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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

#241
11.7k
views
5 answers
48 votes
GATE CSE 2001 | Question: 2.11
Consider the circuit shown below. The output of a $2:1$ MUX is given by the function $(ac' + bc)$.Which of the following is true?$f=X_1'+X_2$$f=X_1'X_2+X_1X_2'$$f=X_1X_2+...
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#242
12.3k
views
4 answers
31 votes
GATE CSE 2001 | Question: 2.10
The $2's$ complement representation of (-539)10 in hexadecimal is$ABE$$DBC$$DE5$$9E7$
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#243
21.8k
views
5 answers
62 votes
GATE CSE 2001 | Question: 2.8
Consider the following circuit with initial state $Q_0 = Q_1 = 0$. The D Flip-flops are positive edged triggered and have set up times 20 nanosecond and hold times $0.$Co...
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#244
7.4k
views
2 answers
30 votes
GATE CSE 2001 | Question: 1.11
Given the following karnaugh map, which one of the following represents the minimal Sum-Of-Products of the map? $XY+Y'Z$$WX'Y' + XY +XZ$$W'X+Y'Z+XY$$XZ+Y$
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#245
3.0k
views
3 answers
19 votes
GATE CSE 2000 | Question: 9
Design a logic circuit to convert a single digit BCD number to the number modulo six as follows (Do not detect illegal input):Write the truth table for all bits. Label th...
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#246
12.3k
views
4 answers
41 votes
GATE CSE 2000 | Question: 2.14
Consider the values of $A = 2.0 \times 10^{30}, B = -2.0 \times 10^{30}, C = 1.0,$ and the sequence X:= A + B Y:= A + C X:= X + C Y:= Y + Bexecuted on a computer where fl...
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#247
11.9k
views
5 answers
38 votes
GATE CSE 2000 | Question: 2.12
The following arrangement of master-slave flip flopshas the initial state of $P, Q$ as $0, 1$ (respectively). After three clock cycles the output state $P, Q$ is (respect...
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#248
7.4k
views
6 answers
36 votes
GATE CSE 2000 | Question: 2.11
Which functions does NOT implement the Karnaugh map given below? $(w + x) y$$xy + yw$$(w + x) (\bar{w} + y) (\bar{x} + y)$None of t...
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#249
7.4k
views
5 answers
42 votes
GATE CSE 2000 | Question: 2.10
The simultaneous equations on the Boolean variables $x, y, z$ and $w$,$x + y + z = 1 $$xy = 0$$xz + w = 1$$xy + \bar{z}\bar{w} = 0$have the following solution for $x, y, ...
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#250
11.2k
views
4 answers
39 votes
GATE CSE 2000 | Question: 1.6
The number $43$ in $2's$ complement representation is$01010101$$11010101$$00101011$$10101011$
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#251
1.1k
views
0 answers
2 votes
GATE CSE 1992 | Question: 06,a,b
A microprocessor is capable of addressing 1 megabyte of memory with a 20-bit address bus. The system to be designed requires 256 K bytes of RAM, 256 K bytes of EPROM, 16 ...
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#252
2.7k
views
3 answers
16 votes
GATE CSE 1992 | Question: 4-a
Consider addition in two's complement arithmetic. A carry from the most significant bit does not always correspond to an overflow. Explain what is the condition for overf...
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#253
11.0k
views
4 answers
26 votes
GATE CSE 1992 | Question: 02-ii
All digital circuits can be realized using onlyEx-OR gatesMultiplexersHalf addersOR gates
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#254
7.7k
views
4 answers
30 votes
GATE CSE 1992 | Question: 02-i
The operation which is commutative but not associative is:ANDOREX-ORNAND
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#255
5.5k
views
5 answers
24 votes
GATE CSE 1992 | Question: 01-i
The Boolean function in sum of products form where K-map is given below (figure) is _______
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#256
1.6k
views
2 answers
6 votes
GATE CSE 1991 | Question: 06,a
Using $\text{D}$ flip-flop gates, design a parallel-in/serial-out shift register that shifts data from left to right with the following input lines:Clock $\text{CLK}$Thre...
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#257
4.0k
views
1 answers
28 votes
GATE CSE 1991 | Question: 5-a
Analyse the circuit in Fig below and complete the following table$${\begin{array}{|c|c|c|}\hline\textbf{a}& \textbf{b}& \bf{ Q_n} \\\hline0&0\\\ 0&1 \\ 1&0 \\ 1...
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#258
8.8k
views
2 answers
30 votes
GATE CSE 1991 | Question: 03-ii
Advantage of synchronous sequential circuits over asynchronous ones is:faster operationease of avoiding problems due to hazardslower hardware requirementbetter noise immu...
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#259
1.7k
views
3 answers
6 votes
GATE CSE 1991 | Question: 03,i
Choose the correct alternatives (more than one may be correct) and write the corresponding letters only:(i). The advantages of CMOS technology over a MOS is:(A). lower po...
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#260
5.1k
views
1 answers
38 votes
GATE CSE 1991 | Question: 01-v
When two $4$-bit numbers $A = a_3a_2a_1a_0$ and $B=b_3b_2b_1b_0$ are multiplied, the bit $c_1$ of the product $C$ is given by ________
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