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What Is Number Base Conversion?
Number base conversion is the process of transforming a number from one positional numeral system to another. The most common systems are decimal (base 10), binary (base 2), octal (base 8), and hexadecimal (base 16). Each system represents the same values using different sets of digits.
Understanding number bases is fundamental to computer science. Computers operate in binary (0s and 1s), while programmers often use hexadecimal for compact representation of binary data. Octal was historically important in Unix file permissions and early computing.
How Base Conversion Works
CheckTown's number base converter lets you convert between any bases from 2 to 36 instantly.
- Binary (base 2) — the foundation of all digital computing, using only 0 and 1
- Hexadecimal (base 16) — uses digits 0-9 and letters A-F, commonly used for colors, memory addresses, and byte representations
- Custom bases — convert between any base from 2 to 36, including less common bases like base 3 (ternary) or base 12 (duodecimal)
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Convert Numbers →When To Use Number Base Conversion
Base conversion is essential in programming, networking, and digital systems.
- Web development — convert hex color codes to RGB values, understand CSS color notation
- Low-level programming — read memory addresses, debug binary data, understand bitwise operations
- Networking — convert IP addresses between decimal and binary, understand subnet masks and CIDR notation
Frequently Asked Questions
Why do computers use binary?
Computers use binary because digital circuits have two stable states: on (1) and off (0). This maps perfectly to binary. All data — text, images, programs — is ultimately stored and processed as sequences of binary digits (bits).
Why is hexadecimal used in programming?
Hexadecimal is popular because each hex digit represents exactly 4 binary digits (bits). This makes it a compact way to write binary values: a byte (8 bits) is just 2 hex digits. Colors like #FF6600 are actually three hex byte values for red (FF=255), green (66=102), and blue (00=0).
How do you convert decimal to binary manually?
Divide the decimal number by 2 repeatedly, recording the remainder each time. Read the remainders from bottom to top to get the binary representation. For example, 13 in binary: 13÷2=6r1, 6÷2=3r0, 3÷2=1r1, 1÷2=0r1. Reading remainders bottom-up: 1101.