Number Base Converter
Convert Between Number Bases
About Number Base Converter
Number Base Systems
A number base (or radix) determines how many digits are used to represent numbers. Decimal (base 10) uses digits 0-9 and is our everyday system. Binary (base 2) uses 0 and 1, fundamental to computing. Octal (base 8) uses 0-7. Hexadecimal (base 16) uses 0-9 and A-F, widely used in programming for colors, memory addresses, and byte representation. Understanding bases is essential for computer science, digital electronics, and programming.
Common Conversions
Decimal to Binary: Repeatedly divide by 2, read remainders bottom-up. 13 = 1101 in binary. Binary to Decimal: Multiply each digit by its position power of 2. 1101 = 8+4+0+1 = 13. Hex to Binary: Replace each hex digit with its 4-bit binary equivalent. FF = 1111 1111. Each hexadecimal digit represents exactly 4 binary bits, making conversion between them straightforward.
How to Use This Converter
Enter a number, select its current base, and choose the target base. The converter instantly shows the result. It supports bases 2 through 36, with all common bases (2, 8, 10, 16) as quick-select options. Results show grouped digits for readability (e.g., binary in groups of 4).
Frequently Asked Questions
Why do computers use binary?
Electronic circuits have two stable states (on/off, high/low voltage). Binary maps perfectly to this: 1 = on, 0 = off. This makes hardware design reliable and simple.
Why is hexadecimal popular in programming?
One hex digit represents exactly 4 binary bits. A byte (8 bits) is exactly 2 hex digits. This makes hex a compact, human-readable representation of binary data. Colors like #FF0000 represent RGB bytes.
What bases higher than 16 are used?
Base 36 uses 0-9 and A-Z (all alphanumeric characters). Base 64 is used for encoding binary data as text (emails, URLs). Base 60 is used in time (60 seconds/minutes).
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