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

$$\scriptsize{\overset{{\large{\textbf{Mark Distribution in Previous GATE}}}}{\begin{array}{|c|c|c|c|c|c|c|c|}\hline
\textbf{Year}& \textbf{2022} & \textbf{2021-1}&\textbf{2021-2}&\textbf{2020}&\textbf{2019}&\textbf{2018}&\textbf{2017-1}&\textbf{2017-2}&\textbf{2016-1}&\textbf{2016-2}&\textbf{Minimum}&\textbf{Average}&\textbf{Maximum}
\\\hline\textbf{1 Mark Count} & 1&2&3&2&4&2&3&2&3&3&1&2.5&4
\\\hline\textbf{2 Marks Count} & 2&2&2&1&2&2&0&4&2&0&0&1.7&4
\\\hline\textbf{Total Marks} & 5&6&7&4&8&6&3&10&7&3&\bf{3}&\bf{5.9}&\bf{10}\\\hline
\end{array}}}$$

Recent questions in Digital Logic

27 votes
1 answer
3221
29 votes
2 answers
3222
37 votes
1 answer
3224
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 ________
25 votes
5 answers
3225
Consider the number given by the decimal expression:$$16^3*9 + 16^2*7 + 16*5+3$$The number of $1’s$ in the unsigned binary representation of the number is ______
31 votes
4 answers
3226
If $P, Q, R$ are Boolean variables, then$(P + \bar{Q}) (P.\bar{Q} + P.R) (\bar{P}.\bar{R} + \bar{Q})$ simplifies to$P.\bar{Q}$$P.\bar{R}$$P.\bar{Q} + R$$P.\bar{R} + Q$
29 votes
2 answers
3228
Let $r$ denote number system radix. The only value(s) of $r$ that satisfy the equation $\sqrt{121_r}={11}_r$ is/aredecimal $10$decimal $11$decimal $10$ and $11$any value ...
38 votes
2 answers
3230
2 votes
2 answers
3231
43 votes
3 answers
3234
The amount of ROM needed to implement a $4\text{-bit}$ multiplier is$64$ bits$128$ bits$1$ Kbits$2$ Kbits