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

$$\scriptsize{\overset{{\large{\textbf{Mark Distribution in Previous GATE}}}}{\begin{array}{|c|c|c|c|c|c|c|c|}\hline
\textbf{Year}& \textbf{2024-1} & \textbf{2024-2}  & \textbf{2023}& \textbf{2022} & \textbf{2021-1}&\textbf{2021-2}&\textbf{Minimum}&\textbf{Average}&\textbf{Maximum}
\\\hline\textbf{1 Mark Count} & 2&2&2&1&2&3&1&2&3
\\\hline\textbf{2 Marks Count} & 2&2&2&2&2&2&2&2&2
\\\hline\textbf{Total Marks} & 6&6&6&5&6&7&\bf{5}&\bf{6}&\bf{7}\\\hline
\end{array}}}$$

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Previous GATE Questions in Digital Logic

#1
3.0k
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1 answers
1 votes
GATE CSE 2024 | Set 2 | Question: 4
​​The format of a single-precision floating-point number as per the $\text{IEEE 754}$ standard is:Sign ExponentMantissa$(1 \mathrm{bit})$ $(8 \mathrm{bits})$ $(23 \ma...
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#2
2.5k
views
4 answers
2 votes
GATE CSE 2024 | Set 2 | Question: 20
​​​​For a Boolean variable $x$, which of the following statements is/are FALSE?$x .1=x$$x+1=x$$x \cdot x=0$$x+\bar{x}=1$
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#3
2.1k
views
1 answers
2 votes
GATE CSE 2024 | Set 2 | Question: 39
Which of the following is/are EQUAL to $224$ in radix - $5$ (i.e., base - $5$) notation?$64$ in radix -10$100$ in radix -8$50$ in radix -16$121$ in radix -7
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#4
2.2k
views
1 answers
4 votes
GATE CSE 2024 | Set 2 | Question: 40
Consider $4$-variable functions $f 1, f 2, f 3, f 4$ expressed in sum-of-minterms form as given below.$$\begin{array}{l}f 1=\sum(0,2,3,5,7,8,11,13) \\f 2=\sum(1,3,5,7,11,...
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#5
4.5k
views
5 answers
4 votes
GATE CSE 2024 | Set 1 | Question: 3
Consider a system that uses $5$ bits for representing signed integers in $2$ 's complement format. In this system, two integers $A$ and $B$ are represented as $A$=$01010$...
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#6
2.8k
views
1 answers
3 votes
GATE CSE 2024 | Set 1 | Question: 18
​​Consider the circuit shown below where the gates may have propagation delays. Assume that all signal transitions occur instantaneously and that wires have no delays...
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#7
2.4k
views
2 answers
1 votes
GATE CSE 2024 | Set 1 | Question: 37
Consider a Boolean expression given by $\text{F(X, Y, Z)}=\sum(3,5,6,7)$.Which of the following statements is/are CORRECT?$\text{F(X, Y, Z)}=\Pi(0,1,2,4)$ $\text{F(X, Y, ...
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#8
2.6k
views
3 answers
2 votes
GATE CSE 2024 | Set 1 | Question: 54
Consider a digital logic circuit consisting of three $2$-to-$1$ multiplexers $\text{M1, M2}$, and $\text{M3}$ as shown below. $\mathrm{X} 1$ and $\mathrm{X} 2$ are inputs...
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#9
405
views
1 answers
1 votes
GATE CSE 1996 Question 1.25
I can’t understand what is ment by that: I can’t understand what is the bit required by the exponent and the mantissa.Question link: https:/...
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#10
11.3k
views
3 answers
9 votes
GATE CSE 2023 | Question: 11
The output of a $2$-input multiplexer is connected back to one of its inputs as shown in the figure.Match the functional equivalence of this circuit to one of the followi...
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#11
13.2k
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2 answers
7 votes
GATE CSE 2023 | Question: 22
A particular number is written as $132$ in radix-$4$ representation. The same number in radix-$5$ representation is _____________.
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#12
9.7k
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1 answers
8 votes
GATE CSE 2023 | Question: 33
Consider a sequential digital circuit consisting of $\mathrm{T}$ flip-flops and $\mathrm{D}$ flip-flops as shown in the figure. $\text{CLKIN}$ is the clock input to the c...
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#13
10.3k
views
3 answers
21 votes
GATE CSE 2023 | Question: 34
A Boolean digital circuit is composed using two $4$-input multiplexers $\text{(M1 and M2)}$ and one $2$-input multiplexer $\text{(M3)}$ as shown in the figure. $\text{X0-...
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#14
11.2k
views
2 answers
10 votes
GATE CSE 2023 | Question: 35
Consider the $\textsf{IEEE-754}$ single precision floating point numbers $\text{P} = \textsf{0xC1800000}$ and $\text{Q} = \textsf{0x3F5C2EF4}.$Which one of the following ...
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#15
1.2k
views
1 answers
2 votes
GATE CSE 2023 | Memory Based Question: 22
The initial state of a given sequential circuit is $Q_0 Q_1 Q_2=011$. Which of the following state does not occur$101$$111$$001$$100$
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#16
9.2k
views
2 answers
11 votes
GATE CSE 2022 | Question: 8
Let $\text{R1}$ and $\text{R2}$ be two $4 – \text{bit}$ registers that store numbers in $2\text{’s}$ complement form. For the operation $\text{R1 + R2},$ which one of...
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#17
5.1k
views
2 answers
13 votes
GATE CSE 2022 | Question: 30
Consider a digital display system $\text{(DDS)}$ shown in the figure that displays the contents of register $\text{X}.$ A $16 – \text{bit}$ code word is used to load a...
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#18
8.9k
views
3 answers
7 votes
GATE CSE 2022 | Question: 31
Consider three floating point numbers $\textit{A, B}$ and $\textit{C}$ stored in registers $\text{R}_{\text{A}}, \text{R}_{\text{B}}$ and $\text{R}_{\text{C}},$ respectiv...
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#19
10.5k
views
3 answers
21 votes
GATE CSE 2021 Set 2 | Question: 4
The format of the single-precision floating point representation of a real number as per the $\text{IEEE 754}$ standard is as follows:$$\begin{array}{|c|c|c|} \hline \tex...
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#20
9.5k
views
6 answers
18 votes
GATE CSE 2021 Set 2 | Question: 5
Which one of the following circuits implements the Boolean function given below?$f(x,y,z) = m_0+m_1+m_3+m_4+m_5+m_6$, where $m_i$ is the $i^{\text{th}}$ minterm.
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