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

$$\small{\overset{{\large{\textbf{Mark Distribution in Previous GATE}}}}{\begin{array}{|c|c|c|c|c|c|c|c|}\hline \textbf{Year}&\textbf{2019}&\textbf{2018}&\textbf{2017-1}&\textbf{2017-2}&\textbf{2016-1}&\textbf{2016-2}&\textbf{Minimum}&\textbf{Average}&\textbf{Maximum} \\\hline\textbf{1 Mark Count}&4&2&3&2&3&3&2&2.8&4 \\\hline\textbf{2 Marks Count}&2&2&0&4&2&0&0&1.7&4 \\\hline\textbf{Total Marks}&8&6&3&10&7&3&\bf{3}&\bf{6.2}&\bf{10}\\\hline \end{array}}}$$

# Recent questions in Digital Logic

1
ECL is the fastest of all logic families. High speed in ECL is possible because transistors are used in difference amplifier configuration, in which they are never driven into ________. Race condition Saturation Delay High impedance
2
A binary $3$-bit down counter uses $J$-$K$ flip-flops, $FF_{i}$ with inputs $J_{i}$, $K_{i}$ and outputs $Q_{i}$, $i$ = $0, 1, 2$ respectively. The minimized expression for the input from following is : $J_{0} = K_{0} = 0$ $J_{0} = K_{0} = 1$ $J_{1} = K_{1} = Q_{0}$ ... $J_{2} = K_{2} =\overline{Q}_{1} \overline{Q}_{0}$ I, III, V I, IV, VI II, III, V II, IV, VI
3
Convert the octal number $0.4051$ into its equivalent decimal number. $0.5100098$ $0.2096$ $0.52$ $0.4192$
4
The hexadecimal equivalent of the octal number $2357$ is : $2EE$ $2FF$ $4EF$ $4FE$
5
If $X$ is a binary number which is power of $2$, then the value of $X \& (X-1)$ is : $11\dots11$ $00\dots00$ $100\dots0$ $000\dots1$
6
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 register will move to the accumulator. The number of select lines needed for the multiplexer is ______.
7
If there are $m$ input lines $n$ 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 ________ .
8
Consider the Boolean function $z(a,b,c)$. Which one of the following minterm lists represents the circuit given above? $z=\sum (0,1,3,7)$ $z=\sum (1,4,5,6,7)$ $z=\sum (2,4,5,6,7)$ $z=\sum (2,3,5)$
9
Consider the (decimal) number $182$, whose binary representation is $10110110$. How many positive integers are there in the following set?$\{n\in \mathbb{N}: n\leq 182 \text{ and n has } \textit{exactly four} \text{ ones in its binary representation}\}$ $91$ $70$ $54$ $35$ $27$
10
Consider the following Boolean valued function on $n$ Boolean variables: $f(x_{1},\dots,x_{n}) = x_{1} + \dots + x_{n}(\text{mod } 2)$, where addition is over integers, mapping $\textbf{ FALSE'}$ to $0$ and $\textbf{ TRUE'}$ to $1.$ Consider Boolean circuits (with no feedback) that use ... $n^{c}$, for some fixed constant $c$ $n^{\omega(1)}$, but $n^{O(\log n)}$ $2^{\Theta(n)}$ None of the others
11
The following circuit compares two $2$-bit binary numbers, $X$ and $Y$ represented by $X_1X_0$ and $Y_1Y_0$ respectively. ($X_0$ and $Y_0$ represent Least Significant Bits) Under what conditions $Z$ will be $1$? $X>Y$ $X<Y$ $X=Y$ $X!=Y$
12
To send same bit sequence, $\text{NRZ}$ encoding require Same clock frequency as Manchester encoding Half the clock frequency as Manchester encoding Twice the clock frequency as Manchester encoding A clock frequency which depend on number of zeroes and ones in the bit sequence
13
A new flipflop with inputs $X$ and $Y$, has the following property $\begin{array}{|c|c|c|}\hline \bf{X}& \bf{Y}& \bf{Current\ state}&\bf{ Next\ state} \\\hline 0&0&Q&1 \\ 0&1&Q&\overline{Q}\\ 1& 1&Q&0 \\ 1&0&Q&Q \\ \hline \end{array}$ Which of the following expresses the next ... $(X\wedge \overline{Q })\vee (Y \wedge Q)$ $(X\wedge \overline{Q })\vee (\overline{Y } \wedge Q)$
14
If $ABCD$ is a $4$-bit binary number, then what is the code generated by the following circuit? BCD code Gray code $8421$ code Excess-$3$ code
15
Minimum number of NAND gates required to implement the following binary equation $Y = (\overline{A}+\overline{B})(C+D)$ $4$ $5$ $3$ $6$
16
Consider the following circuit The function by the network above is $\overline{AB}E+EF+\overline{CD}F$ $(\overline{E}+AB\overline{F})(C+D+\overline{F})$ $(\overline{AB}+E)(\overline{E}+\overline{F})(C+D+\overline{F})$ $(A+B)\overline{E} +\overline{EF}+CD\overline{F}$
17
Following Multiplexer circuit is equivalent to Sum equation of full adder Carry equation of full adder Borrow equation for full subtractor Difference equation of a full subtractor
In a $8$-bit ripple carry adder using identical full adders, each full adder takes $34$ ns for computing sum. If the time taken for $8$-bit addition is $90$ ns, find time taken by each full adder to find carry. $6$ ns $7$ ns $10$ ns $8$ ns
The value of the Boolean expression (with usual definitions) $(A’BC’)’ +(AB’C)’$ is $0$ $1$ $A$ $BC$