Number Systems Explained: Binary, Hex, Octal & Decimal
Understanding binary, octal, decimal, and hexadecimal number systems and their uses in computing.
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Number Base Converter
Encode & DecodeConvert between binary, hex, octal, and decimal
Binary
0b11111111
Octal
0o377
Decimal
255
Input baseHexadecimal
0xFF
Quick Reference
Binary (2)
0, 1
Octal (8)
0-7
Decimal (10)
0-9
Hex (16)
0-9, A-F
Learn More About Number Base Converter
2 articles to help you understand and use this tool effectively
Number Base Converter FAQ
Common questions about using the Number Base Converter tool
Enter a decimal number, select 'Decimal' as input base. The binary equivalent appears instantly. Manual method: repeatedly divide by 2, read remainders bottom-up. Example: 13 → 1101 (13÷2=6r1, 6÷2=3r0, 3÷2=1r1, 1÷2=0r1).
Enter binary digits (0s and 1s), select 'Binary' as input base. Manual method: multiply each digit by its position power of 2, sum results. Example: 1101 = 1×8 + 1×4 + 0×2 + 1×1 = 13.
Hexadecimal (hex) is base-16 using digits 0-9 and A-F (10-15). Compact representation of binary (4 bits = 1 hex digit). Common in: colors (#FF0000), memory addresses, MAC addresses, programming. Example: 255 = FF, 16 = 10.
Enter hex value (e.g., FF), select 'Hexadecimal' as input. Manual: multiply each digit by power of 16. Example: 2F = 2×16 + 15×1 = 47. Hex digits: A=10, B=11, C=12, D=13, E=14, F=15.
Octal is base-8 using digits 0-7. Historically used in computing (3 bits = 1 octal digit). Still seen in Unix file permissions: chmod 755 means rwxr-xr-x. Less common today than hex.
Hex is compact (2 hex digits = 1 byte) and aligns with binary (4 bits = 1 hex digit). Easy to read memory dumps, colors, and byte values. Converting hex↔binary is simpler than decimal↔binary.
Group binary into 4-bit chunks (right to left), convert each to hex. Example: 11111111 → 1111 1111 → F F → FF. Reverse for hex to binary: F → 1111. This direct conversion is why hex is popular in computing.
0x indicates hexadecimal in programming (0xFF = 255). Other prefixes: 0b for binary (0b1111 = 15), 0o for octal (0o17 = 15). Without prefix, numbers are assumed decimal. These prefixes prevent ambiguity.
Computers use two's complement for negative binary numbers. The tool handles standard conversions. For signed interpretation: MSB (most significant bit) indicates sign. -1 in 8-bit is 11111111 (255 unsigned).
Binary (base-2): computer's native language. Octal (base-8): Unix permissions. Decimal (base-10): human-readable. Hexadecimal (base-16): colors, memory, bytes. Base-64: encoding binary as text.