Binary Calculator

Perform binary arithmetic operations, bitwise calculations, and number conversions with real-time results and step-by-step explanations.

Binary Decimal
1 bit

Example Calculations

Click any example to try it instantly

Arithmetic Operations

Binary Addition
1010 + 1100
→ 10110
Binary Subtraction
1111 - 1010
→ 101
Binary Multiplication
101 × 11
→ 1111
Binary Division
1100 ÷ 11
→ 100

Bitwise Operations

Bitwise AND
1010 AND 1100
→ 1000
Bitwise OR
1010 OR 1100
→ 1110
Bitwise XOR
1010 XOR 1100
→ 110
Bitwise NOT
NOT 1010
→ 0101

Number Conversions

Decimal to Binary
255₁₀
→ 11111111₂
Binary to Decimal
11010110₂
→ 214₁₀
Power of 2
1024₁₀
→ 10000000000₂
8-bit Maximum
11111111₂
→ 255₁₀

Quick Reference

Arithmetic Operations

  • Addition (+): Add two binary numbers
  • Subtraction (−): Subtract second from first
  • Multiplication (×): Multiply binary numbers
  • Division (÷): Divide first by second

Bitwise Operations

  • AND: 1 if both bits are 1
  • OR: 1 if either bit is 1
  • XOR: 1 if bits are different
  • NOT: Inverts all bits

Shift Operations

  • Left Shift (<<): Multiply by 2
  • Right Shift (>>): Divide by 2
  • Complement (~): One's complement
  • Negate (±): Two's complement

Keyboard Shortcuts

  • 0, 1: Input binary digits
  • +, -, *, /: Arithmetic operations
  • Enter or =: Calculate result
  • Escape or C: Clear calculator
  • Backspace: Delete last digit

About Our Binary Calculator

The Binary Calculator is a comprehensive tool for performing binary arithmetic operations, bitwise calculations, and number conversions. Whether you're a computer science student, programmer, or digital electronics engineer, our calculator provides accurate binary calculations with real-time results and step-by-step explanations.

Key Features

  • Arithmetic Operations: Addition, subtraction, multiplication, and division of binary numbers
  • Bitwise Operations: AND, OR, XOR, NOT, left shift, and right shift operations
  • Number Conversion: Convert between binary and decimal number systems
  • Real-time Display: See both binary and decimal representations simultaneously
  • Step-by-step Explanations: Understand how calculations are performed
  • Input Validation: Only accepts valid binary digits (0 and 1)
  • Copy Functionality: One-click copying of results to clipboard
  • Mobile-Friendly: Responsive design that works perfectly on all devices
  • Multiple Modes: Switch between arithmetic, bitwise, and converter modes

How to Use the Binary Calculator

  1. Choose your calculation mode: Arithmetic, Bitwise, or Converter
  2. Enter binary numbers using the 0 and 1 buttons or input fields
  3. Select the operation you want to perform
  4. Press equals (=) to see the result
  5. View both binary and decimal representations of the result
  6. Use the step-by-step explanation to understand the calculation
  7. Copy results using the copy button
  8. Try the example calculations for common operations

Understanding Binary Arithmetic

  • Binary Addition: Similar to decimal addition but with carry-over at 2
  • Binary Subtraction: Uses borrowing when subtracting larger digits
  • Binary Multiplication: Shift and add method for efficient calculation
  • Binary Division: Long division method adapted for binary numbers

Understanding Binary Number System

Binary is the fundamental number system used in computer science and digital electronics. It uses only two digits (0 and 1) and forms the basis of all digital computations.

Binary Arithmetic Operations

Our Binary Calculator supports all basic arithmetic operations:

  • Binary Addition: Add binary numbers with automatic carry handling
  • Binary Subtraction: Subtract binary numbers with borrow operations
  • Binary Multiplication: Multiply binary numbers using shift-and-add method
  • Binary Division: Divide binary numbers with remainder calculation

Bitwise Operations

Bitwise operations work on individual bits and are essential in programming:

  • AND Operation: Returns 1 only when both bits are 1
  • OR Operation: Returns 1 when at least one bit is 1
  • XOR Operation: Returns 1 when bits are different
  • NOT Operation: Inverts all bits (0 becomes 1, 1 becomes 0)
  • Left Shift: Moves bits left, effectively multiplying by 2
  • Right Shift: Moves bits right, effectively dividing by 2

Common Use Cases

  • Computer Science Education: Learn binary arithmetic and bitwise operations
  • Programming: Debug bit manipulation and understand binary data
  • Digital Electronics: Design and analyze digital circuits
  • Network Engineering: Work with IP addresses and subnet calculations
  • Embedded Systems: Program microcontrollers and IoT devices
  • Cybersecurity: Analyze binary data and understand encryption

Binary Calculator Tips

  1. Start Simple: Begin with small binary numbers to understand operations
  2. Use Examples: Try the provided examples to see how operations work
  3. Check Decimal: Use the decimal display to verify your understanding
  4. Practice Regularly: Regular use improves binary arithmetic skills
  5. Understand Patterns: Notice how binary operations relate to decimal math

Whether you're learning computer science, developing software, or working with digital systems, our Binary Calculator provides the accuracy and functionality you need for reliable binary calculations and conversions.