For example in the equation a b c d e even if a b

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Unformatted text preview: ables is 1. Note that a result of 1 is also obtained when both the inputs A and B are 1. This is the reason why the + symbol does not have the "normal" meaning, but is a logical addition operator. This concept of logical addition may be extended to any number of variables. For example, in the equation A + B + C + D = E, even if A, B, C, and D all had the value of 1, the sum of the values (the result E) would be 1 only. The equation A + B = C is normally read as "A or B equals C". Inputs A 0 0 1 1 Output + B 0 1 0 1 C 0 1 1 1 Figure 6.1. Truth table for logical OR (+) operator. Logical Multiplication The symbol '.' is used for logical multiplication operator. It is also known as 'AND' operator. We can again define the • symbol (AND operator) by listing all possible combinations of A and B and the resulting value of C in the equation A • B = C. The truth table for logical AND operator is shown in Figure 6.2. Observe from the truth table that the result C is equal to 1 only when both the input variables A and B are 1, otherwise it is 0. The equation A.B=C is normally read as “ A and B equals C”. Inputs Output A • B C 0 0 0 0 1 0 1 0 0 1 1 1 Figure 6.2. Truth table for logical AND (•) operator. Complementation The two operations defined so far (OR and AND) are binary operations because they define an operation on two variables. The complementation operation is a unary operation, which is defined on a single variable. The symbol '-' is normally used for complementation operator. It is also known as 'NOT' operator. Thus we write A, meaning "take the complement of A", or (A + B), meaning "take the complement of A + B." The complementation of a variable is the reverse of its value. Thus, if A = 0 then A = 1 and if A = 1 then A = 0. The truth table for logical NOT (-) operator is shown in Figure 6.3. "complement of A" or "not of A". Tnput Output A A 0 1 1 0 Figure 6.3. Truth table for logical NOT (-) operator. Operator Precedence A is re...
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This document was uploaded on 04/07/2014.

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