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Recent questions tagged boolean-algebra

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GATE ECE 2026 | Question: 38
A Boolean function, $f(x, y, z)$ with $x$ as MSB and $z$ as LSB is realized by $4: 1$ multiplexer (MUX) with select lines, $\mathrm{S}_{1}$ and $\mathrm{S}_{0}\left(\math...
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GATE ECE 2026 | Question: 46
Consider the four-variable Boolean function,$f(w, x, y, z)=\sum m(0,2,5,7,8,10,13,14,15)$ with '$w$' as MSB and '$z$' as LSB.Which of the following expressions is/are the...
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GATE ECE 2025 | Question: 13
A $3$-input majority logic gate has inputs $X, Y$, and $Z$. The output $F$ of the gate is logic '$1$' if two or more of the inputs are logic '$1$'. The output $F$ is logi...
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3 3 votes
2 2 answers
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GATE ECE 2024 | Question: 9
​​​​For the Boolean function\[F(A, B, C, D)=\sum m(0,2,5,7,8,10,12,13,14,15) \text {, }\]the essential prime implicants are $\_\_\_\_\_\_$.$B D, \bar{B} \bar{D}$$B D, A B...
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GATE ECE 2024 | Question: 30
​​​​​A $4$-bit priority encoder has inputs $D_{3}, D_{2}, D_{1}$, and $D_{0}$ in descending order of priority. The two-bit output $A B$ is generated as $00,01,10$, and 11...
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GATE ECE 1997 | Question 4.10
The boolean function $\mathrm{A}+\mathrm{BC}$ is a reduced form of$\mathrm{AB}+\mathrm{BC}$$(\mathrm{A}+\mathrm{B}) \cdot(\mathrm{A}+\mathrm{C})$$\overline{\mathrm{A}} \m...
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GATE ECE 2000 | Question 2.7
For the logic circuit shown in, the simplified Boolean expression for the output $Y$ is$\mathrm{A}+\mathrm{B}+\mathrm{C}$$\mathrm{A}$$\mathrm{B}$$\mathrm{C}$
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GATE ECE 2000 | Question 15
The operating conditions $(O N=1, O F F=0)$ of three pumps $(x, y, z)$ are to be monitored. $x=1$ implies that pump $X$ is on. It is required that the indicator $\text{(L...
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GATE ECE 1999 | Question 1.10
The logical expresion $y=\mathrm{A}+\overline{\mathrm{A}} \mathrm{B} $ is equivalent to$y=\mathrm{AB}$$y=\overline{\mathrm{A}} \mathrm{B}$$y=\bar{A}+\mathrm{B}$$y=\mathr...
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GATE ECE 1999 | Question 2.10
The minimized form of the logical expression $(\bar{A} \bar{B} \bar{C}+\bar{A} B \bar{C}+\bar{A} B C+A B \bar{C})$ is$\overline{\mathrm{A}} \overline{\mathrm{C}}+\mathrm{...
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GATE ECE 1999 | Question 12
In a certain application, four inputs $A, B, C, D$ (both true and complement forms available) are fed to logic circuit, producing an output $F$ which operates a relay. Th...
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GATE ECE 2001 | Question: 11
For the digital block shown in the figure the output $\mathrm{Y}=f\left(\mathrm{~S}_{3}, \mathrm{~S}_{2}, \mathrm{~S}_{1}, \mathrm{~S}_{0}\right)$ where $\mathrm{S}_{3}$ ...
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GATE ECE 1998 | Question 2.9
For the identity $\mathrm{AB}+\overline{\mathrm{A}} C+\mathrm{BC}=\mathrm{AB}+\overline{\mathrm{A}} \mathrm{C}$, the dual form is$(\mathrm{A}+\mathrm{B})(\overline{\mathr...
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GATE ECE 2003 | Question: 16
The number of distinct Boolean expressions of $4$ variables is$16$$256$$1024$$65536$
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GATE ECE 2003 | Question: 19
Without any additional circuitry, an $8: 1 \; \mathrm{MUX}$ can be used to obtainsome but not all Boolean functions of $3$ variablesall functions of $3$ variables but non...
