Enter a value and press Convert.
Every number base represents the same quantity, just grouping digits differently. Decimal (base 10) is what humans use daily. Binary (base 2) is what digital hardware actually stores and computes with — every bit is either 0 or 1, matching a transistor's on/off state. Hexadecimal (base 16) is a compact shorthand for binary, since each hex digit represents exactly 4 bits (a "nibble") — making it far easier for humans to read and write long binary values like memory addresses or register contents. Octal (base 8), where each digit represents exactly 3 bits, was more common in older computing systems and is still occasionally seen in Unix file permissions.
| Base | Digits used | Bits per digit | Typical use |
|---|---|---|---|
| Binary | 0-1 | 1 | What hardware actually stores/computes |
| Octal | 0-7 | 3 | Unix file permissions, legacy systems |
| Decimal | 0-9 | — | Everyday human-readable numbers |
| Hexadecimal | 0-9, A-F | 4 | Memory addresses, register values, color codes |
Multiply each bit by its place value (a power of 2, starting from 2^0 on the right) and add the results. For example, 1010 = 1×8 + 0×4 + 1×2 + 0×1 = 10.
Multiply each hex digit by its place value (a power of 16) and add the results, using A=10, B=11, C=12, D=13, E=14, F=15 for the letter digits. For example, FF = 15×16 + 15 = 255.
Hexadecimal is a compact, human-readable shorthand for binary — each hex digit represents exactly 4 bits, so an 8-bit byte becomes just 2 hex digits (e.g. 11111111 = FF) instead of 8 hard-to-read binary digits.
255 in decimal, FF in hex, 11111111 in binary, and 377 in octal — all the same value, representing all 8 bits set to 1.
Multiply each octal digit by its place value (a power of 8) and add the results. For example, 777 (octal) = 7×64 + 7×8 + 7×1 = 511.
It encodes red, green, and blue intensity as three hex byte pairs: FF (255, full red), 57 (87, some green), 22 (34, a little blue) — each pair ranges from 00 (none) to FF (255, maximum) for that color channel.
Because each of the three permission groups (owner, group, others) uses exactly 3 bits (read/write/execute), and octal digits represent exactly 3 bits each — making one octal digit per permission group a natural, compact fit.
2^n - 1 for n bits (unsigned): 1 bit gives 0-1, 4 bits give 0-15, 8 bits give 0-255, 16 bits give 0-65,535, and so on — each added bit doubles the range of representable values.
Not directly — computers most commonly use "two's complement" representation for signed (negative-capable) binary numbers, which is a specific encoding scheme beyond simple base conversion; this calculator handles unsigned (non-negative) base conversion.
Convert each hex digit individually to its 4-bit binary equivalent and concatenate them — since each hex digit maps to exactly 4 bits, there's no need to go through decimal at all (e.g. hex "A5" = binary "1010" + "0101" = "10100101").
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