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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

#21
5.1k
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3 answers
13 votes
GATE CSE 2021 Set 2 | Question: 18
If $x$ and $y$ are two decimal digits and $(0.1101)_2 = (0.8xy5)_{10}$, the decimal value of $x+y$ is ___________
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#22
15.1k
views
6 answers
30 votes
GATE CSE 2021 Set 2 | Question: 44
If the numerical value of a $2$-byte unsigned integer on a little endian computer is $255$ more than that on a big endian computer, which of the following choices represe...
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#23
13.8k
views
3 answers
27 votes
GATE CSE 2021 Set 2 | Question: 52
Consider a Boolean function $f(w,x,y,z)$ such that $$\begin{array}{lll} f(w,0,0,z) & = & 1 \\ f(1,x,1,z) & =& x+z \\ f(w,1,y,z) & = & wz +y \end{array}$$The number of li...
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#24
9.1k
views
4 answers
9 votes
GATE CSE 2021 Set 1 | Question: 6
Let the representation of a number in base $3$ be $210$. What is the hexadecimal representation of the number?$15$$21$$\text{D}2$$528$
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#25
8.3k
views
5 answers
9 votes
GATE CSE 2021 Set 1 | Question: 24
Consider the following representation of a number in $\text{IEEE 754}$ single-precision floating point format with a bias of $127$.$$S: 1\quad\quad E:\; 10000001\quad\qu...
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#26
7.6k
views
3 answers
12 votes
GATE CSE 2021 Set 1 | Question: 28
Consider a $3$-bit counter, designed using $T$ flip-flops, as shown below:Assuming the initial state of the counter given by $\text{PQR}$ as $000$, what are the next thre...
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#27
10.7k
views
6 answers
22 votes
GATE CSE 2021 Set 1 | Question: 42
Consider the following Boolean expression.$F=(X+Y+Z)(\overline X +Y)(\overline Y +Z)$Which of the following Boolean expressions is/are equivalent to $\overline F$ (comple...
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#28
6.9k
views
2 answers
13 votes
GATE CSE 2020 | Question: 19
A multiplexer is placed between a group of $32$ registers and an accumulator to regulate data movement such that at any given point in time the content of only one regist...
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#29
10.0k
views
4 answers
17 votes
GATE CSE 2020 | Question: 20
If there are $m$ input lines and $n$ output lines for a decoder that is used to uniquely address a byte addressable $1$ KB RAM, then the minimum value of $m+n$ is _______...
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#30
8.3k
views
4 answers
15 votes
GATE CSE 2020 | Question: 28
Consider the Boolean function $z(a,b,c)$. Which one of the following minterm lists represents the circuit given above?$z=\sum (0,1,3,7)$$z=\sum (1,4,5,6,7)$$z=\sum (2,4,5...
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#31
18.8k
views
4 answers
27 votes
GATE CSE 2020 | Question: 29
Consider three registers $R1$, $R2$, and $R3$ that store numbers in $\textsf{IEEE-754}$ single precision floating point format. Assume that $R1$ and $R2$ contain the valu...
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#32
11.3k
views
4 answers
20 votes
GATE CSE 2019 | Question: 4
In $16$-bit $2$’s complement representation, the decimal number $-28$ is:$1111 \: 1111 \: 0001 \: 1100$$0000 \: 0000 \: 1110 \: 0100$$1111 \: 1111 \: 1110 \: 0100$$1000...
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#33
12.1k
views
4 answers
22 votes
GATE CSE 2019 | Question: 6
Which one of the following is NOT a valid identity?$(x \oplus y) \oplus z = x \oplus (y \oplus z)$$(x + y) \oplus z = x \oplus (y+z)$$x \oplus y = x+y, \text{ if } xy=0$$...
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#34
13.9k
views
5 answers
20 votes
GATE CSE 2019 | Question: 8
Consider $Z=X-Y$ where $X, Y$ and Z are all in sign-magnitude form. X and Y are each represented in $n$ bits. To avoid overflow, the representation of $Z$ would require a...
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#35
20.4k
views
9 answers
36 votes
GATE CSE 2019 | Question: 22
Two numbers are chosen independently and uniformly at random from the set $\{1,2,\ldots,13\}.$The probability (rounded off to $3$ decimal places) that their $4\text{-bit}...
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#36
14.7k
views
7 answers
33 votes
GATE CSE 2019 | Question: 30
Consider three $4$-variable functions $f_1, f_2$, and $f_3$, which are expressed in sum-of-minterms as$f_1=\Sigma(0,2,5,8,14),$$f_2=\Sigma(2,3,6,8,14,15),$$f_3=\Sigma (2,...
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#37
31.1k
views
11 answers
38 votes
GATE CSE 2019 | Question: 50
What is the minimum number of $2$-input NOR gates required to implement a $4$ -variable function expressed in sum-of-minterms form as $f=\Sigma(0,2,5,7, 8, 10, 13, 15)?$ ...
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#38
16.9k
views
3 answers
30 votes
GATE CSE 2018 | Question: 49
Consider the minterm list form of a Boolean function $F$ given below.$$F(P, Q, R, S) = \Sigma m(0, 2, 5, 7, 9, 11) + d(3, 8, 10, 12, 14)$$Here, $m$ denotes a minterm and ...
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#39
10.1k
views
4 answers
23 votes
GATE CSE 2018 | Question: 33
Consider the unsigned 8-bit fixed point binary number representation, below,$$b_7 \: \: b_6 \: \: b_5 \: \: b_4 \: \: b_3 \: \: \cdot b_2 \: \: b_1 \: \: b_0$$where the p...
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#40
23.8k
views
9 answers
42 votes
GATE CSE 2018 | Question: 22
Consider the sequential circuit shown in the figure, where both flip-flops used are positive edge-triggered $\text{D}$ flip-flops.The number of states in the state trans...
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