Number base converter

A number system is a set of symbols and rules for writing numbers. The most common is decimal (base 10). Binary (2), octal (8) and hexadecimal (16) are widely used in computing.

Binary uses only 0 and 1. Each position represents a power of 2 (from right: 2⁰, 2¹, 2², …). Example: 1010₂ = 0×1 + 1×2 + 0×4 + 1×8 = 10.

Hex uses digits 0–9 and letters A–F (A=10 … F=15). One byte (8 bits) = exactly two hex digits, so hex gives a compact way to write binary data. Example: 255₁₀ = FF₁₆.

To convert any base to decimal: multiply each digit by the corresponding power of the base and sum. To convert decimal to another base: divide repeatedly by the target base and collect remainders.

Octal (base 8) uses digits 0–7. Each octal digit equals exactly 3 binary bits. Example: 377₈ = 011 111 111₂ = 255₁₀.

Divide the decimal number by 2 and record remainders. Read remainders from last to first. Example: 13 → 1101₂.

A byte is 8 bits (binary digits) and stores values 0–255 (00000000₂ to 11111111₂), equivalent to two hex digits (00₁₆ to FF₁₆).

#RRGGBB encodes red, green and blue components as pairs of hex digits (00–FF, i.e. 0–255 decimal). Example: #FF0000 = pure red.

Electronic components (transistors) have two stable states: on (1) and off (0). Binary representation is noise-resistant and supports logical and arithmetic operations with simple circuits.

In memory addresses (hex), bitmasks and flags (bin/hex), colour coding (hex), network protocols (MAC and IP addresses in hex), microcontroller programming and binary data debugging.