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Boolean algebra. Combinational and sequential circuits. Minimization. Number representations and computer arithmetic (fixed and floating point)

$$\scriptsize{\overset{{\large{\textbf{Mark Distribution in Previous GATE}}}}{\begin{array}{|c|c|c|c|c|c|c|c|}\hline
\textbf{Year}& \textbf{2022} & \textbf{2021-1}&\textbf{2021-2}&\textbf{2020}&\textbf{2019}&\textbf{2018}&\textbf{2017-1}&\textbf{2017-2}&\textbf{2016-1}&\textbf{2016-2}&\textbf{Minimum}&\textbf{Average}&\textbf{Maximum}
\\\hline\textbf{1 Mark Count} & 1&2&3&2&4&2&3&2&3&3&1&2.5&4
\\\hline\textbf{2 Marks Count} & 2&2&2&1&2&2&0&4&2&0&0&1.7&4
\\\hline\textbf{Total Marks} & 5&6&7&4&8&6&3&10&7&3&\bf{3}&\bf{5.9}&\bf{10}\\\hline
\end{array}}}$$

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Previous GATE Questions in Digital Logic

31 votes
6 answers
121
GATE CSE 1995 | Question: 2.12, ISRO2015-9
The number of $1$'s in the binary representation of $(3\ast4096 + 15\ast256 + 5\ast16 + 3)$ are: $8$ $9$ $10$ $12$
The number of $1$'s in the binary representation of $(3\ast4096 + 15\ast256 + 5\ast16 + 3)$ are:$8$$9$$10$$12$
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25 votes
4 answers
122
GATE CSE 1995 | Question: 2.5
What values of $A, B, C$ and $D$ satisfy the following simultaneous Boolean equations? $\overline{A} + AB =0, AB=AC, AB+A\overline{C}+CD=\overline{C}D$ $A=1, B=0, C=0, D=1$ $A=1, B=1, C=0, D=0$ $A=1, B=0, C=1, D=1$ $A=1, B=0, C=0, D=0$
What values of $A, B, C$ and $D$ satisfy the following simultaneous Boolean equations?$\overline{A} + AB =0, AB=AC, AB+A\overline{C}+CD=\overline{C}D$$A=1, B=0, C=0, D=1$...
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25 votes
2 answers
124
GATE CSE 1994 | Question: 11
Find the contents of the flip-flop $Q_2, Q_1$ and $Q_0$ in the circuit of figure, after giving four clock pulses to the clock terminal. Assume $Q_2Q_1Q_0=000$ initially.
Find the contents of the flip-flop $Q_2, Q_1$ and $Q_0$ in the circuit of figure, after giving four clock pulses to the clock terminal. Assume $Q_2Q_1Q_0=000$ initially.
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21 votes
2 answers
126
GATE CSE 1994 | Question: 2.7
Consider $n$-bit (including sign bit) $2's$ complement representation of integer numbers. The range of integer values, $N$, that can be represented is ______ $\leq N \leq $______ .
Consider $n$-bit (including sign bit) $2's$ complement representation of integer numbers. The range of integer values, $N$, that can be represented is ______ $\leq N \leq...
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19 votes
1 answer
127
GATE CSE 1994 | Question: 2-1
The number of flip-flops required to construct a binary modulo $N$ counter is __________
The number of flip-flops required to construct a binary modulo $N$ counter is __________
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25 votes
1 answer
128
GATE CSE 1994 | Question: 1.8
The logic expression for the output of the circuit shown in figure below is: $\overline{AC} + \overline{BC} +CD$ $\overline{A}C + \overline{B}C + CD$ $ABC +\overline {C}\; \overline{D}$ $\overline{A}\; \overline{B} + \overline{B}\; \overline{C} +CD$
The logic expression for the output of the circuit shown in figure below is:$\overline{AC} + \overline{BC} +CD$$\overline{A}C + \overline{B}C + CD$$ABC +\overline {C}\; \...
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17 votes
2 answers
130
GATE CSE 1993 | Question: 9
Assume that only half adders are available in your laboratory. Show that any binary function can be implemented using half adders only.
Assume that only half adders are available in your laboratory. Show that any binary function can be implemented using half adders only.
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21 votes
2 answers
131
GATE CSE 1993 | Question: 6.1
Identify the logic function performed by the circuit shown in figure. exclusive OR exclusive NOR NAND NOR None of the above
Identify the logic function performed by the circuit shown in figure. exclusive ORexclusive NORNANDNORNone of the above
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20 votes
3 answers
132
GATE CSE 1993 | Question: 6.5
Convert the following numbers in the given bases into their equivalents in the desired bases: $(110.101)_{2} = (x)_{10} $ $(1118)_{10} = (y)_{H}$
Convert the following numbers in the given bases into their equivalents in the desired bases:$(110.101)_{2} = (x)_{10} $$(1118)_{10} = (y)_{H}$
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27 votes
2 answers
136
GATE CSE 1997 | Question: 5.4
Given $\sqrt{(224)_r} =(13)_r$. The value of the radix $r$ is: $10$ $8$ $5$ $6$
Given $\sqrt{(224)_r} =(13)_r$.The value of the radix $r$ is:$10$$8$$5$$6$
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39 votes
9 answers
137
GATE CSE 1997 | Question: 5.1
Let $f(x, y, z)=\bar{x} + \bar{y}x + xz$ be a switching function. Which one of the following is valid? $\bar{y} x$ is a prime implicant of $f$ $xz$ is a minterm of $f$ $xz$ is an implicant of $f$ $y$ is a prime implicant of $f$
Let $f(x, y, z)=\bar{x} + \bar{y}x + xz$ be a switching function. Which one of the following is valid?$\bar{y} x$ is a prime implicant of $f$$xz$ is a minterm of $f$$xz$ ...
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27 votes
4 answers
139
GATE CSE 1997 | Question: 2-1
Let $*$ be defined as $x * y = \bar{x} + y$. Let $z = x * y$. Value of $z * x$ is $\bar{x} + y$ $x$ $0$ $1$
Let $*$ be defined as $x * y = \bar{x} + y$. Let $z = x * y$. Value of $z * x$ is $\bar{x} + y$$x$$0$$1$
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53 votes
10 answers
140
GATE CSE 2010 | Question: 32
In the sequential circuit shown below, if the initial value of the output $Q_1Q_0$ is $00$. What are the next four values of $Q_1Q_0$? $11$, $10$, $01$, $00$ $10$, $11$, $01$, $00$ $10$, $00$, $01$, $11$ $11$, $10$, $00$, $01$
In the sequential circuit shown below, if the initial value of the output $Q_1Q_0$ is $00$. What are the next four values of $Q_1Q_0$? $11$, $10$, $01$, $00$$10$, $11$, $...
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