数值分析-2-NumberRepresentation.pdf

2. umber Representation How numbers are stored in computers? Number system: a convention for representing quantities. 2.1 Integer representations: 2.1.1 Unsigned integers: positive integers only Decimal (base10) number system – what we are most familiar with [Start from the rightmost position, the ith rightmost position represents multiples of 10^(i1).] Range: 4 digits: 0 – 9999 Binary (base2) system – what computers use, the primary logic units of digital computers are ON/OFF electronic components. From decimal to binary: 243 121 60 30 15 7 3 1 0 (stop) 1 1 0 0 1 1 1 1 reverse 1111 0011 Range of unsigned integers: 8 bit: 0 ~ 2^81 = 255 16 bit: 0 ~ 2^16 1 = 65,535 Examples of storing unsigned numbers in two different computers Page 1 of 5 Decimal Decimal 8bit allocation 16bit allocation 8bit allocation 16bit allocation 7 0000000000000111 234 0000000011101010 258 overflow 0000000100000010 24,760 overflow 0110000010111000 1,245,678 overflow overflow 2.1.2 Signed integers: (source of information – ) To represent signed integers, use the leftmost bit to represent the sign bit (0 for positive integers and 1 for negative integers), and use the rest bits to represent the magnitude. The most commonly used method in comput