Integer Base Converter

Free online tool. All processing is client-side. No signup needed.

How to Use the Integer Base Converter

1. Enter your input values above
2. Results update automatically
3. Copy or download the output

What is a Integer Base Converter?

An Integer Base Converter transforms numbers between binary (base-2), octal (base-8), decimal (base-10), hexadecimal (base-16), and any custom base up to base-36. Number base conversion is fundamental to computer science: binary is how computers process data, hexadecimal is how humans compactly represent bytes (two hex digits = one byte), and octal is used in Unix file permissions. This converter handles large integers and explains each conversion step.

How Does It Work?

Enter a number, select the source base, and choose the target base. The converter first translates the input to decimal (value = Σ digit × base^position), then from decimal to the target base (repeated division: remainder = digit, quotient continues). Custom bases beyond 16 use letters (G-Z) after F. Step-by-step breakdown is shown so you can learn the conversion method. Common presets for binary↔hex↔decimal speed up frequent conversions.

Formula

From any base to decimal: Value = Σ(digit_i × base^i)\nExample: 2A (hex) = 2×16¹ + 10×16⁰ = 42\n\nFrom decimal to base B: repeated division by B, reading remainders bottom-up\n\nCommon conversions: Binary↔Hex (group 4 bits), Binary↔Octal (group 3 bits)\nProgrammer interest: hex FF = 255 dec = 11111111 binary (1 byte max)

Who Uses This Tool?

• Programmers converting between hex color codes and RGB decimals
• Computer science students learning number systems and conversion algorithms
• Embedded developers working with binary and hex memory addresses
• Linux users converting octal file permissions to human-readable format
• Cryptography enthusiasts working with different number bases for encoding

Pro Tips

• Hex to binary is trivially easy: each hex digit = exactly 4 binary digits. F=1111, A=1010. No calculation needed — just concatenate the nibbles
• For negative numbers, computers use two's complement representation. Our converter handles both signed and unsigned modes
• Base64 is NOT a true base — it's an encoding scheme with a specific alphabet and padding. Use our Base64 Encoder for that purpose
• The highest practical base with standard characters is base-36 (0-9 + A-Z). Beyond that, you need additional symbol sets

Frequently Asked Questions about Integer Base Converter

Why do programmers use hexadecimal instead of decimal?

Hexadecimal maps directly to binary: 1 hex digit = 4 bits = 1 nybble. Two hex digits = 8 bits = 1 byte. This makes reading memory addresses, color codes, and binary data much simpler than decimal would.

What's the highest base this converter supports?

Base-36 (0-9 + A-Z). Beyond base-36, you'd need more symbols than the Latin alphabet provides. For arbitrary precision with very large numbers, use our Big Number mode.

Free online Integer Base Converter — no signup, 100% client-side processing. All data stays in your browser.