Ch 2 covers number systems (binary, octal, decimal, hexadecimal), inter-conversion techniques, binary arithmetic, signed number representation, and character encoding schemes (ASCII, ISCII, Unicode).
Binary: digits 0,1 (base 2). Octal: 0-7 (base 8). Hex: 0-9, A-F (base 16). Decimal→Binary: repeated division by 2. Binary→Decimal: positional values (place × 2ⁿ). Binary↔Octal: group 3 bits. Binary↔Hex: group 4 bits. Fractional conversion: multiply fractional part by base repeatedly. Signed numbers: sign-magnitude (MSB = sign), 1's complement (flip bits), 2's complement (flip + add 1, most used). Range with n bits: -2ⁿ⁻¹ to 2ⁿ⁻¹ - 1 (2's complement).
ASCII: 7-bit, 128 characters (A=65, a=97, 0=48). Extended ASCII: 8-bit, 256 chars — includes some European characters. ISCII: Indian Standard Code, 8-bit, supports Indian scripts (Devanagari, Tamil, etc.). Unicode: universal, supports ALL world scripts. UTF-8: variable length (1-4 bytes), most popular on web, backward compatible with ASCII. UTF-16: 2 or 4 bytes. UTF-32: fixed 4 bytes (simple but wasteful). Emojis are Unicode characters! 😊 = U+1F60A.
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2's complement advantages: (1) Single representation of zero (sign-magnitude has +0 and -0). (2) Addition and subtraction use the same hardware circuit (no special handling for signs). (3) One extra negative number: with 8 bits, range is -128 to +127 (vs -127 to +127 in sign-magnitude). (4) Overflow detection is simpler. These advantages make CPU design simpler and faster, which is why virtually all modern computers use 2's complement for signed integers.
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