Number Base Converter

Hexadecimal (base-16) uses digits 0–9 and letters A–F. Each hex digit maps to exactly 4 binary bits (a nibble), making it a compact way to represent binary data. For example, 0xFF = 11111111 in binary = 255 in decimal. Programmers use hex for memory addresses, color codes, byte values, and bitwise operations because it is far more readable than long binary strings while maintaining a direct relationship with the underlying binary system.

Each octal digit corresponds to exactly 3 binary bits. To convert octal to binary, replace each digit with its 3-bit binary equivalent: 0=000, 1=001, 2=010, 3=011, 4=100, 5=101, 6=110, 7=111. For example, octal 357 = 011 101 111 in binary. To go from binary to octal, group binary digits into sets of 3 from the right and convert each group to its octal equivalent.

The most common bases are: Binary (base-2) — the fundamental language of computers, using 0s and 1s. Octal (base-8) — used in Unix file permissions and some legacy systems. Decimal (base-10) — the standard human numeral system. Hexadecimal (base-16) — widely used for memory addresses, color codes, and representing byte values compactly. Some systems also use base-36 (digits + entire alphabet) for compact ID encoding.

Unsigned binary numbers represent only non-negative values — an 8-bit unsigned number ranges from 0 to 255. Signed binary uses the most significant bit (MSB) as a sign indicator. In two's complement (the most common signed representation), an 8-bit signed number ranges from −128 to 127. The binary value 11111111 is 255 when unsigned, but −1 in signed two's complement. Understanding this distinction is crucial for low-level programming and bitwise operations in languages like C and Rust.