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GATE ECE 2003 | Question: 54
If the functions $W, X, Y$ and $Z$ are as follows\[\begin{array}{l}W=R+\bar{P} Q+\bar{R} S \\X=P Q \bar{R} \bar{S}+\bar{P} \bar{Q} \bar{R} \bar{S}+P \bar{Q} \bar{R} \bar{...
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GATE ECE 2004 | Question: 52
The Boolean expression $\text{AC + B} \overline{\text{C}}$ is equivalent to$\overline{\mathrm{A}} \mathrm{C}+\mathrm{B} \overline{\mathrm{C}}+\mathrm{AC}$$\overline{\math...
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GATE ECE 2004 | Question: 58
A Boolean function $f$ of two variables $x$ and $y$ is defined as follows:\[f(0,0)=f(0,1)=f(1,1)=1 ; \quad f(1,0)=0\]Assuming complements of $x$ and $y$ are not available...
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GATE ECE 2005 | Question: 54
The Boolean expression for the truth table shown is$$\begin{array}{|c|c|c|c|}\hline \mathrm{A} & \mathrm{B} & \mathrm{C} & \mathrm{F} \\\hline 0 & 0 & 0 & 0 \\\hline 0 & ...
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GATE ECE 1995 | Question 1.29
The minimum number of $\text{NAND}$ gates required to implement the Boolean function $\mathrm{A}+\mathrm{A} \overline{\mathrm{B}}+\mathrm{A} \overline{\mathrm{B}} \mathrm...
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GATE ECE 2006 | Question: 13
The number of product terms in the minimized sum-of-product expression obtained through the following $\text{K}$-map is (where, " $d$ " denotes don't care states)$$\begin...
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GATE ECE 2007 | Question: 14
The Boolean function $Y=A B+C D$ is to be realized using only $2$ -input NAND gates. The minimum number of gates required is$2$$3$$4$$5$
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GATE ECE 2007 | Question: 41
The Boolean expression $Y=\overline{A} \;\overline{B}\; \overline{C} D+\overline{A} B C \overline{D}+A \overline{B}\; \overline{C} D+A B \overline{C}\; \overline{D}$ can ...
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GATE ECE 2008 | Question: 57
Which of the following Boolean Expressions correctly represents the relation between $\text{P, Q, R}$ and $\mathrm{M}_{1}?$ $\text{M}_{1} = \text{(P OR Q) XOR R}$$\text{M...
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GATE ECE 1993 | Question 6.13
Boolean expression for the output of $\text{XNOR}$ (Equivalent) logic gate with inputs $A$ and $B$ is$\mathrm{A} \overline{\mathrm{B}}+\overline{\mathrm{A}} \mathrm{B}$$\...
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GATE ECE 2009 | Question: 36
If $X=1$ in the logic equation $[X+Z\{\overline{Y}+(\overline{Z}+X \overline{Y})\}]\{\overline{X}+\overline{Z}(X+Y)\}=1$, then$Y=Z$$Y=\overline{Z}$$Z=1$$Z=0$
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GATE ECE 2022 | Question: 17
Select the Boolean function(s) equivalent to $x+yz,$ where $x, y,$ and $z$ are Boolean variables, and $+$ denotes logical $\text{OR}$ operation.$x + z + xy$$(x + y)(x + z...
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2 2 votes
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GATE ECE 2015 Set 2 | Question: 36
A function of Boolean variables $X, Y$ and $Z$ is expressed in terms of the min-terms as $$F(X, Y, Z) = \Sigma (1, 2, 5, 6, 7)$$Which one of the product of sums given bel...
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GATE ECE 2015 Set 1 | Question: 36
The Boolean expression $F(X,Y,Z) = \overline{X} \: Y \: \overline{Z}+ X \: \overline{Y} \: \overline{Z}+ X \: Y \: \overline{Z} + X \: Y \: Z$ converted into the canonica...
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GATE ECE 2014 Set 2 | Question: 14
For an $n$-variable Boolean function, the maximum number of prime implicants is$2(n-1)$$n/2$$2^{n}$$2^{n-1}$
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