Base Converter

How base conversion works

A "base" is how many unique digits a numbering system uses before it carries over to a new place value. Base 10 (decimal) uses digits 0-9; base 2 (binary) uses only 0 and 1; base 16 (hexadecimal) uses 0-9 then A-F for 10-15. Any positive integer can be written in any base from 2 to 36 (36 being the point where the alphabet A-Z is used up as extra digit symbols). This tool always routes a conversion through decimal internally: it reads your input in the "from" base, computes the equivalent decimal value, then re-expresses that decimal value in the "to" base.

Worked example: binary to hexadecimal

Enter 1011 with "From base" set to Binary (2) and "To base" set to Hexadecimal (16). Step one expands the binary digits by place value: 1×2³ + 0×2² + 1×2¹ + 1×2⁰ = 8 + 0 + 2 + 1 = 11 in decimal. Step two converts 11 to base 16 by repeated division: 11 ÷ 16 = 0 remainder 11, and 11 in hex notation is B. Reading the single remainder gives the final answer: 1011₂ = B₁₆.

Custom bases and validation

Choosing "Custom" on either side unlocks a numeric field for any base from 2 to 36. Before converting, the tool checks every character in your input against the valid digit set for the selected "from" base — for base 8 that's 0-7, for base 20 that's 0-9 and A-J — and reports the specific invalid character rather than failing silently. If both bases are set to the same value, it tells you no conversion is needed instead of returning your input unchanged with no explanation.

Typical uses

Binary and hexadecimal show up constantly in programming (memory addresses, color codes, bitmasks); octal appears in Unix file permissions; bases outside the usual four are mostly useful for coursework on positional numeral systems or for encoding schemes like base36 short URLs.