Computers process everything in binary (0s and 1s). Understanding number systems and how text is encoded as numbers is essential for computer science and programming.
Decimal (base 10): everyday numbers. Binary (base 2): computer language (0,1). Octal (base 8): groups of 3 binary digits. Hexadecimal (base 16): groups of 4 binary digits, uses A-F for 10-15. Decimal→Binary: repeatedly divide by 2, read remainders bottom-up. 13 → 1101. Binary→Decimal: positional values. 1101 = 1×8 + 1×4 + 0×2 + 1×1 = 13. Binary→Hex: group 4 bits. 10110011 → B3. Shortcut: Decimal→Octal via divide by 8; Decimal→Hex via divide by 16.
Binary addition: 0+0=0, 0+1=1, 1+0=1, 1+1=10 (carry 1). Example: 1011 + 1101 = 11000. Binary subtraction: using 2's complement. Character encoding: ASCII — 7-bit, 128 characters (A=65, a=97, 0=48). Extended ASCII: 8-bit, 256 chars. Unicode: supports ALL world scripts (Hindi, Chinese, Arabic, emojis). UTF-8: variable-length encoding — 1 byte for ASCII, 2-4 bytes for other characters. Computers store everything — text, images, audio — as binary numbers.
Computers use electronic switches (transistors) that have two states: ON (1) and OFF (0). Binary perfectly maps to this physical reality. Using more states (like 10 for decimal) would require distinguishing between many voltage levels, making circuits more complex, slower, and error-prone. Binary is simple, reliable, and fast. Two clear states are easy to distinguish even with electrical noise. All complex data (images, video, AI) ultimately reduces to billions of 0s and 1s.
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