Binary Converter | Binary, Decimal, Octal, Hex Converter

📖 How to Use This Binary Converter

Enter the number - Type or paste the number you want to convert.

Select the source base - Choose from Binary (base-2), Decimal (base-10), Octal (base-8), or Hexadecimal (base-16).

Select the target base - Choose the number system you want to convert to.

Get instant results - The converted value appears automatically as you type or change selections.

💻 Understanding Number Systems

A number system (or base) defines how many unique digits are used to represent numbers. Each position in a number represents a power of the base.

Binary (Base-2): Uses digits 0 and 1. The fundamental language of computers. Each digit is called a bit (binary digit).
Decimal (Base-10): Uses digits 0-9. The standard number system for everyday human use.
Octal (Base-8): Uses digits 0-7. Used in some computing contexts as a shorthand for binary (3 bits = 1 octal digit).
Hexadecimal (Base-16): Uses digits 0-9 and letters A-F (A=10, B=11, C=12, D=13, E=14, F=15). Widely used in programming, memory addresses, and colors (#FF0000 = red).

📊 Conversion Methods

Step 1: Convert to Decimal
Multiply each digit by (base^position) and sum.
Example: Binary 1011₂ = 1×8 + 0×4 + 1×2 + 1×1 = 11₁₀

Step 2: Convert from Decimal to Target Base
Repeatedly divide by target base, read remainders backwards.
Example: 11₁₀ to binary = 1011₂

💡 Common Conversions & Examples

Binary to Decimal: 1010₂ = 1×8 + 0×4 + 1×2 + 0×1 = 10₁₀
Decimal to Binary: 25₁₀ = 11001₂ (25 ÷ 2 = 12 r1, 12÷2=6 r0, 6÷2=3 r0, 3÷2=1 r1, 1÷2=0 r1 → read backwards: 11001)
Hexadecimal to Decimal: FF₁₆ = 15×16 + 15 = 255₁₀
Octal to Binary: 17₈ = 001 111₂ = 1111₂ (each octal digit converts to 3 binary bits)
Hexadecimal to Binary: A3₁₆ = 1010 0011₂ (each hex digit converts to 4 binary bits)

❓ Frequently Asked Questions (FAQ)

Why do computers use binary?

Computers use binary because electronic circuits have two stable states: on (1) and off (0). This makes binary the most reliable and efficient representation for digital electronics, transistors, and memory storage.

What is the difference between octal and hexadecimal?

Octal uses base-8 (digits 0-7) and each digit represents 3 bits. Hexadecimal uses base-16 (digits 0-9, A-F) and each digit represents 4 bits. Hex is more common because it aligns with 8, 16, 32, 64-bit computer architectures.

How do I convert decimal to binary quickly?

Use the "divide by 2" method: repeatedly divide the decimal number by 2, recording remainders. Read remainders from last to first. Our converter does this automatically with step-by-step logic.

What is the largest number this converter can handle?

This converter supports up to 64-bit numbers (up to 18,446,744,073,709,551,615 in decimal, or 16 hex digits). This covers all common programming and computing needs.

What are valid hexadecimal digits?

Hexadecimal digits are 0-9 and A-F (case-insensitive). A=10, B=11, C=12, D=13, E=14, F=15. Our converter accepts both uppercase and lowercase letters.

Why is hexadecimal used for colors?

Hexadecimal represents colors efficiently with 2 digits per color channel (Red, Green, Blue). #FF0000 represents maximum red, no green, no blue. Each pair (FF, 00, 00) is one byte (0-255).