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1.9 BOOLEAN ALGEBRA
              Boolean Algebra gets its name from the famous mathematician George Boole who developed symbolic logic which
              states the relation between mathematics and logic. Like Algebra, it also has variables, but they can store only two
              values 0 (off) and 1 (on). They are termed Boolean variables.

              Boolean algebra has laws that help in simplifying a complex Boolean expression, which further reduces the number of
              digital gates required to represent a circuit.

              1.9.1 Logical Operators and Logic Gates
              An operator is a symbol used to perform different operations. The operators used in Boolean algebra are logical
              operators which join two or more relational statements.
              There are three types of logical operators: NOT, AND and OR.


              Logical NOT
              This operator is used to complement a Boolean variable or expression. NOT inverts 1 to 0 and 0 to 1. If A is a Boolean
              variable then NOT A is represented as A' or A.

              The truth table for NOT is as follows:

                                                            A           A'
                                                            0           1
                                                            1           0
                                                       Truth table for Logical NOT

              Logical OR
              This  operator  returns  0  (false)  when  all  the  operands  are  0  (false).  It   A  B       A+B
              returns 1(true) if any one operand is 1 (true). It is represented using the   0       0           0
              symbol + (plus). This operator works on two or more operands. It does not
              check the second condition if the first condition is true.               0            1           1
                                                                                       1            0           1
              Let us consider the following logical expressions                        1            1           1

              Expression 1: A%2 == 0                                               Truth table for OR operation

              Expression 2: A%3 == 0
                                        Value of A   A%2==0      A%3==0            A+B
                                                                            A%2==0 OR A%3==0

                                           25      False       False        False
                                           16      True        False        True
                                           39      False       True         True
                                           24      True        True         True

              Logical AND
                                                                                       A            B          A.B
              This operator produces 1 (true) when all operands are 1 (true). If any one   0        0           0
              operand is 0 (false) then the result is 0 (false). It is represented by a dot (.)
              symbol. This operator works on two or more operands. It does not check   0            1           0
              the second condition if the first condition is false.                    1            0           0
                                                                                       1            1           1
                                                                                   Truth table for AND operation


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