Binary Calculator

First Number:
Second Number:

Table of Contents

Introduction

Binary numbers form the foundation of digital computing and electronic systems. Our Binary Calculator is designed to help you perform calculations and conversions between different number systems efficiently. Whether you're a student learning computer science, a programmer, or an electronics enthusiast, this tool simplifies binary arithmetic and logical operations.

What is a Binary Calculator?

A Binary Calculator is a specialized tool that performs arithmetic and logical operations on binary numbers (base-2) and facilitates conversions between different number systems. It helps users:

  • Convert between binary, decimal, hexadecimal, and octal number systems
  • Perform basic arithmetic operations (+, -, ×, ÷)
  • Execute bitwise operations (AND, OR, XOR, NOT)
  • Understand the step-by-step process of binary calculations

Number Systems

Binary (Base-2)

Binary is a base-2 number system that uses only two digits: 0 and 1. Each position represents a power of 2, making it fundamental to computer systems.

Example: 1010₂ = (1×2³) + (0×2²) + (1×2¹) + (0×2⁰) = 8 + 0 + 2 + 0 = 10₁₀

Decimal (Base-10)

The decimal system is our standard number system using digits 0-9. Each position represents a power of 10.

Example: 42₁₀ = (4×10¹) + (2×10⁰) = 40 + 2 = 42

Hexadecimal (Base-16)

Hexadecimal uses 16 digits (0-9 and A-F) to represent numbers. It's commonly used in programming as a more concise way to represent binary values.

Example: 2A₁₆ = (2×16¹) + (10×16⁰) = 32 + 10 = 42₁₀

Octal (Base-8)

Octal is a base-8 number system using digits 0-7. It's useful in computing for representing groups of 3 binary digits.

Example: 52₈ = (5×8¹) + (2×8⁰) = 40 + 2 = 42₁₀

Operations

Operation Description Example
Addition (+) Adds two numbers in binary 1010₂ + 1011₂ = 10101₂
Subtraction (-) Subtracts second number from first 1010₂ - 0011₂ = 0111₂
Multiplication (×) Multiplies two binary numbers 1010₂ × 0011₂ = 11110₂
Division (÷) Divides first number by second 1010₂ ÷ 0010₂ = 0101₂
AND Bitwise AND operation 1010₂ AND 1100₂ = 1000₂
OR Bitwise OR operation 1010₂ OR 1100₂ = 1110₂
XOR Bitwise XOR operation 1010₂ XOR 1100₂ = 0110₂
NOT Bitwise NOT operation NOT 1010₂ = 0101₂

How to Use

  1. Enter Numbers: Input your numbers in any supported format (binary, decimal, hexadecimal, or octal)
  2. Select Number System: Choose the input number system for each number
  3. Choose Operation: Select the desired operation from the dropdown menu
  4. Calculate: Click the "Calculate" button to see results
  5. View Results: Results will be shown in all number systems with step-by-step explanation

Examples

Binary Addition

1010₂ + 1011₂ = 10101₂
(10₁₀ + 11₁₀ = 21₁₀)

Binary to Decimal Conversion

1010₂ = 1×2³ + 0×2² + 1×2¹ + 0×2⁰
= 8 + 0 + 2 + 0 = 10₁₀

Bitwise Operations

1010₂ AND 1100₂ = 1000₂
1010₂ OR 1100₂ = 1110₂
1010₂ XOR 1100₂ = 0110₂