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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

11 votes
2 answers
62
GATE CSE 1989 | Question: 4-ix
Explain the behaviour of the following logic circuit with level input $A$ and output $B$.
Explain the behaviour of the following logic circuit with level input $A$ and output $B$.
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10 votes
3 answers
63
GATE CSE 1989 | Question: 4-iii
Show that {NOR} is a functionally complete set of Boolean operations.
Show that {NOR} is a functionally complete set of Boolean operations.
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17 votes
2 answers
64
GATE CSE 1990 | Question: 1-viii
The condition for overflow in the addition of two $2's$ complement numbers in terms of the carry generated by the two most significant bits is ___________.
The condition for overflow in the addition of two $2's$ complement numbers in terms of the carry generated by the two most significant bits is ___________.
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5 votes
1 answer
66
GATE CSE 1990 | Question: 8b
State the Booth's algorithm for multiplication of two numbers. Draw a block diagram for the implementation of the Booth's algorithm for determining the product of two $8$-bit signed numbers.
State the Booth's algorithm for multiplication of two numbers. Draw a block diagram for the implementation of the Booth's algorithm for determining the product of two $8$...
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23 votes
6 answers
68
GATE CSE 1990 | Question: 5-b
Show with the help of a block diagram how the Boolean function : $f=AB+BC+CA$ can be realised using only a $4:1$ multiplexer.
Show with the help of a block diagram how the Boolean function :$f=AB+BC+CA$can be realised using only a $4:1$ multiplexer.
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19 votes
3 answers
69
GATE CSE 1990 | Question: 5-a
Find the minimum product of sums of the following expression $f=ABC + \overline{A}\;\;\overline{B}\;\;\overline{C}$
Find the minimum product of sums of the following expression$f=ABC + \overline{A}\;\;\overline{B}\;\;\overline{C}$
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10 votes
1 answer
70
GATE CSE 1990 | Question: 4-i
State whether the following statements are TRUE or FALSE with reason: RAM is a combinational circuit and PLA is a sequential circuit.
State whether the following statements are TRUE or FALSE with reason:RAM is a combinational circuit and PLA is a sequential circuit.
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21 votes
4 answers
72
GATE CSE 1990 | Question: 1-iv-a
A $32$-bit floating-point number is represented by a $7$-bit signed exponent, and a $24$-bit fractional mantissa. The base of the scale factor is $16,$ The range of the exponent is ___________
A $32$-bit floating-point number is represented by a $7$-bit signed exponent, and a $24$-bit fractional mantissa. The base of the scale factor is $16,$The range of the ex...
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34 votes
1 answer
73
GATE CSE 1990 | Question: 1-i
Fill in the blanks: In the two bit full-adder/subtractor unit shown in below figure, when the switch is in position $2$ ___________ using _________ arithmetic.
Fill in the blanks:In the two bit full-adder/subtractor unit shown in below figure, when the switch is in position $2$ ___________ using _________ arithmetic.
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21 votes
3 answers
74
GATE CSE 1987 | Question: 16-a
A Boolean function $f$ is to be realized only by $\text{NOR}$ gates. Its $K$-map is given below: The realization is
A Boolean function $f$ is to be realized only by $\text{NOR}$ gates. Its $K$-map is given below:The realization is
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18 votes
3 answers
75
GATE CSE 1987 | Question: 13-a
The below figure shows four $\text{D}$-type flip-flops connected as a shift register using a $\text{XOR}$ ... $Q_{A} Q_{B} Q_{C} Q_{D}$ after the fourth clock pulse is $0000$ $1111$ $1001$ $1000$
The below figure shows four $\text{D}$-type flip-flops connected as a shift register using a $\text{XOR}$ gate. The initial state and three subsequent states for three cl...
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28 votes
3 answers
76
GATE CSE 1987 | Question: 12-a
The Boolean expression $A \oplus B \oplus A$ is equivalent to $AB + \overline {A}\;\;\overline B$ $\overline{A}\;B+A\;\overline{B}$ $B$ $\overline{A}$
The Boolean expression $A \oplus B \oplus A$ is equivalent to$AB + \overline {A}\;\;\overline B$$\overline{A}\;B+A\;\overline{B}$$B$$\overline{A}$
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6 votes
1 answer
77
GATE CSE 1987 | Question: 10c
Give a minimal DFA that performs as a $\mod - 3,\;$ $1$'s counter, i.e. outputs a $1$ each time the number of $1$'s in the input sequence is a multiple of $3$.
Give a minimal DFA that performs as a $\mod - 3,\;$ $1$'s counter, i.e. outputs a $1$ each time the number of $1$'s in the input sequence is a multiple of $3$.
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1 votes
0 answers
79
GATE CSE 1987 | Question: 3a
Design an $8 \times 8$ multiplier using five $4$-bits adders and $4$ ROM's each programmed to realise $4 \times 4$ multiplier.
Design an $8 \times 8$ multiplier using five $4$-bits adders and $4$ ROM's each programmed to realise $4 \times 4$ multiplier.
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22 votes
2 answers
80
GATE CSE 1987 | Question: 1-vii
The exponent of a floating-point number is represented in excess-$\text{N}$ code so that: The dynamic range is large. The precision is high. The smallest number is represented by all zeros. Overflow is avoided.
The exponent of a floating-point number is represented in excess-$\text{N}$ code so that:The dynamic range is large.The precision is high.The smallest number is represent...
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