the number. Two shifts left multiply by 4, three shifts left multiply by 8, and so on.
Can binary multiplication result in a longer number?
Yes. Just like decimal multiplication, the product can have more digits than either input.
What if my binary number is very long?
This calculator supports long binary inputs because it computes the result using big-integer math.
Brittany Anas is a freelance lifestyle journalist and editorial writer with experience covering culture, food, lifestyle, entertainment, and evergreen guides for digital publications. Her writing focuses on clear research, approachable storytelling, and practical ideas designed for everyday readers.
On Fiestasline, Brittany contributes editorial content across lifestyle, ideas, food & drink, culture, and curated guides, helping readers discover inspiration that’s timely, accessible, and easy to enjoy.
