Binary Division Calculator

Divide binary numbers using long division with step-by-step solutions

Calculate Binary Division

Maximum positive value: 255

Division Results

Enter valid binary numbers to see the division result
Enter dividend • Enter divisor •

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

1100 ÷ 11 = ?
= 100 (quotient)
= 0 (remainder)

12 ÷ 3 = 4 remainder 0 in decimal

With Remainder

1101 ÷ 101 = ?
= 10 (quotient)
= 11 (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.