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.
The decimal system (base 10) that most people use daily is just one of many ways to represent numbers, built around the fact that humans have 10 fingers. Computers use binary (base 2) at the hardware level because electronic circuits most naturally represent two states — on and off, or 1 and 0. Programmers frequently work with hexadecimal (base 16) as a more human-readable shorthand for binary, since each hex digit represents exactly 4 binary digits, making it far more compact than writing out long strings of 1s and 0s.
Octal (base 8) shows up in older computing contexts and certain file permission systems (like Unix file permissions, which are often expressed as three octal digits). Understanding how to convert between these bases is a foundational skill in computer science, digital electronics, and low-level programming, where numbers frequently need to move between human-readable decimal and machine-oriented binary or hexadecimal representations.
Converting from any base to decimal involves multiplying each digit by the base raised to its positional power and summing the results — for example, hexadecimal 2F converts to decimal by calculating (2 × 16) + (15 × 16^0) = 47, where F represents 15 in hexadecimal. Converting from decimal to another base works in reverse, using repeated division by the target base and reading the remainders in reverse order, a process that becomes tedious and error-prone by hand for larger numbers, which is exactly where a dedicated converter becomes useful.
A frequent error when converting to hexadecimal is forgetting that digits beyond 9 are represented by letters A through F, and mixing up which letter corresponds to which value (A=10 through F=15) is a common source of manual conversion mistakes. Another common error in binary conversion is losing track of place value when a number has many digits, since each additional binary digit doubles the place value rather than increasing it by a fixed amount as in decimal.
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.
