Binary Multiplication Calculator
Multiply two binary numbers instantly with BinaryCon’s Binary Multiplication Calculator. Enter values containing only 0 and 1 to get the exact binary product, decimal verification, partial products, and a clear multiplication layout.
What Is Binary Multiplication?
Binary multiplication is the process of multiplying numbers written in base 2. It follows the same general idea as long multiplication in decimal, but binary uses only the digits 0 and 1.
Because there are only two possible multiplier bits, each partial product is especially simple: multiplying by 0 gives 0, while multiplying by 1 reproduces the original binary value.
Binary Multiplication Table
| First Bit | Second Bit | Product |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
How to Multiply Binary Numbers
1. Align the numbers
Write the multiplicand above the multiplier, aligned on the right.
2. Start with the rightmost multiplier bit
Multiply the entire first binary number by that bit.
3. Create the partial product
A multiplier bit of 1 copies the multiplicand; a multiplier bit of 0 produces zero.
4. Shift each next row
Move each successive partial product one binary place to the left.
5. Add the partial products
Use ordinary binary addition to combine all non-zero shifted rows.
6. Read the product
The final binary sum is the multiplication result.
Example: 1011 × 101
Binary 1011 equals decimal 11, while 101 equals decimal 5.
Why Are Partial Products Shifted?
Each position in a binary number represents a power of 2. Moving one position to the left therefore multiplies the value by 2.
During long binary multiplication, the multiplier’s second bit corresponds to 2¹, the third bit corresponds to 2², and so on. The partial products must therefore be shifted by the corresponding number of positions.
Multiplying Binary by 0
Any binary number multiplied by zero equals zero.
Multiplying Binary by 1
Multiplying a binary value by 1 leaves the value unchanged.
Multiplying by Powers of Two
Multiplying an unsigned binary integer by a power of two can be performed by appending zeros to the right.
| Operation | Binary Result | Effect |
|---|---|---|
101 × 10 |
1010 |
Multiply by 2 |
101 × 100 |
10100 |
Multiply by 4 |
101 × 1000 |
101000 |
Multiply by 8 |
Binary Multiplication vs Decimal Multiplication
| Feature | Binary | Decimal |
|---|---|---|
| Base | 2 | 10 |
| Digits | 0 and 1 | 0 through 9 |
| Single-digit products | Only 0 or 1 | 0 through 81 |
| Place shift | Multiply by 2 | Multiply by 10 |
Binary Multiplication Using Shift and Add
Binary multiplication can be understood as a sequence of shifts and additions. For every 1 bit in the multiplier, a shifted copy of the multiplicand contributes to the final product.
101 has 1 bits in positions 0 and 2:
1011
+
1011 shifted left 2 positions
= 1011 + 101100
= 110111
Binary Multiplication in Digital Computers
Processors can implement multiplication using combinations of shifting, addition, registers, control logic, and specialized multiplier circuits. The exact architecture varies between processors and hardware designs.
The underlying binary arithmetic still follows the same positional principle demonstrated by this calculator.
Can Large Binary Numbers Be Multiplied?
Yes. The core calculation on this page works directly with binary strings. It does not first convert the complete operands to ordinary JavaScript numbers.
The multiplier is processed bit by bit, shifted partial values are produced, and those values are combined using string-based binary addition.
Binary Multiplication Examples
| First Number | Second Number | Binary Product |
|---|---|---|
0 |
101 |
0 |
1 |
101 |
101 |
10 |
10 |
100 |
101 |
11 |
1111 |
111 |
11 |
10101 |
1011 |
101 |
110111 |
101010 |
101 |
11010010 |
Common Binary Multiplication Mistakes
Forgetting the shift
Each successive partial product must move one additional binary place left.
Using decimal multiplication rules
A binary digit can only be 0 or 1, so each single-bit partial product is simple.
Adding partial products incorrectly
The shifted rows must be combined using binary addition rather than decimal addition.
Using invalid digits
Valid binary operands contain only 0 and 1.
Related BinaryCon Tools
Binary Multiplication Calculator FAQs
How do you multiply binary numbers?
What is 1 × 1 in binary?
1 × 1 = 1.
What is 10 × 10 in binary?
10₂ × 10₂ = 100₂. This is decimal 2 × 2 = 4.
What is 101 × 11 in binary?
101₂ × 11₂ = 1111₂, equivalent to decimal 5 × 3 = 15.
What is 1011 × 101 in binary?
110111₂, equivalent to decimal 55.
Why do binary partial products shift left?
What happens when a binary number is multiplied by zero?
0.
What happens when a binary number is multiplied by one?
How do you multiply binary by 2?
101 × 10 = 1010.