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Recent questions tagged boolean-algebra

20 votes

2 answers

331

GATE CSE 1991 | Question: 5-b
Find the minimum sum of products form of the logic function $ f(A,B,C,D) = \Sigma_{m}(0,2,8,10,15)+ \Sigma _{d}(3,11,12,14)$ where $m$ and $d$ represent minterm and don't care term respectively.

ibia asked in Digital Logic Nov 14, 2015

by ibia

3.2k views

5 votes

3 answers

332

Boolean Algebra
Consider a Hasse Diagram for a Boolean Algebra of Order 3 What can we comment about it? How is it successfully able to represent the Boolean Algebra System? Is there an easy way to check for distributive lattice, or any other properties of a lattice? ... that one should provide a complete answer to all parts of the question. Whatever one can supply to support its answer is welcomed.

amarVashishth asked in Set Theory & Algebra Nov 11, 2015

by amarVashishth

4.3k views

7 votes

3 answers

333

ISRO2011-6
Evaluate $\text{(X xor Y) xor Y}?$ All $\text{1's}$ All $\text{0's}$ $\text{X}$ $\text{Y}$

amarVashishth asked in Digital Logic Oct 11, 2015

by amarVashishth

6.6k views

3 votes

3 answers

334

How many of $16$ boolean functions in $2$ variables $x$ and $y$ can be represented using only
How many of $16$ boolean functions in $2$ variables $x$ and $y$ can be represented using only the given set of operators, variables $x$ and $y$ ,and values $0$ and $1$? a) $\{\, \sim \,\}$ b) $\{\, \cdot \,\}$ c) $\{\, + \,\}$ d) $\{\, \cdot \,,\, + \,\}$

Pooja Palod asked in Digital Logic Oct 7, 2015

1.5k views

33 votes

3 answers

335

TIFR CSE 2010 | Part B | Question: 21
For $x \in \{0,1\}$, let $\lnot x$ denote the negation of $x$, that is $\lnot \, x = \begin{cases}1 & \mbox{iff } x = 0\\ 0 & \mbox{iff } x = 1\end{cases}$. If $x \in \{0,1\}^n$, then $\lnot \, x$ denotes the component wise negation of $x$; that ... $g(x) = f(x) \land f(\lnot x)$ $g(x) = f(x) \lor f(\lnot x)$ $g(x) = \lnot f(\lnot x)$ None of the above.

makhdoom ghaya asked in Digital Logic Oct 5, 2015

by makhdoom ghaya

3.4k views

4 votes

3 answers

336

How to solve this boolean Exp?
Boolean Expression is (A+B).(B+C) Please give a detailed explanation.

iarnav asked in Digital Logic Oct 2, 2015

by iarnav

554 views

3 votes

2 answers

337

How do I solve this Boolean expression?
How do I solve this Boolean expression? $(A+B) \cdot (B+C) \cdot (C+A)$ Kindly write the step wise explanation with properties used.

iarnav asked in Digital Logic Sep 23, 2015

by iarnav

689 views

94 votes

8 answers

338

GATE CSE 2015 Set 1 | Question: 39
Consider the operations $\textit{f (X, Y, Z) = X'YZ + XY' + Y'Z'}$ and $\textit{g (X, Y, Z) = X'YZ + X'YZ' + XY}$ Which one of the following is correct? Both $\left\{\textit{f} \right\}$ and ... $\left\{ \textit{f}\right\}$ nor $\left\{\textit{g}\right\}$ is functionally complete

makhdoom ghaya asked in Digital Logic Feb 13, 2015

by makhdoom ghaya

27.0k views

56 votes

12 answers

339

GATE CSE 2015 Set 2 | Question: 37
The number of min-terms after minimizing the following Boolean expression is _______. $[D'+AB'+A'C+AC'D+A'C'D]'$

go_editor asked in Digital Logic Feb 12, 2015

18.7k views

42 votes

4 answers

340

GATE IT 2005 | Question: 7
Which of the following expressions is equivalent to $(A \oplus B) \oplus C$ $(A + B + C) (\bar A +\bar B +\bar C)$ $(A + B + C) (\bar A +\bar B + C)$ $ABC + \bar A (B \oplus C) + \bar B(A \oplus C)$ None of these

