Convert numbers between binary, decimal, hexadecimal, octal and any base.
Number base conversion transforms a number from one numeral system to another. Our number system converter supports decimal (base 10), binary (base 2), octal (base 8), and hexadecimal (base 16) — the four most important number systems in computing and digital electronics.
Decimal (Base 10): Digits 0-9. The number system humans use naturally. Binary (Base 2): Digits 0-1. The language of computers — all data is ultimately stored as binary. Octal (Base 8): Digits 0-7. Used historically in computing; still used in Unix/Linux file permissions (chmod 755). Hexadecimal (Base 16): Digits 0-9 and A-F. Used extensively in programming, color codes, memory addresses, and debugging.
To convert decimal to binary: repeatedly divide by 2 and record the remainders bottom to top. Example: 25 in binary: 25÷2=12R1, 12÷2=6R0, 6÷2=3R0, 3÷2=1R1, 1÷2=0R1. Reading remainders bottom to top: 25 = 11001 in binary. Verify: 16+8+0+0+1 = 25. ✓
Hex is everywhere in web development. CSS colors: #FF5733 (R=FF=255, G=57=87, B=33=51). Memory addresses: 0x1A3F. Unicode characters: U+0041 is 'A'. ASCII values: 0x41 = 65 = 'A'. Hexadecimal compactly represents binary data — each hex digit represents exactly 4 binary bits (a "nibble"), making it much shorter than binary for human reading.
All computer data — text, images, videos, programs — is ultimately stored as binary (sequences of 0s and 1s). 1 bit = one binary digit (0 or 1). 8 bits = 1 byte = can represent 256 values (0-255). A typical photo is millions of bytes. Understanding binary is fundamental for computer science, programming, networking (IP addresses, subnet masks), and digital electronics design.
Number base conversion changes a number from one numeral system to another, such as from decimal (base 10) to binary (base 2) or hexadecimal (base 16).
Binary is the base-2 number system using only digits 0 and 1. It is the fundamental language of computers and digital systems.
Hexadecimal is the base-16 number system using digits 0-9 and letters A-F. It is widely used in programming, color codes, and memory addresses.
Computers use binary because electronic circuits have two states: on (1) and off (0). This makes binary the most natural system for digital hardware.
