DiscreteMathSetTheory分析.pptVIP

* Binary number system From binary to decimal: The number 1101011 is equivalent to 1 one 1 x20 = 1 1 two 1x21 = 2 0 four 0x22 = 0 1 eight 1x23 = 8 0 sixteen 0x24 = 0 1 thirty-two 1x25 =32 1 sixty-four 1x26 = 64 107 in decimal base * From decimal to binary The number 7310 is equivalent to 73 = 2 x 36 + remainder 1 36 = 2 x 18 + remainder 0 18 = 2 x 9 + remainder 0 9 = 2 x 4 + remainder 1 4 = 2 x 2 + remainder 0 2 = 2 x 1 + remainder 0 7310 =Write the remainders in reverse order preceded by the quotient * Adding binary numbers Binary addition table Example: add 1001012 + 1100112 ? 0 1 0 0 1 1 1 10 * Hexadecimal number system Decimal system 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 0 1 2 3 4 5 6 7 8 9 A B C D E F Hexadecimal system * Hexadecimal to decimal The hexadecimal number 3A0B16 is equal to 11 x 160 = 11 0 x 161 = 0 10 x 162 = 2560 3 x 163 = 12288 1485910 * Decimal to hexadecimal Given the number 234510 16 2345 remainder = 9 (least significant) 16 146 remainder = 2 16 9 remainder = 9 (most significant) 234510 is equivalent to the hexadecimal number 92916 * Hexadecimal addition Add 23A16 + 8F16 Let’s color-code Hex and Decimal as seen Since A = 10 and F = 15 Add, then A+F = 25 = 19 23A16 + 8F16 2C916 * The End L5 * L5 * Set Operations Symmetric Difference: Elements in exactly one of the two sets. A?B = { x | x?A ? x?B } = (A–B) ? (A–B) Example: A = {a, b}, B = {b, c, d} A?B = {a,c,d} * A B U A?B Set Operations Complement: Elements not in the set (unary operator). Ac = { x | x ? A } Example: U = N, A = {250, 251, 252, …} Ac = {0, 1, 2, …, 248, 249} * A U Ac * Disjoint Sets Disjoint: If A and B have no common elements, they are said to be disjoint. A ?B = ? A B U * Examples for set operations If A={1, 4, 7, 10}, B={1, 2, 3, 4, 5} A ? B =? A ? B =? A – B =? B – A =? A ? B =? * Example for