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:

$(a+b)\cdot (\overline{b}+c)+b\cdot (\overline{a}+\overline{c})$ 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 $((p\wedge q)\to r)\vee ((p\wedge q)\to -r)$. 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 $z=xy+uv$.

[2014, 10M]

7) For any Boolean variables $x$ and $y$, show that $x+xy=x$.

[2014, 15M]

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

[2011, 6M]

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

[2011, 20M]

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

[2010, 6M]

11) Using Boolean algebra, simplify the following expressions:

(a) $a+a^{\mathrm{\prime }}b+a^{\mathrm{\prime }}{b}^{\mathrm{\prime }}c+a^{\mathrm{\prime }}{b}^{\mathrm{\prime }}{c}^{\mathrm{\prime }}d+\dots$
(b) $x^{\mathrm{\prime }}{y}^{\mathrm{\prime }}z+yz+xz$, where $x^{\prime }$ 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:
$$\begin{gathered} \overline{A}+AB=0 \\ AB+AC \\ AB+A\overline{C}+CD=\overline{C}D \end{gathered}$$
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 $A.B^{\mathrm{\prime }}+A^{\mathrm{\prime }}.B=C$, show that $A.C^{\mathrm{\prime }}+A^{\mathrm{\prime }}\cdot C=B$.

[2001, 6M]