Page 85 - Computer Science Class 11 With Functions
P. 85

Ans.  The resultant SOP expression is:
                  U'VW' + U'VW + UV'W' + UVW


                  Case Based Questions


               1.  Srikeerti is new to logic gates. She wants to create a ready reckoner, in the form of a table, for herself so that she can refer
                  to the same whenever she is studying Boolean algebra. Help her complete the task.

                         Sr No     Name of gate            Symbol             Example Boolean Expression
                          1     AND                                                      A.B
                          2     OR                                                      A+B
                          3     NOT                                                      A'

                          4     XOR


                          5     NAND


             Ans.


                         Sr No     Name of gate            Symbol            Resultant Boolean Expression
                          1     AND                                                      A.B


                          2     OR                                                      A+B

                          3     NOT                                                      A'




                          4     XOR                                               A XOR B =  AB' + BA'



                          5     NAND                                                   (A●B)'


               2.  Ramya is learning about logic gates. Her friend tells her that out of all gates,   NOR and NAND are called fundamental gates.
                  But he could not explain to her any reason for the same. Do you know why NAND and NOR are called universal gates?
                  Explain to Ramya using Boolean expressions and using a logic circuit for AND gate.
             Ans.   NAND and NOR are called universal gates because all other gates can be implemented using these gates. For example, an
                  AND gate can be implemented using NAND gates, as shown below:
                  AND gate: A ● B = ((A ●B)')' = ((A ● B)' ● (A ● B)')'
                      = ((A NAND B) NAND (A NAND B)
                  Logic Circuit  using NAND gate

                                               A

                                               B

                  Also,    A●B = ( (A+A)'  +  (B+B)' )'
                                      = (A NOR A) NOR (B NOR B)
                  Logic Circuit using NOR gate




                                                                                                  Boolean Logic  83
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