Binary Division Calculator
Divide binary numbers using long division with step-by-step solutions
Calculate Binary Division
Maximum positive value: 255
Division Results
Binary Division Rules
Step 1
Start from the leftmost bit of dividend
Step 2
If current bits ≥ divisor, subtract and write 1
Step 3
If current bits < divisor, write 0
Step 4
Bring down next bit and repeat
Quick Examples
Simple Division
12 ÷ 3 = 4 remainder 0 in decimal
With Remainder
13 ÷ 5 = 2 remainder 3 in decimal
Power of 2 Division
Division by 2¹ (10)
Right shift by 1 bit
1100 → 110
Division by 2² (100)
Right shift by 2 bits
1100 → 11
Division by 2³ (1000)
Right shift by 3 bits
1100 → 1
Signed Numbers
Two's Complement
For signed binary numbers, the leftmost bit represents the sign (0 = positive, 1 = negative).
Negative Division
Division with negative numbers follows the same rules as decimal: negative ÷ positive = negative.
Understanding Binary Division
What is Binary Division?
Binary division is the process of dividing numbers in the binary (base-2) number system. It follows the same principles as long division in decimal, but uses only binary digits (0 and 1) and binary arithmetic operations.
Long Division Algorithm
The algorithm examines each bit of the dividend from left to right. For each bit, it determines whether the current partial dividend can be divided by the divisor. If yes, it places a 1 in the quotient and subtracts; if no, it places a 0.
Division Steps
- •Start with the leftmost bit of the dividend
- •Compare current bits with the divisor
- •If ≥ divisor: subtract divisor, write 1 in quotient
- •If < divisor: write 0 in quotient, bring down next bit
- •Repeat until all bits are processed
Real-World Applications
Computer Processors
CPUs use binary division in arithmetic logic units (ALUs) for integer and floating-point calculations in programs and applications.
Digital Signal Processing
Binary division is essential in DSP applications for scaling, filtering, and mathematical transformations of digital signals.
Memory Management
Operating systems use binary division for memory allocation, address calculation, and resource distribution algorithms.
Optimization Techniques
When dividing by powers of 2, computers use bit shifting instead of division for faster performance, as shifting is much more efficient than division.