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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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Highest voted questions in Digital Logic

44 votes
7 answers
45
GATE CSE 2015 Set 3 | Question: 43
The total number of prime implicants of the function $f(w, x, y, z) = \sum (0, 2, 4, 5, 6, 10)$ is __________
The total number of prime implicants of the function $f(w, x, y, z) = \sum (0, 2, 4, 5, 6, 10)$ is __________
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44 votes
5 answers
46
GATE CSE 2004 | Question: 61
Consider the partial implementation of a $2-bit$ counter using $T$ flip-flops following the sequence $0-2-3-1-0,$ as shown below. To complete the circuit, the input $X$ should be $Q_2^c$ $Q_2 + Q_1$ $\left(Q_1 + Q_2\right)^c$ $Q_1 \oplus Q_2$
Consider the partial implementation of a $2-bit$ counter using $T$ flip-flops following the sequence $0-2-3-1-0,$ as shown below.To complete the circuit, the input $X$ sh...
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43 votes
6 answers
48
GATE CSE 2009 | Question: 6
What is the minimum number of gates required to implement the Boolean function $\text{(AB+C)}$ if we have to use only $2\text{-input NOR}$ gates? $2$ $3$ $4$ $5$
What is the minimum number of gates required to implement the Boolean function $\text{(AB+C)}$ if we have to use only $2\text{-input NOR}$ gates?$2$$3$$4$$5$
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43 votes
6 answers
49
GATE CSE 2007 | Question: 32
Let $f(w, x, y, z) = \sum {\left(0,4,5,7,8,9,13,15\right)}$. Which of the following expressions are NOT equivalent to $f$? P: $x'y'z' + w'xy' + wy'z + xz$ Q: $w'y'z' + wx'y' + xz$ ... $x'y'z' + wx'y'+ w'y$ P only Q and S R and S S only
Let $f(w, x, y, z) = \sum {\left(0,4,5,7,8,9,13,15\right)}$. Which of the following expressions are NOT equivalent to $f$?P: $x'y'z' + w'xy' + wy'z + xz$Q: $w'y'z' + wx'y...
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43 votes
3 answers
50
GATE CSE 2012 | Question: 19
The amount of ROM needed to implement a $4\text{-bit}$ multiplier is $64$ bits $128$ bits $1$ Kbits $2$ Kbits
The amount of ROM needed to implement a $4\text{-bit}$ multiplier is$64$ bits$128$ bits$1$ Kbits$2$ Kbits
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42 votes
4 answers
51
GATE IT 2005 | Question: 7
Which of the following expressions is equivalent to $(A \oplus B) \oplus C$ $(A + B + C) (\bar A +\bar B +\bar C)$ $(A + B + C) (\bar A +\bar B + C)$ $ABC + \bar A (B \oplus C) + \bar B(A \oplus C)$ None of these
Which of the following expressions is equivalent to $(A \oplus B) \oplus C$$(A + B + C) (\bar A +\bar B +\bar C)$$(A + B + C) (\bar A +\bar B + C)$$ABC + \bar A (B \oplus...
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42 votes
4 answers
52
GATE CSE 1998 | Question: 1.13
What happens when a bit-string is XORed with itself $n$-times as shown: $\left[B \oplus (B \oplus ( B \oplus (B \dots n \text{ times}\right]$ complements when $n$ is even complements when $n$ is odd divides by $2^n$ always remains unchanged when $n$ is even
What happens when a bit-string is XORed with itself $n$-times as shown:$\left[B \oplus (B \oplus ( B \oplus (B \dots n \text{ times}\right]$complements when $n$ is evenco...
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41 votes
6 answers
56
GATE CSE 1999 | Question: 2.16
The number of full and half-adders required to add $16$-bit numbers is $8$ half-adders, $8$ full-adders $1$ half-adder, $15$ full-adders $16$ half-adders, $0$ full-adders $4$ half-adders, $12$ full-adders
The number of full and half-adders required to add $16$-bit numbers is$8$ half-adders, $8$ full-adders$1$ half-adder, $15$ full-adders$16$ half-adders, $0$ full-adders$4$...
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40 votes
5 answers
59
GATE CSE 1996 | Question: 2.23
Consider the following state table for a sequential machine. The number of states in the minimized machine will be ... $4$ $3$ $2$ $1$
Consider the following state table for a sequential machine. The number of states in the minimized machine will be$$\begin{array}{|l|l|ll|}\hline \text{} & \text{} & \tex...
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