Introduction to Numerical Computing Number Systems in the Decimal System We Use the 10 Numeric Symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 to Represent Numbers
Statistics 580 Introduction to Numerical Computing Number Systems In the decimal system we use the 10 numeric symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 to represent numbers. The relative position of each symbol determines the magnitude or the value of the number. Example: 6594 is expressible as 6594 = 6 103 + 5 102 + 9 101 + 4 100 Example: · · · · 436.578 is expressible as 436:578 = 4 102 + 3 101 + 6 100 + 5 10−1 + 7 10−2 + 8 10−3 · · · · · · We call the number 10 the base of the system. In general we can represent numbers in any system in the polynomial form: z = ( akak− a a : b b bm )B · · · 1 · · · 1 0 0 1 · · · · · · where B is the base of the system and the period in the middle is the radix point. In com- puters, numbers are represented in the binary system. In the binary system, the base is 2 and the only numeric symbols we need to represent numbers in binary are 0 and 1. Example: 0100110 is a binary number whose value in the decimal system is calculated as follows: 0 26 + 1 25 + 0 24 + 0 23 + 1 22 + 1 21 + 0 20 = 32 + 4 + 2 · · · · · · · = (38)10 The hexadecimal system is another useful number system in computer work. In this sys- tem, the base is 16 and the 16 numeric and arabic symbols used to represent numbers are: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F Example: Let 26 be a hexadecimal number.
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