Number Base Converter

Convert Between Number Systems Instantly

Computers think in binary. Humans think in decimal. Developers and engineers often need to bridge this gap, working with binary, octal, decimal, and hexadecimal representations of the same value. Our free number base converter makes these translations effortless, showing you the equivalent value in all four bases simultaneously.

Understanding Number Bases

Binary (Base 2)

Binary uses only two digits: 0 and 1. It is the fundamental language of all digital computers, where each bit represents an on or off state. Binary is essential for understanding low-level operations, bitwise logic, subnet masks, and hardware registers.

Octal (Base 8)

Octal uses digits 0-7. Each octal digit maps to exactly three binary digits, making it a compact way to represent binary values. Octal is commonly used in Unix file permissions (e.g., chmod 755) and some legacy computing contexts.

Decimal (Base 10)

Decimal is the standard human numbering system using digits 0-9. It is what we use in everyday life for counting, arithmetic, and most non-technical contexts. All other bases are typically converted to decimal for human readability.

Hexadecimal (Base 16)

Hexadecimal uses digits 0-9 and letters A-F. Each hex digit maps to exactly four binary digits, making it extremely efficient for representing binary data. Hex is ubiquitous in programming for memory addresses, color codes, MAC addresses, and byte values.

Common Conversion Reference

Decimal	Binary	Octal	Hex
0	0000	0	0
8	1000	10	8
10	1010	12	A
15	1111	17	F
16	10000	20	10
255	11111111	377	FF

Where You Encounter These Bases

Web development: CSS colors use hexadecimal (e.g., #FF5733). Understanding hex lets you read and modify color values directly.

Networking: IP addresses, subnet masks, and MAC addresses are often displayed or manipulated in binary and hexadecimal notation.

Unix/Linux: File permissions use octal notation. Knowing that 755 means rwxr-xr-x requires understanding octal-to-binary conversion.

Debugging: Memory dumps, register values, and byte-level data are typically shown in hexadecimal. Converting to decimal or binary can help identify patterns and diagnose issues.

Computer science education: Understanding number bases is a fundamental concept in CS curricula, from digital logic courses to data structures and algorithms.