Computer Number System

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A NUMBER SYSTEM USED WITH COMPUTERS The Binary Number System Modern computers convert information in the form of numbers, letters, and special characters into electrical impulses, which can have two possible values. This situation makes the binary number system, a system that includes only two digits, (0 and 1), very important to an understanding of how computers work. A number system is a code that uses symbols to refer to a number of items. The decimal number system uses the symbols, 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. The decimal number system contains 10 symbols and is sometimes called the base 10 system. The binary number system uses only two symbols, 0 and 1, and is sometimes called the base 2 system. Both number systems use the idea of place value to represent numbers larger than the number of symbols in the system. Consider the decimal number 359. The digit 3 represents 300 because of its placement three positions to the left of the decimal point. The digit 5 represent 50 because of its placement two positions to the left. The digit 9 represents nine because of its placement one position to the left of the decimal point. The total number 359 then, represent three hundred and fifth-nine units. This is an example of place value in the decimal number system. Hundreds Tens Ones 359 = 300 + 50 + 9 . decimal point The binary number system also uses the idea of place value. Place values in the binary number system are shown below. 512s 256s 128s 64s 32s 16s 8s 4s 2s 1s . binary point Notice that each place value is determined by multiplying the one to the right by 2. The term Òbase 2Ó for binary comes from this idea. Using place values the value of the binary number 1010 (say Òone zero one zeroÓ) can be determined. Eights Fours Twos Ones 1010 = 8 + 0 + 2 + 0 The binary number 1010, then represent 10 units. The value of the binary number

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