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Voltage  ∼

                                                                      A OR B
                                                            A
                                                            B

                                             Fig 3.2: Electric circuit for OR operator

        3.2.3 NOT Operator

        The NOT operator (often called NOT gate) is denoted by writing NOT before the variable or by putting a bar over it or
        by appending a prime ('). Thus, NOT A, Ā, A' all mean the negation of A. The operator NOT A yields 1 if A = 0; and 0, if
        A = 1. The truth table for the NOT operator appears in Table 3.4.


                                                 A                 NOT A
                                                 0                   1
                                                 1                   0
                                      Table 3.4: Result of NOT operator using values 0 and 1



                 1.  Which Boolean operator yields True if either or both the operands are true?
                 2.  Which Boolean operator inverts the value of the operand?


        3.2.4 Logic Gates

        As mentioned above, the basic digital circuits (NOT, AND, OR) used to manipulate the digital logic signals are also called
        logic gates. The AND gate yields 1 if both the incoming signals are 1, and 0 otherwise. Similarly, the OR gate yields 1 if
        either of the input symbols is 1 and 0 otherwise. Finally, NOT gate yields 1 if the input signal is 0 and 1 otherwise. Fig
        3.3 shows the symbols that denote the logic gates.

                         A              A  B        A            A + B         A             A
                         B                           B
                              AND gate                  OR gate                    NOT gate
                                               Fig 3.3: AND, OR, and NOT gate


        3.3 Boolean Algebra
        George Boole developed Boolean algebra, which provides a sound basis for studying logic circuits. Although one can
        define a Boolean algebra of 2, 4, 8, or more elements, in this book, we will restrict ourselves to the Boolean algebra of
        two elements as it serves as the basis of designing computer circuits.

        3.3.1 Definition

        Boolean algebra β is defined by a triplet β = < S, +, ●>, where S is a set having two elements 0 and 1. The symbols
        + and ● denote binary operators that denote OR and AND, respectively. These operators satisfy certain properties,
        called postulates. While describing the properties of Boolean algebra, we will use two symbols: ∀ and ∈. The symbol
        ∀ denotes for each or for all. The symbol ∈ denotes in or belong(s) to. In a boolean expression involving OR(+) and
        AND(●) binary operators, AND(●) is evaluated before OR(+).



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