101 1 x2 0x22 1001 1 x21 0x2 x23and 1001

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Unformatted text preview: ystem, 0.235 = (2 x 10"') + (3 x 10"2) + (5 x 10"3) and 68.53 = (6 x 10') + (8x 10°) +(5 + (3 x 10"2) Similarly, in the binary number system, 0.101 =(1 x2"') + (0x2"2) 10.01 =(1 x21) + <0x2°) + x2"3)and 10.01 = (1x21) + (0x20) + 0x1-1) + (1x2-2) Thus, the binary point serves the same purpose as the decimal point. Some of the positional values in the binary number system are given below. Position 4 -4 Position Value 24 2-4 Quantity 16 1/16 Represented 3 2 1 0 Binary Point -1 -2 -3 23 22 21 20 Binary Point 2-1 2-2 2-3 8 4 2 1 Binary Point ½ ¼ 1/8 In general, a number in a number system with base b would be written as: an an.i... ao. a.i a_2... a.m and would be interpreted to mean an x bn + an., x b"'1 + ... + ao x b° + a4 x b"1 + a.2 x b"2 + .;. + a.m x b"m The symbols an, an.h ..., a.m used in the above representation should be one of the b symbols allowed in the number system. Thus, as per the above mentioned general rule, 46.328 = (4 x 81) + (6 x 8°) + (3 x 8'1) + (2 x 8"2) and 5A.3C16 = (5 x 161) + (A x 16°) + (3 x 16"1) + (C x 16"2) Example 3.26. Find the decimal equivalent of the binary number 110.101 Solution: 110.1012 = 1 x22+ 1 x2' + 0x2° + 1 x2" 0 x 2"1 + 0x2-2 + 1 x 2-3 = 4 + 2 + 0 + 0.5 + 0 + 0.125 = 6 + 0.5 + 0.125 = 6.62510 Points to Remember 1. Number systems are basically of two types: non-positional and positional. 2. In a non-positional number system, each symbol represents the same value regardless of its position in the number and the symbols are simply added to find out the value of a particular number. It is very difficult to perform arithmetic with such a number system. 3. 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. • The digit itself, • The position of the digit in t...
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This document was uploaded on 04/07/2014.

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