Since it is very difficult to perform an arithmetic

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Unformatted text preview: f its position in the number and the symbols are simply added to find out the value of a particular number. Since it is very difficult to perform an arithmetic with such a number system, positional number systems were developed as the centuries passed. POSITIONAL NUMBER SYSTEMS In a positional number system, there are only a few symbols called digits, and these symbols represent different values depending on the position they occupy in the number. The value of each digit in such a number is determined by three considerations: 1. The digit itself, 2. The position of the digit in the number, and 3. The base of the number system (where base is defined as the total number of digits available in the number system). The number system that we use in our day-to-day life is called the decimal number system. In this system, the base is equal to 10 because there are altogether ten symbols or digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9). You know that in the decimal system, the successive positions to the left of the decimal point represent units, tens, hundreds, thousands, etc. But you may not have given much attention to the fact that each position represents a specific power of the base (10). For example, the decimal number 2586 (written as 258610) consists of the digit 6 in the units position, 8 in the tens position, 5 in the hundreds position, and 2 in the thousands position, and its value can be written as: (2x1000)+ (5x100)+ (8x10)+ (6xl), or 2000 + 500 + 80 + 6, or 2586 It may also be observed that the same digit signifies different values depending on the position it occupies in the number. For example, In 2586io the digit 6 signifies 6 x 10° = 6 In 2568io the digit 6 signifies 6 x 10 1 = 60 In 2658,o the digit 6 signifies 6 x 102 = 600 In 6258io the digit 6 signifies 6 x 103 = 6000 Thus any number can be represented by using the available digits and arranging them in various positions. The principles that apply to the decimal number system also apply to any other positional...
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