Number Base Converter

How Base Conversion Works

Every numeral system we use in computing is positional: the value of a digit depends on where it sits. Reading right to left, position 0 is worth b⁰ = 1, position 1 is worth b¹, position 2 is worth b², and so on, where b is the base. Multiplying each digit by its positional weight and adding the products gives the value:

value = d_n×bⁿ + … + d₂×b² + d₁×b¹ + d₀×b⁰

So hexadecimal FF expands to 15×16¹ + 15×16⁰ = 240 + 15 = 255, and binary 1101 expands to 1×8 + 1×4 + 0×2 + 1×1 = 13. Going the other way — decimal to another base — uses repeated division: divide by the base, write down the remainder, repeat with the quotient, then read the remainders bottom to top. Converting 13 to binary gives remainders 1, 0, 1, 1, which read upward as 1101.

This converter does both halves in one pass. It parses your input into an internal decimal integer, then re-renders that integer in every target base, so base 3 to base 29 is no harder than binary to hex. Digits above 9 are written as letters, which is why base 36 — ten digits plus twenty-six letters — is the practical ceiling for a single-character-per-digit alphabet.

Common Bases and Where They Show Up

Binary, octal and hexadecimal fit together neatly because 8 and 16 are powers of 2. One octal digit is exactly three bits and one hex digit is exactly four bits, so you can convert between them by grouping bits rather than doing any arithmetic: 11111111 splits into 1111 1111, which is F F. That property is the whole reason hex survives as the working notation for byte-level data — it is binary you can actually read aloud.

Two's Complement and the Signed Byte

The same bit pattern means different things depending on whether it is read as unsigned or signed. Two's complement is the near-universal way processors store negative integers: to negate a value you invert every bit and add one. In eight bits, that makes the range −128 to +127 instead of 0 to 255, and it means 11111111 is 255 when unsigned and −1 when signed. The advantage is that ordinary binary addition works unchanged for both signs, so hardware needs only one adder. The two's complement panel above shows the signed reading of whatever you enter, which is useful when a debugger prints a large unsigned number where you expected a small negative one.

Bytes, ASCII and Character Codes

Values from 0 to 127 double as ASCII character codes. The printable range runs from 32 (space) to 126 (tilde), with the uppercase letters at 65–90 and lowercase at 97–122 — exactly 32 apart, which is why flipping a single bit changes case. Codes below 32 are control characters such as tab (9) and newline (10) and have no visible glyph. The ASCII panel shows the character for any value in the printable range and reports non-printable otherwise. Beyond 127, byte values belong to a specific encoding such as UTF-8, and a single number no longer maps to a single character.

Use Cases

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