Binary Multiplication Calculator
Multiply binary numbers with step-by-step long multiplication method and detailed explanations
Binary Multiplication Calculator
Number of bits for the result representation
Only 0s and 1s allowed
Only 0s and 1s allowed
Example: 1011 × 101
Binary Multiplication Rules
Binary Multiplication Steps
Set Multiplier
Choose the longer number as multiplier
Multiply Each Digit
Multiply by each digit of multiplicand
Position Products
Shift intermediate products by position
Sum Products
Add all intermediate products
Quick Reference
Binary Powers of 2
Tips & Tricks
Multiplying by powers of 2 = left bit shift
Binary multiplication is simpler than decimal
Order doesn't matter (commutative property)
Check your work with decimal conversion
Understanding Binary Multiplication
Binary Number System
Binary (base-2) numbers use only digits 0 and 1, representing the two states in digital electronics: OFF and ON. Each position represents a power of 2, making binary multiplication fundamental to computer operations.
Multiplication Rules
- •0 × 0 = 0 (Nothing times nothing equals nothing)
- •0 × 1 = 0 (Zero times anything equals zero)
- •1 × 0 = 0 (Same as above, commutative)
- •1 × 1 = 1 (One times one equals one)
Long Multiplication Method
Algorithm Steps
- 1. Set the longer number as the multiplier
- 2. Multiply multiplier by each digit of multiplicand
- 3. Position each product according to digit position
- 4. Add all intermediate products using binary addition
- 5. The sum is your final product
Bit Shifting Optimization
For powers of 2, binary multiplication can be optimized using bit shifting. Multiplying by 2 = shift left by 1 bit, by 4 = shift left by 2 bits, etc. This is why binary multiplication is so efficient in computers.
Applications in Computing
Computer Science: Binary multiplication is fundamental to processor arithmetic units, graphics processing, cryptography, and digital signal processing. Understanding binary operations helps in optimizing algorithms and understanding how computers perform calculations at the hardware level.