✖️ Binary Multiplication Calculator
Multiply two binary numbers with step-by-step solution
How to Use This Calculator
Enter Binary Numbers
Input two binary numbers you want to multiply. The calculator accepts only 0s and 1s. Examples: 1010, 1100, 1111. You can enter numbers of different lengths.
Click Calculate Multiplication
Press the "Calculate Multiplication" button to perform binary multiplication. The calculator uses the long multiplication method, generating partial products and adding them together.
Review Results
The result shows the binary product, decimal equivalent, and a detailed step-by-step breakdown showing how partial products were generated and added together.
Formula
Binary Multiplication: Long multiplication with partial products
Product = Sum of (multiplicand × bit × 2^position) for each bit in multiplier
How it works:
Binary multiplication works similarly to decimal long multiplication. For each bit in the multiplier, if it's 1, you add a shifted copy of the multiplicand (shifted by the bit position). Then add all partial products together.
Binary Multiplication Rules:
- 0 × 0 = 0
- 0 × 1 = 0
- 1 × 0 = 0
- 1 × 1 = 1
- Multiplying by 2^n means shifting left by n positions
Example 1: 1010 × 1100 (10 × 12 = 120)
1010
× 1100
-----
0000 (1010 × 0, position 0)
0000 (1010 × 0, position 1)
1010 (1010 × 1, position 2)
1010 (1010 × 1, position 3)
-----
1111000
Result: 1111000 (binary) = 120 (decimal)
Example 2: 1111 × 101 (15 × 5 = 75)
1111
× 101
-----
1111 (1111 × 1, position 0)
0000 (1111 × 0, position 1)
1111 (1111 × 1, position 2)
-----
1001011
Result: 1001011 (binary) = 75 (decimal)
Frequently Asked Questions
How does binary multiplication work?
Binary multiplication uses the same long multiplication algorithm as decimal multiplication. For each bit in the multiplier, if it's 1, you add a shifted copy of the multiplicand. The shift amount corresponds to the bit position. Then all partial products are added together.
Why is binary multiplication simpler than decimal multiplication?
In binary, you only multiply by 0 or 1, so each partial product is either 0 or a shifted copy of the multiplicand. There are no multiplication tables to remember - just shift and add operations. This makes binary multiplication very efficient for computers.
Can I multiply binary numbers of different lengths?
Yes! The calculator handles binary numbers of any length. The multiplication process works the same way regardless of length differences between the two numbers.
What is a partial product in binary multiplication?
A partial product is the result of multiplying the multiplicand by a single bit of the multiplier. For each bit position in the multiplier, if the bit is 1, the partial product is the multiplicand shifted left by that position. All partial products are then added to get the final result.
Why is binary multiplication important in computer science?
All arithmetic operations in computers use binary. Processors have dedicated multiplication circuits that use binary multiplication algorithms. Understanding binary multiplication helps in algorithm optimization, understanding computer arithmetic, and designing efficient hardware.
How does binary multiplication relate to bit shifting?
Multiplying a binary number by 2^n is equivalent to shifting it left by n positions. This is why binary multiplication often involves shifting operations. For example, 1010 × 1000 (8 in decimal) = 1010000, which is 1010 shifted left by 3 positions.