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 

   Solution :    https://www.youtube.com/watch?v=x_pBfG9g-8w

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')

   Solution :    https://www.youtube.com/watch?v=TVdLzstLObk

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