Math
Binary Multiplication Calculator
Enter two binary numbers and the calculator multiplies them with the shift-and-add method.
Each bit of the multiplier produces one partial product (the top number shifted left, or all zeros), and the rows are added to give the product, which is checked in decimal.
Digits 0 and 1 only. A leading minus sign is allowed; spaces or underscores can group bits (1011 0110).
Digits 0 and 1 only.
Try an example
Result
Binary result
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- Decimal check
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- Hexadecimal
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- Octal
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Student quick launch
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Study path
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Follow these when you want the formula behind the answer, a short lesson, or nearby tools in the same topic.
What the binary multiplication calculator solves
Binary multiplication is simpler than decimal multiplication because every digit of the multiplier is 0 or 1. Each partial product is either zero or a shifted copy of the multiplicand, so the whole method is copy, shift, add. This page lists every partial product and sums them so you can follow the work.
Binary multiplication rules
| Bits | Product |
|---|---|
| 0 × 0 | 0 |
| 0 × 1 or 1 × 0 | 0 |
| 1 × 1 | 1 |
How to use it
- Enter the multiplicand (top number) and the multiplier (bottom number).
- Read the grid: each partial row is labeled with the multiplier bit and how many places it was shifted (« n).
- Add the partial rows with binary addition rules to get the product.
- Confirm using the decimal check.
How to read the answer
The product can have as many bits as the two inputs combined. For example, a 4-bit number times a 3-bit number needs up to 7 bits. If you are working in fixed-width hardware, bits beyond that width would be lost (overflow). The hex and octal equivalents help when reading the product as a memory address or color.
Common mistakes and edge cases
- Forgetting to shift: the partial product for the second multiplier bit must move one place left, the third two places, and so on.
- Adding the partial products in decimal by accident; use binary addition with carries.
- Multiplying by 0 gives 0 no matter how long the other number is.
- Multiplying by 10 (binary) is a single left shift, by 100 a double shift.
- One negative factor makes the product negative; two negatives make it positive.
Worked examples
Typical product
1011 × 101
Binary result
110111
Multiply by a power of two
1101 × 100
Binary result
110100
Multiply by zero
10110 × 0
Binary result
0
Negative factor
−101 × 11
Binary result
-1111
Both negative
−101 × −11
Binary result
1111
Invalid digit
12 × 1
Binary result
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Frequently asked questions
How do you multiply binary numbers?+
For each bit of the multiplier from right to left, write the multiplicand shifted left by that bit's position if the bit is 1, or a row of zeros if it is 0. Then add all the rows using binary addition.
Why is binary multiplication just shifting and adding?+
Because each multiplier digit is 0 or 1, every partial product is either nothing or a copy of the top number. Shifting left by one place doubles the value, which is what each higher bit position means.
How many bits can the product have?+
Up to the total number of bits in both inputs. An m-bit number times an n-bit number fits in m + n bits.
What is 1011 × 101 in binary?+
110111, which is 11 × 5 = 55 in decimal. The partial products are 1011, 0000 shifted one place, and 1011 shifted two places.
Does the calculator handle negative binary numbers?+
Yes. Put a minus sign in front of a number. The multiplication is done on magnitudes and the sign rule (different signs give a negative product) is applied at the end.
About this calculator
- Written by
- mathcheck editorial team
- Last reviewed
- September 4, 2026
Method
- Uses the values entered by the user and stable formulas documented on the page.
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Last updated: September 4, 2026