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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

7 votes
1 answer
41
GATE CSE 1995 | Question: 15-b
What is the equivalent minimal Boolean expression (in sum of products form) for the Karnaugh map given below?
What is the equivalent minimal Boolean expression (in sum of products form) for the Karnaugh map given below?
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6 votes
1 answer
43
GATE CSE 1996 | Question: 24-b
Consider the synchronous sequential circuit in the below figure Given that the initial state of the circuit is $S_4,$ identify the set of states, which are not reachable.
Consider the synchronous sequential circuit in the below figureGiven that the initial state of the circuit is $S_4,$ identify the set of states, which are not reachable.
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32 votes
4 answers
45
GATE CSE 2017 Set 2 | Question: 42
The next state table of a $2-$ ... $T_1 = Q_1+Q_0, \quad T_0= \bar{Q_1} \bar{Q_0}$ $T_1 = \bar{Q_1}Q_0, \quad T_0= Q_1 + Q_0$
The next state table of a $2-$bit saturating up-counter is given below.$\begin{array}{cc|cc} Q_1 & Q_0 & Q_1^+ & Q_0^+ \\ \hline 0 & 0 & 0 & 1 \\ 0 & 1 & 1 & 0 \\ 1 & 0...
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24 votes
7 answers
49
GATE CSE 2017 Set 2 | Question: 1
The representation of the value of a $16\text{-bit}$ unsigned integer $X$ in hexadecimal number system is $\textsf{BCA9}$. The representation of the value of $X$ in octal number system is $571244$ $736251$ $571247$ $136251$
The representation of the value of a $16\text{-bit}$ unsigned integer $X$ in hexadecimal number system is $\textsf{BCA9}$. The representation of the value of $X$ in octal...
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7 votes
2 answers
54
GATE CSE 1988 | Question: 4ii
Using binary full adders and other logic gates (if necessary), design an adder for adding $4$-bit number (including sign) in $2’s$ complement notation.
Using binary full adders and other logic gates (if necessary), design an adder for adding $4$-bit number (including sign) in $2’s$ complement notation.
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14 votes
1 answer
56
GATE CSE 1988 | Question: 2-vi
Define the value of $r$ in the following: $\sqrt {(41)_{r}} = (7)_{10}$
Define the value of $r$ in the following: $\sqrt {(41)_{r}} = (7)_{10}$
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20 votes
1 answer
58
GATE CSE 1988 | Question: 2-iii
Let $*$ be defined as a Boolean operation given as $x*y = \overline{x}\;\;\overline{y}+xy$ and let $C=A*B$. If $C=1$ then prove that $A=B$.
Let $*$ be defined as a Boolean operation given as $x*y = \overline{x}\;\;\overline{y}+xy$ and let $C=A*B$. If $C=1$ then prove that $A=B$.
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26 votes
3 answers
60
GATE CSE 1989 | Question: 5-a
Find values of Boolean variables $A, B, C$ which satisfy the following equations: A+ B = 1 AC = BC A + C = 1 AB = 0
Find values of Boolean variables $A, B, C$ which satisfy the following equations:A+ B = 1AC = BCA + C = 1AB = 0
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