GATE PYQ

Digital Logic

Q21.
Consider the following gate networkWhich one of the following gates is redundant?

Q22.
Let, x_{1} \oplus x_{2} \oplus x_{3} \oplus x_{4}=0 where x_{1}, x_{2} , x_{3} , x_{4} are Boolean variables, and \oplus is the XOR operator. Which one of the following must always be TRUE?

Q23.
The minimum number of \text{NAND} gates required to implement the Boolean function A + A\bar{B} + A\bar{B}C is equal to

Q24.
Consider the Boolean operator with the following properties: x \# 0=x, x \# 1=\bar{x}, x \# x=0 and x \# \bar{x}=1. Then x \# y is equivalent to

Q25.
The boolean expression A B+A B^{\prime}+A^{\prime} C+A C is independent of the boolean variable

Q26.
The complement of the Boolean expression A B(\bar{B} C+A C) is

Q27.
The number of min-terms after minimizing the following Boolean Algebra is _________. {[{D}'+A{B}'+{A}'C+A{C}'D+{A}'{C}'{D}]}'

Q28.
Consider the operations f(X,Y,Z)=X'YZ+XY'+Y'Z' and g(X,Y,Z)=X'YZ+X'YZ'+XY. Which one of the following is correct?

Q29.
Given the function F=P'+QR , where F is a function in three Boolean variables P,Q and R and P'=!P, consider the following statements. (S1) F=\Sigma(4,5,6) (S2) F=\Sigma(0,1,2,3,7) (S3) F=\Pi(4,5,6) (S4) F=\Pi(0,1,2,3,7) Which of the following is true?

Q30.
Consider the logic circuit given below.The inverter, AND and OR gates have delays of 6, 10 and 11 nanoseconds respectively. Assuming that wire delays are negligible, what is the duration of glitch for Q before it becomes stable?