Ishrat Jahan asked in Digital Logic Nov 3, 2014

by Ishrat Jahan

10.2k views

36 votes

4 answers

341

GATE IT 2004 | Question: 44
The function $A \bar B C + \bar A B C + AB \bar C+ \bar A \bar B C+ A \bar B \bar C$ is equivalent to $A \bar C + AB+ \bar A C$ $A \bar B+ A \bar C+ \bar A C$ $\bar A B+ A \bar C+ A \bar B$ $\bar AB+ AC+ A \bar B$

Ishrat Jahan asked in Digital Logic Nov 2, 2014

by Ishrat Jahan

6.8k views

46 votes

3 answers

342

GATE IT 2008 | Question: 37
Consider the following state diagram and its realization by a JK flip flop The combinational circuit generates J and K in terms of x, y and Q. The Boolean expressions for J and K are : $\overline {x \oplus y}$ and $\overline {x \oplus y}$ $\overline {x \oplus y}$ and $ {x \oplus y}$ $ {x \oplus y}$ and $\overline {x \oplus y}$ $ {x \oplus y}$ and $ {x \oplus y}$

Ishrat Jahan asked in Digital Logic Oct 28, 2014

by Ishrat Jahan

14.1k views

25 votes

4 answers

343

GATE CSE 1995 | Question: 2.5
What values of $A, B, C$ and $D$ satisfy the following simultaneous Boolean equations? $\overline{A} + AB =0, AB=AC, AB+A\overline{C}+CD=\overline{C}D$ $A=1, B=0, C=0, D=1$ $A=1, B=1, C=0, D=0$ $A=1, B=0, C=1, D=1$ $A=1, B=0, C=0, D=0$

Kathleen asked in Digital Logic Oct 8, 2014

7.6k views

31 votes

1 answer

344

GATE CSE 1994 | Question: 4
Let $\ast$ be a Boolean operation defined as $A\ast B = AB + \overline{A}\;\overline{B}$. If $C=A\ast B$ then evaluate and fill in the blanks: $A\ast A=$______ $C\ast A=$______ Solve the following boolean equations for the values of $A, B$ and $C:$ $AB+\overline{A}C=1$ $AC+B=0$

Kathleen asked in Digital Logic Oct 5, 2014

4.6k views

27 votes

4 answers

345

GATE CSE 1997 | Question: 2-1
Let $*$ be defined as $x * y = \bar{x} + y$. Let $z = x * y$. Value of $z * x$ is $\bar{x} + y$ $x$ $0$ $1$

Kathleen asked in Digital Logic Sep 29, 2014

5.3k views

45 votes

7 answers

346

GATE CSE 2014 Set 3 | Question: 55
Let $\oplus$ denote the exclusive OR (XOR) operation. Let '$1$' and '$0$' denote the binary constants. Consider the following Boolean expression for $F$ over two variables $P$ and $Q$ ... $F$ is $P+Q$ $\overline{P+Q}$ $P \oplus Q$ $\overline {P \oplus Q}$

go_editor asked in Digital Logic Sep 28, 2014

10.6k views

22 votes

3 answers

347

GATE CSE 1998 | Question: 2.8
Which of the following operations is commutative but not associative? AND OR NAND EXOR

Kathleen asked in Digital Logic Sep 25, 2014

9.1k views

42 votes

4 answers

348

GATE CSE 1998 | Question: 1.13
What happens when a bit-string is XORed with itself $n$-times as shown: $\left[B \oplus (B \oplus ( B \oplus (B \dots n \text{ times}\right]$ complements when $n$ is even complements when $n$ is odd divides by $2^n$ always remains unchanged when $n$ is even

Kathleen asked in Digital Logic Sep 25, 2014

10.0k views

31 votes

7 answers

349

GATE CSE 2013 | Question: 21
Which one of the following expressions does NOT represent exclusive NOR of $x$ and $y$? $xy + x′ y′$ $x\oplus y′$ $x′\oplus y$ $x′\oplus y′$

