The base sets each digit’s place value
Decimal uses ten digits, 0 through 9. Binary uses 0 and 1; octal uses 0 through 7; hexadecimal uses 0 through 9 followed by A through F. In hex, A means ten and F means fifteen.
For hexadecimal FF, the left F contributes 15 × 16¹, and the right F contributes 15 × 16⁰. Together, 240 + 15 = 255 in decimal. That same value is 11111111 in binary and 377 in octal.
Exact integers, without a bit-width assumption
The tool reads each digit, multiplies the accumulated total by the input base, and adds the next digit. It then expresses that exact integer in all four bases. Short entries include the expanded place-value sum; longer entries use the same method without printing hundreds of terms.
Fractions, exponent notation, and separators are not supported. A decimal 10 and a hexadecimal 10 represent different amounts, so choose the input base before entering or pasting a value.