信息学奥赛知识（Knowledge of Olympiad in Informatics）.doc

信息学奥赛知识（Knowledge of Olympiad in Informatics） Two, hexadecimal and coding The transformation between the four kinds of system and their: Radix number, cardinal number, weights, law of input 0, 1, 2 decimal, 3, 4, 5, 6, 7, 8, 910 10I every one decimal Binary 0, 12 2I, two in one Octal 0, 1, 2, 3, 4, 5, 6,, 78, eight, one Sixteen hexadecimal 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F,, 16, 16i, every sixteen into a. A decimal number converted into binary, octal, and sixteen decimal numbers: Binary number, octal number, sixteen decimal number converted to decimal number method: by right expansion and summation method 1. conversion between binary and decimal systems: (1) binary to decimal Methods: according to the right to expand Example: (1011.01) 2 (= 1 * * * * 230 221 211 200 * * 211 2-2) 10 (802100.25 = 10) = (11.25) 10 Rule: the number of digits on the digit is 0, the number of digits on the ten digit is 1, and the number increases by ten The number of divided digits is -1, and the number of digits in the percentile is -2, and then decreases in turn. Note: not any decimal number can be converted into a limited number of binary digits. (2) decimal to binary Decimal integer to binary number: divided by 2, in reverse order (short division elimination method) Example: (89) 10 = (1011001) 2 289 244...... One 222...... Zero 211...... Zero 25...... One 22...... One 21...... Zero 0...... One Decimal to binary number? Multiplied by 2, order (by 2 rounding method) Example: (0.625) 10= (0.101) 2 Zero point six two five X 2 1.251 X 2 0.50 X 2 1.01 2. octal to binary conversion: The binary number is converted into an octal number: starting from the decimal integer, decimal part of left to right, every 3 to indicate a group with an octal number, less than 3 bits to use 0 make up 3, get an octal number. Octal numbers are converted into binary numbers: each octal digit is converted into a binary number of 3 bits, and a binary number is obtained. Example: converts octal 37.416