Number Base Converter: Frequently Asked Questions

With N digits: Binary (base 2) = 2^N - 1. Octal (base 8) = 8^N - 1. Decimal (base 10) = 10^N - 1. Hexadecimal (base 16) = 16^N - 1. For example, with 8 digits: binary max = 255, hex max = 4,294,967,295 (32 bits).

Binary numbers get very long quickly — the decimal number 255 is 11111111 in binary (8 digits). In hex it is just FF (2 digits). Hex is more compact while still having a direct relationship to binary (1 hex digit = 4 binary bits), making it easier to read and write.

0x is a prefix used in C, C++, JavaScript, Python, and many other languages to indicate a hexadecimal literal. 0x1F means the hex number 1F (decimal 31). Similarly, 0b prefix indicates binary in Python and JavaScript (0b1010 = decimal 10).

Negative numbers in computer systems use two's complement representation. To negate a number in binary: invert all bits, then add 1. This makes binary arithmetic circuits simpler. The converter shows unsigned binary representations.

Primarily for Unix file permissions (chmod), where 3-bit groups map naturally to octal digits. Also used in some network protocols and embedded systems. It appears in C source code (octal literals start with 0, so 010 = decimal 8, which is a common source of bugs).