PYQs

1) Realize the following expressions by using NAND gates only:
\(g=(\overline{a}+\overline{b}+c) \overline{d}(\overline{a}+e) f\),
where \(\overline{x}\) represents the complement of \(x\).

[2009, 6M]

2) Represent \((\overline{A}+\overline{B}+\overline{C})(A+\overline{B}+C)(A+B+\overline{C})\) in NOR to NOR logic network.

[2008, 6M]

3) Prove De Morgan’s Theorem $(p+q)^{\prime}=p^{\prime} \cdot q^{\prime}$ by means of a truth table.

[6M]

1) Given the Boolean expression

(i) Draw the logical diagram for the expression.
(ii) Minimize the expression.
(iii) Draw the logical diagram for the reduced expression.

[2019, 15M]

2) Simplify the boolean expression:

\((a+b)\cdot( \bar{b}+c)+b\cdot( \bar{a}+ \bar{c})\) by using the laws of boolean algebra. From its truth table write it in minterm normal form.

[2018, 15M]

3) Write the Boolean expression \(z(y+z)(x+y+z)\) in the simplest form using Boolean postulate rules. Mention the rules used during simplification. Verify your result by constructing the truth table for the given expression and for its simplest form.

[2017, 10M]

4) Let \(A\), \(B\), \(C\) be Boolean variable denote complement \(A\), \(A+B\) of is an expression for \(A\) OR \(B\) and \(B.A\) is an expression for \(A\) AND \(B\). Then simplify the following expression and draw a block diagram of the simplified expression using AND and OR gates.
\(A .(A+B, C) .(\overline{A}+B+C) \cdot(A+\overline{B}+C) .(A+B+\overline{C})\).

[2016, 15M]

5) Find the principal (or canonical) disjunctive normal form in three variables \(p\), \(q\), \(r\) for the Boolean expression \(((p \wedge q) \rightarrow r) \vee((p \wedge q) \rightarrow-r)\). Is the given Boolean expression a contradiction or a tautology?

[2015, 10M]

6) Use only AND and OR logic gates to construct a logic circuit for the Boolean expression \(z=x y+u v\).

[2014, 10M]

7) For any Boolean variables \(x\) and \(y\), show that \(x+x y=x\).

[2014, 15M]

8) Let \(A\) be an arbitrary but fixed Boolean algebra with operations \(\wedge\), \(\vee\) and \('\), and the zero and the unit element denoted by 0 and 1 respectively. Let \(x\), \(y\), \(z \ldots\) be elements of \(A\). If \(x, y\in A\) be such that \(x \wedge y=0\) and \(x \vee y=1\), then prove that \(y=x^{\prime}\).

[2011, 6M]

9) Find the logic circuit that represents the following Boolean function. Find also an equivalent simpler circuit:
\(\quad \begin{array}{|c|c|c|c|}\hline x & {y} & {z} & {f(x, y, z)} \\ \hline 1 & {1} & {1} & {1} \\ \hline 1 & {1} & {0} & {0} \\ \hline 1 & {0} & {1} & {0} \\ \hline 1 & {0} & {1} & {0} \\ \hline 0 & {1} & {1} & {1} \\ \hline 0 & {1} & {0} & {0} \\ \hline 0 & {0} & {1} & {0} \\ \hline 0 & {0} & {0} & {0} \\ \hline\end{array}\)

[2011, 20M]

10) If \(A \oplus B=A B^{\prime}+A^{\prime} B\), find the value of \(x \oplus y \oplus z\).

[2010, 6M]

11) Using Boolean algebra, simplify the following expressions:

(a) \(a+a^{\prime} b+a^{\prime} b^{\prime} c+a^{\prime} b^{\prime} c^{\prime} d+\ldots\)
(b) \(x^{\prime} y^{\prime} z+y z+x z\), where \(x'\) represents the complement of \(x\).

[2010, 5M]

12) Find the values of two valued Boolean variables \(A\), \(B\), \(C\), \(D\) by solving the following simultaneous equations:
\({\quad \overline{A}+A B=0} \\ {\quad A B+A C} \\ {\quad A B+A \overline{C}+C D=\overline{C} D}\)
where \(\overline{x}\) represents the complement of \(x\).

[2009, 6M]

13) State the principle of duality in Boolean algebra and give the dual of the Boolean expressions \((X+Y) \cdot(\overline{X} . \overline{Z}) \cdot(Y+Z)\) and \(X \overline{X}=0\).

[2008, 6M]

14) Given \(A.B^{\prime}+A^{\prime}.B=C\), show that \(A.C^{\prime}+A^{\prime} \cdot C=B\).

[2001, 6M]