Page 79 - Computer Science Class 11 With Functions
P. 79

for no other combination of values of x, y, z. The sum of the three expressions obtained above clearly meets this
            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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