Thursday, November 13, 2014

Previous GATE Questions on K-Map, SOP and POS expressions (1987 - Till Date)



1991

1.       The four variable function f is given in terms of min-terms as f(A, B, C, D) = m(2,3,8,10,11,12,14,15). Using the K-map minimize the function in the sum of products form. Also, give the realization using only two input NAND gates.

Answer:     f = AD' + AC + B'C and No.of NAND gates required = 6 




1993

1.       The truth table for the output Y in terms of three inputs A, B and C are given. Draw a logic circuit realization using only NOR gates.
Answer:      Y = (A' + B')(B' + C')(A' + C')




1996

1.       Given the Boolean function F in three variables R, S and T as

                          F = R’ST’ + RS’T + RST 
        a.       Express F in the minimum sum of products form
        b.      Express F in the minimum product of sums form
        c.       Assuming that both true and complement forms of the input variables are available,     draw a circuit to implement F using the minimum number of 2 input NAND gates only.
               Solution :     https://www.youtube.com/watch?v=sXPb2zE-Q8M 



1997

1.   The Boolean function A + BC is a reduced form of
        a.       AB + BC
        b.      (A + B)(A + C)
        c.       A’B + AB’C
        d.      (A + C)B

Answer:      B
                 Solution :     https://www.youtube.com/watch?v=R64pdVEnmxI 



1998

1.   The K – map for a Boolean function is shown in the figure. The number of essential prime implicants for this function is
        a.       4
        b.      5
        c.       6
        d.      7
Answer:     A
                 Solution :      https://www.youtube.com/watch?v=gRJoq9yB70U    



2.       For the identity, AB + A’C + BC = AB + A’C, the dual form is 
                 Answer:     A
                  Solution :     https://www.youtube.com/watch?v=j77yeexgCk0     


1999

1.       The logical expression Y = A + A’B is equivalent to
        a.       AB
        b.      A’B
        c.       A’ + B
        d.      A + B
Answer:     D
                 Solution :     https://www.youtube.com/watch?v=72bTzRCe16Y 


2.       The minimized form of the logical expression
Answer:     A
                 Solution :        https://www.youtube.com/watch?v=fLpKAlIGnxE



2003

1.       The number of distinct Boolean expressions of 4 variables is
        a.       16
        b.      256
        c.       1024
        d.      65536

Answer:   D  
                  Solution :  https://www.youtube.com/watch?v=muIlwRZ7kY4

2.       If the functions W, X, Y and Z are as given below,

Answer:      A
                  Solution :  https://www.youtube.com/watch?v=E1_42NLgjOY



2004

1.       The Boolean expression AC + BC’ is equivalent to
Answer:     D
                    Solution :  https://www.youtube.com/watch?v=ln-baJRcMlY



2005

1.       The Boolean expression for the truth table shown is
Answer:     A
                  Solution :  https://www.youtube.com/watch?v=xCS-TTQvhp8




2006

1.       The number of product terms in the minimized sum of product expression obtained through the following K-map (where “d” denotes don’t care states)
1
0
0
1
0
d
0
0
0
0
d
1
1
0
0
1
        a.       2
        b.      3
        c.       4
        d.      5
Answer:     A
                Solution :     https://www.youtube.com/watch?v=0DZuZvT9Ays






2007

1.       The Boolean function Y = AB + CD is to be realized using only 2 input NAND gates. The minimum number of gates required is
        a.       2
        b.      3
        c.       4
        d.      5
Answer:     B
               Solution :    https://www.youtube.com/watch?v=NrSGprNRg7s

2.       The following Boolean expression Y = A’B’C’D +  A’BCD’ + AB’C’D + ABC’D’

      can be minimized to 

Answer:    D 
               Solution :    https://www.youtube.com/watch?v=haH_7TtDohU
  



2009

1.       If X = 1 in the given logic equation, then 
        a.       Y = Z
        b.      Y = Z’
        c.       Z = 1
        d.      Z = 0
Answer:     D
               Solution :   https://www.youtube.com/watch?v=qHzk5M1H6DU



2012

1.       In the sum of products function, f(X,Y,Z) = (2,3,4,5), the prime implicants are
Answer:     A
                 Solution : https://www.youtube.com/watch?v=6_fJIVxu2do




2014

1.       The Boolean expression simplifies to

           Answer:     A
                Solution :  https://www.youtube.com/watch?v=YyIX-T6Bsi0


2.       For the given Boolean function, which one of the following is the complete set of essential prime implicants?

Answer:    D 
                  Solution : https://www.youtube.com/watch?v=tGOgs59wtFc







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