Logic Minimization and Optimization Welcome to your QUIZ onÂ Logic Minimization and Optimization Your Name Please Enter Your Email 1. The following expression is corresponds to \[AB + \overline{A}C + BC = AB + \overline{A}C \] \[(A + B).(\overline{A} + C).(B + C) = (A + B).(\overline{A} + C)\] \[AB + \overline{A}C + BC = AB + BC \] \[AB + \overline{A}C + BC = (A + B).(\overline{A} + C).(B + C)\] \[(A + B).(\overline{A} + C).(B + C) = AB + \overline{A}C\] 2. Following expression represents (M is a maxterm) \[Y = f(A,B) = \prod M(0,1,2,3)\] NOR gate NAND gate OR gate a situation where output is independent of input. 3. Which one of the followings is equivalent to \[ \overline{A} \hspace{2pt}\overline{B} + \overline{B}\hspace{2pt}\overline{C} + \overline{C}\hspace{2pt} \overline{A}\] \[ \overline {AB +BC + CA}\] \[(\overline{A} + \overline{B})(\overline{B} + \overline{C})(\overline{C} + \overline{A})\] \[ \overline {(A+B)(B+C)(C+A)}\] \[ \overline {(A + B)}\hspace{5pt}\overline {(B + C)}\hspace{5pt}\overline {(C + A)}\] 4. Simplified form of X is \[ABCD + A\overline{B}CD + \overline{A}BCD+ \overline{A}C\overline{B}D\] \[ \overline{C} + \overline{D} \] BC CD AB 5. The following expression simplifies to \[ (\bar{A} + B) + (A + \bar{C}) + (\bar{B}+\bar{C})\] \[(A+B)\bar{C}\] \[(A+\bar{B})\bar{C}\] \[(\bar{A}+B)\bar{C}\] \[(\bar{A}+\bar{B})\bar{C}\] 6. Which expression can not be minimized further? \[ z = a.\bar{b}.\bar{c}+ a.b.\bar{c} + a.b.c + \bar{a}.\bar{b}.\bar{c}\] \[ z = a.\bar{b}.c+ a.b.\bar{c} + a.b.c + \bar{a}.\bar{b}.\bar{c}\] \[ z = a.\bar{b}.\bar{c}+ \bar{a}.\bar{b}.c + a.b.c + \bar{a}.b.\bar{c}\] \[ z = \bar{a}.b.\bar{c}+ a.b.\bar{c} + a.b.c + \bar{a}.\bar{b}.c\] 7. The following expression is equal to which expression? \[ (A + B).(\overline{A} + C).(B + C)\] \[ (A + B).(B + C)\] \[(\overline{A} + C).(B + C)\] \[ (A + B).(\overline{A} + C)\] \[ (A + B).(A + \overline{C})\] 8. Which one of the followings is the dual form of the expression shown below?\[AB + \bar{A}C = (A + C)(\bar{A} + B)\] \[AB + \bar{A}C = AC + \bar{A}B\] \[(A + B)(\bar{A} + C) = (A + C)(\bar{A} + B)\] \[(A + B)(\bar{A} + C) = AC + \bar{A}B\] \[AB + \bar{A}C = \bar{A}C + BC\] 9. The Boolean expression Y(A,B,C) = A + BC is to be realized using 2-input gates of only one type. What is the minimum number of gates required for realization? 1 3 2 4 or more 10. Realize the below mentioned expression using two 2-input gates. \[ X(P,Q,R) = \prod (0,5)\] AND and OR NAND and OR AND and XOR OR and XOR 11. Minimize the following expression \[AD + ABCD + ACD + \bar{A}B + ACD + \bar{A}\bar{B}\] A +D \[AD + \bar{A}\] AD \[D + \bar{A}\] 12. Minimize the following expression \[(A+B).(A+\bar{B})\] B A A + B AB 13. Expand the following expression \[A\oplus B\] \[AB + \bar{A}\bar{B}\] \[A\bar{B} + \bar{A}B\] B \[\bar{A}\] 14. Find the boolean expression \[F(x1,x2,x3) = \sum (0,1,2,3) + \sum_{X}(4,5,6,7)\] 1 0 x1 x3 15. Boolean functions can be expressed in SOP and POS form. Such two functions are for the following expression \[Y =(A + \bar{B}C)\] \[Y=\sum(1,2,6,7)\hspace{3pt}and\hspace{3pt} Y = \prod (0,2,4)\] \[Y=\sum(1,4,5,6,7)\hspace{3pt} and\hspace{3pt} Y = \prod (0,2,3)\] \[Y=\sum(1,2,5,6,7) \hspace{3pt}and \hspace{3pt}Y = \prod (0,1,3)\] \[Y=\sum(1,2,4,5,6,7) \hspace{3pt}and \hspace{3pt}Y = \prod (0,2,3,4)\] 16. The boolean expression (A + BC) is reduced form of which of the following AB + BC \[A\bar{B} + A\bar{B}C\] (A+B).(A+C) None of the above 17. Which of the following statements is not correct? \[ X + \bar{X}Y = X\] \[X(\bar{X} + Y) = XY\] \[ XY + X\bar{Y} = X\] \[ZX + Z\bar{X}Y + ZX + ZY \] 18. Minimize the following expression \[ \overline{\bar{B} + C} + \overline{\bar{A} + \bar{B} + C } + \overline{A + \bar{B} + \bar{C}} + ABC \] A B C A + B + C 19. Find the standard SOP expression for the following boolean expression. \[A\bar{B} + AC + BC\] \[A\bar{B}C + \bar{A}BC+ A\bar{B}\bar{C}+ABC\] \[AB\bar{C} + \bar{A}BC+ABC\] \[A\bar{B}C + AB\bar{C}+ABC\] \[\bar{A}\bar{B}C + AB\bar{C}+ A\bar{B}\bar{C}\] 20. Find the complement of the following expression. \[ Y = ABC + AB\bar{C} + \bar{A}\bar{B}C+\bar{A}BC\] \[(A + \bar{B})(A + \bar{C})\] \[(\bar{A} + B)(A + C)\] \[(A + \bar{B})(\bar{A} + C)\] \[(\bar{A} + \bar{B})(A + \bar{C})\] 21. The minimum boolean function derived from the K-map is \[ \bar{x}\bar{y} + \bar{z} + yz \] \[ x\bar{z} + z + z\bar{y}\] \[ xy + z + \bar{y}z\] \[\bar{x}z + \bar{z} + yz \] 22. The minimum expression derived from the K-map is \[A + \bar{B}C\] B + AC C + AB ABC 23. Minimum expression for the K-map is xz \[\bar{w}x\bar{y} + \bar{w}yz + w\bar{y}z + wxy \] \[\bar{w}x\bar{y} + \bar{w}yz + w\bar{y}\bar{z} + wx\bar{y} \] \[xz+ \bar{w}yz + \bar{w}x\bar{y} + wxy + w\bar{y}z \] Please fill in the comment box below. Time's up +20