Binary Calculator

Convert between binary, decimal, and hexadecimal numbers.

Calculator

Enter a Number

Enter a binary number (e.g., 1010)

Select the type of conversion you want to perform

Table of Contents

1 Binary Number System
2 Conversion Methods
3 Binary - Practical Examples
Concept

Binary Number System

The binary number system is a base-2 number system that uses only two digits: 0 and 1. Each position in a binary number represents a power of 2.

Binary Digits:
0, 1
Steps

Conversion Methods

Here are the methods for converting between number systems:

  1. 1
    Binary to Decimal: Multiply each digit by its corresponding power of 2 and sum the results
  2. 2
    Decimal to Binary: Divide by 2 repeatedly and use the remainders
  3. 3
    Binary to Hexadecimal: Group binary digits into sets of 4 and convert each group
  4. 4
    Hexadecimal to Binary: Convert each hex digit to its 4-bit binary equivalent

For example, to convert 1010 from binary to decimal:

Example Calculation:
1010 = (1 × 2³) + (0 × 2²) + (1 × 2¹) + (0 × 2⁰) = 8 + 0 + 2 + 0 = 10
Examples

Binary - Practical Examples

Example 1 Computer Data

Binary is the fundamental language of computers, where each bit represents a 0 or 1.

1 byte = 8 bits = 2⁸ possible values

Example 2 Digital Images

Binary is used to represent pixel values in digital images.

Black and white image: 0 = black, 1 = white

Example 3 Boolean Logic

Binary is used to represent boolean values in programming.

false = 0, true = 1

Tools

Mathematics Calculators

Significant Figures Exponent Mean Standard Form Mean Median Mode

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