Computers count in binary, memory addresses are written in hex, Unix file permissions use octal, and humans think in decimal. Converting between them by hand is tedious and error-prone. Type a value in any base and this converter shows the equivalent in all the common ones at once.
Base 16 needs sixteen digit symbols, but we only have ten numerals. A to F stand in for the values 10 to 15, so a single hex digit maps exactly onto four binary bits.
One hex digit is exactly four bits and two hex digits are one byte, making hex a compact, lossless shorthand for binary. That is why colours, memory addresses, and hashes are written that way.
Mostly Unix file permissions. Each group of three permission bits — read, write, execute — maps neatly onto one octal digit, which is why chmod 755 is written the way it is.
It converts non-negative integers. Fractional and two’s-complement negative representations depend on word size and format, which the tool does not attempt to guess.
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