Arjun asked in Digital Logic Sep 24, 2014

by Arjun

9.4k views

19 votes

5 answers

350

GATE CSE 1999 | Question: 1.7
Which of the following expressions is not equivalent to $\bar{x}$? $x \text{ NAND } x$ $x \text{ NOR } x$ $x \text{ NAND } 1$ $x \text{ NOR } 1$

Kathleen asked in Digital Logic Sep 23, 2014

8.5k views

42 votes

5 answers

351

GATE CSE 2007 | Question: 33
Define the connective $*$ for the Boolean variables $X$ and $Y$ as: $X * Y = XY + X'Y'.$ Let $Z = X * Y$. Consider the following expressions $P$, $Q$ and $R$. $P : X = Y * Z, \\ Q :Y = X * Z, \\ R : X *Y * Z = 1$ Which of the following is TRUE? Only $P$ and $Q$ are valid. Only $Q$ and $R$ are valid. Only $P$ and $R$ are valid. All $P$, $Q$, $R$ are valid.

Kathleen asked in Digital Logic Sep 21, 2014

8.8k views

43 votes

6 answers

352

GATE CSE 2007 | Question: 32
Let $f(w, x, y, z) = \sum {\left(0,4,5,7,8,9,13,15\right)}$. Which of the following expressions are NOT equivalent to $f$? P: $x'y'z' + w'xy' + wy'z + xz$ Q: $w'y'z' + wx'y' + xz$ ... $x'y'z' + wx'y'+ w'y$ P only Q and S R and S S only

Kathleen asked in Digital Logic Sep 21, 2014

10.3k views

28 votes

5 answers

353

GATE CSE 2004 | Question: 17
A Boolean function $x’y’ + xy + x’y$ is equivalent to $x' + y'$ $x + y$ $x + y'$ $x' + y$

Kathleen asked in Digital Logic Sep 18, 2014

7.8k views

30 votes

1 answer

354

GATE CSE 2002 | Question: 2-3
Let $f(A,B) = A'+B$. Simplified expression for function $f(f(x+y, y), z)$ is $x' + z$ $xyz$ $xy' + z$ None of the above

Kathleen asked in Digital Logic Sep 15, 2014

7.8k views

41 votes

5 answers

355

GATE CSE 2000 | Question: 2.10
The simultaneous equations on the Boolean variables $x, y, z$ and $w$, $x + y + z = 1 $ $xy = 0$ $xz + w = 1$ $xy + \bar{z}\bar{w} = 0$ have the following solution for $x, y, z$ and $w,$ respectively: $0 \ 1 \ 0 \ 0$ $1 \ 1 \ 0 \ 1$ $1 \ 0 \ 1 \ 1$ $1 \ 0 \ 0 \ 0$

Kathleen asked in Digital Logic Sep 14, 2014

7.1k views

30 votes

4 answers

356

GATE CSE 1992 | Question: 02-i
The operation which is commutative but not associative is: AND OR EX-OR NAND

Kathleen asked in Digital Logic Sep 12, 2014

7.2k views

31 votes

4 answers

357

GATE CSE 2008 | Question: 26
If $P, Q, R$ are Boolean variables, then $(P + \bar{Q}) (P.\bar{Q} + P.R) (\bar{P}.\bar{R} + \bar{Q})$ simplifies to $P.\bar{Q}$ $P.\bar{R}$ $P.\bar{Q} + R$ $P.\bar{R} + Q$

Kathleen asked in Digital Logic Sep 11, 2014

10.5k views

34 votes

3 answers

358

GATE CSE 2012 | Question: 6
The truth table ${\begin{array}{|c|c|c|}\hline \textbf{X}& \textbf{Y}& \textbf{(X,Y)} \\\hline 0& 0& 0 \\ \hline 0& 1&0\\ \hline 1& 0& 1 \\\hline 1& 1& 1 \\\hline \end{array}}$ represents the Boolean function $X$ $X + Y$ $X \oplus Y$ $Y$

gatecse asked in Digital Logic Aug 5, 2014

4.3k views

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Recent questions tagged boolean-algebra