Binary Calculator

Convert and calculate with binary numbers. Perform bitwise operations and understand digital logic.

Binary Calculator

Convert between binary, decimal, hexadecimal, and octal number systems with arithmetic operations

Number System Converter

Enter a whole number (0-999999)

💡 Number System Reference

Binary (Base 2): Uses digits 0, 1
Octal (Base 8): Uses digits 0-7
Decimal (Base 10): Uses digits 0-9
Hexadecimal (Base 16): Uses 0-9, A-F

Decimal

42

Base 10

Binary

101010

Base 2

Octal

52

Base 8

Hexadecimal

2A

Base 16

Binary Details

8-bit:00101010
16-bit:0000000000101010
Formatted:1010 10

Common Conversions

Dec
Bin
Oct
Hex
0
0
0
0
1
1
1
1
2
10
2
2
3
11
3
3
4
100
4
4
5
101
5
5
6
110
6
6
7
111
7
7
8
1000
10
8
9
1001
11
9
10
1010
12
A
15
1111
17
F

1Mastering Binary Calculations

Convert between binary, decimal, hexadecimal, and octal number systems. Whether you're a student, educator, or professional, understanding the mathematical principles behind binary will enhance your problem-solving abilities. This guide breaks down complex concepts into understandable components and provides practical applications for real-world scenarios.

Mathematical Foundations

The underlying mathematics involves fundamental principles that have wide-ranging applications. Understanding these concepts helps you: • Verify calculator results manually • Apply knowledge to related problems • Develop mathematical intuition • Solve more complex variations • Teach others effectively

Step-by-Step Problem Solving

Approach problems systematically: 1. Identify what you're solving for 2. Gather all necessary information 3. Choose the appropriate formula 4. Perform calculations carefully 5. Verify results make sense 6. Consider alternative methods


2Real-World Applications

Mathematical concepts aren't just theoretical - they have practical applications in many fields.

Professional Applications

Professionals in various fields use these calculations: • Engineers for design and analysis • Scientists for research and experiments • Financial analysts for modeling • Architects for planning and construction • Data scientists for analysis and predictions

Educational Value

For students and educators: • Builds foundational math skills • Develops logical thinking • Prepares for advanced topics • Provides exam preparation • Enables peer tutoring and collaboration

This comprehensive guide is regularly updated to ensure accuracy. Last reviewed: 7/25/2025

Frequently Asked Questions

What is binary?

Binary is base-2 numbering using only 0 and 1. It's the fundamental language of computers where each digit (bit) represents an on/off state.

How do I convert decimal to binary?

Repeatedly divide by 2 and track remainders. Read remainders from bottom to top. Example: 13 = 1101 in binary.

What are bitwise operations?

Operations that work on individual bits: AND (&), OR (|), XOR (^), NOT (~), and bit shifts (<<, >>). Essential for low-level programming.