Convert between number systems
Binary (base-2) uses 0 and 1, fundamental to computers. Octal (base-8) uses 0-7. Decimal (base-10) uses 0-9, standard for humans. Hexadecimal (base-16) uses 0-9 and A-F, common for colors and memory addresses.
Computers use binary because electronic circuits have two states: on (1) and off (0). This simplicity makes circuits reliable, fast, and less prone to errors. All data—text, images, videos—is ultimately stored and processed as binary digits (bits).
Divide the decimal number by 2, record the remainder. Repeat with the quotient until it reaches 0. Read remainders bottom-to-top for binary. Example: 13 ÷ 2 = 6 R1, 6 ÷ 2 = 3 R0, 3 ÷ 2 = 1 R1, 1 ÷ 2 = 0 R1. So 13 = 1101 in binary.
Hexadecimal represents binary data compactly—each hex digit equals 4 binary bits. It's used for: colors (#FF0000 = red), memory addresses, MAC addresses, Unicode characters, and debugging. Programmers prefer it because it's more readable than binary.
Each hex digit converts to exactly 4 binary digits. Memorize: 0=0000, 1=0001, ..., 9=1001, A=1010, B=1011, C=1100, D=1101, E=1110, F=1111. Example: 2F hex = 0010 1111 binary. Group binary by 4 for the reverse.
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