Page 79 - Computer Science Class 11 Without Functions
P. 79

requirement. Therefore, F = x'yz' + xy'z + xyz'. Note that each of the three terms in the expression for F is a
            product of literals. The expression so obtained for F is called the canonical sum of products or simply the sum of
            products.




                 Let's Summarise


              Ø   A Boolean variable is also known as binary variable or logical variable that takes its values from the Boolean
                  algebra.
              Ø   The  values  which  are  stored  in  binary  variables  are  known  as  Boolean  constants.  For  example,
                  true/false,
              Ø   The two values of a binary signal may be called 1-0, true-false, high-low, etc.
              Ø   A Truth table is a representation of a Boolean function or expression containing all possible combinations of
                  input.

              Ø   Values and their result in a tabular format Boolean operators are operators used in Boolean algebra For
                  example, AND, OR, NOT, NOR, NAND and XOR.

              Ø   The AND operator (often called AND gate) is denoted by writing AND, putting a dot, or simply by the absence
                  of an operator. Thus, A AND B, A ● B, and AB all mean the same.


                                              A                B              A ● B
                                              0                0                 0
                                              0                1                 0
                                              1                0                 0
                                              1                1                 1

              Ø   The OR operator (often called OR gate) is denoted by writing OR or +.

                                              A                B              A + B
                                              0                0                 0
                                              0                1                 1
                                              1                0                 1
                                              1                1                 1

              Ø   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.


                                                       A             NOT A
                                                       0                1
                                                       1                0

              Ø   The basic digital circuits (NOT, AND, OR) used to manipulate the digital logic signals are also called logic gates.
              Ø   The AND gate yields 1 if both the incoming signals are 1, and 0 otherwise.
              Ø   The OR gate yields 1 if either of the input symbols is 1 and 0 otherwise.

              Ø   The NOT gate yields 1 if the input signal is 0 and 1 otherwise.
              Ø   + and ● are also called disjunction and conjunction, respectively.





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