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

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

Previous GATE Questions in Digital Logic

14 votes
4 answers
1
In $16$-bit $2$’s complement representation, the decimal number $-28$ is: $1111 \: 1111 \: 0001 \: 1100$ $0000 \: 0000 \: 1110 \: 0100$ $1111 \: 1111 \: 1110 \: 0100$ $1000 \: 0000 \: 1110 \: 0100$
asked Feb 7, 2019 in Digital Logic Arjun 4.8k views
11 votes
4 answers
2
Which one of the following is NOT a valid identity? $(x \oplus y) \oplus z = x \oplus (y \oplus z)$ $(x + y) \oplus z = x \oplus (y+z)$ $x \oplus y = x+y, \text{ if } xy=0$ $x \oplus y = (xy+x’y’)’$
asked Feb 7, 2019 in Digital Logic Arjun 5.3k views
9 votes
5 answers
3
Consider $Z=X-Y$ where $X, Y$ and Z are all in sign-magnitude form. X and Y are each represented in $n$ bits. To avoid overflow, the representation of $Z$ would require a minimum of: $n$ bits $n-1$ bits $n+1$ bits $n+2$ bits
asked Feb 7, 2019 in Digital Logic Arjun 6k views
23 votes
7 answers
4
Two numbers are chosen independently and uniformly at random from the set $\{1,2,\ldots,13\}.$ The probability (rounded off to 3 decimal places) that their $4-bit$ (unsigned) binary representations have the same most significant bit is _______________.
asked Feb 7, 2019 in Digital Logic Arjun 9.2k views
17 votes
6 answers
5
Consider three $4$-variable functions $f_1, f_2$, and $f_3$, which are expressed in sum-of-minterms as $f_1=\Sigma(0,2,5,8,14),$ $f_2=\Sigma(2,3,6,8,14,15),$ $f_3=\Sigma (2,7,11,14)$ For the following circuit with one AND gate and one XOR gate the output function $f$ can be expressed as: $\Sigma(7,8,11)$ $\Sigma (2,7,8,11,14)$ $\Sigma (2,14)$ $\Sigma (0,2,3,5,6,7,8,11,14,15)$
asked Feb 7, 2019 in Digital Logic Arjun 6.1k views
17 votes
11 answers
6
What is the minimum number of $2$-input NOR gates required to implement a $4$ -variable function expressed in sum-of-minterms form as $f=\Sigma(0,2,5,7, 8, 10, 13, 15)?$ Assume that all the inputs and their complements are available. Answer: _______
asked Feb 7, 2019 in Digital Logic Arjun 13.4k views
–1 vote
1 answer
7
Answer for Minimum no of nor gates question
asked Feb 3, 2019 in Digital Logic Ashubhai Ashu 1.3k views
21 votes
3 answers
8
Consider the minterm list form of a Boolean function $F$ given below. $F(P, Q, R, S) = \Sigma m(0, 2, 5, 7, 9, 11) + d(3, 8, 10, 12, 14)$ Here, $m$ denotes a minterm and $d$ denotes a don't care term. The number of essential prime implicants of the function $F$ is ___
asked Feb 14, 2018 in Digital Logic gatecse 6.6k views
16 votes
4 answers
9
Consider the unsigned 8-bit fixed point binary number representation, below, $b_7 \: \: b_6 \: \: b_5 \: \: b_4 \: \: b_3 \: \: \cdot b_2 \: \: b_1 \: \: b_0$ where the position of the primary point is between $b_3$ and $b_2$ . Assume ... be exactly represented Only $ii$ cannot be exactly represented Only $iii$ and $iv$ cannot be exactly represented Only $i$ and $ii$ cannot be exactly represented
asked Feb 14, 2018 in Digital Logic gatecse 5.1k views
30 votes
7 answers
10
Consider the sequential circuit shown in the figure, where both flip-flops used are positive edge-triggered D flip-flops. The number of states in the state transition diagram of this circuit that have a transition back to the same state on some value of "in" is ____
asked Feb 14, 2018 in Digital Logic gatecse 10k views
16 votes
7 answers
11
Let $\oplus$ and $\odot$ denote the Exclusive OR and Exclusive NOR operations, respectively. Which one of the following is NOT CORRECT? $\overline{P \oplus Q} = P \odot Q$ $\overline{P} \oplus Q = P \odot Q$ $\overline{P} \oplus \overline{Q} = P \oplus Q$ $P \oplus \overline{P} \oplus Q = ( P \odot \overline{P} \odot \overline{Q})$
asked Feb 14, 2018 in Digital Logic gatecse 3.8k views
4 votes
1 answer
12
What is the equivalent minimal Boolean expression (in sum of products form) for the Karnaugh map given below?
asked Feb 12, 2018 in Digital Logic jothee 1k views
9 votes
3 answers
13
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 ___________, if the scale factor is represented in excess-64 format.
asked Feb 12, 2018 in Digital Logic jothee 1.7k views
10 votes
1 answer
14
A sequential circuit takes an input stream of 0's and 1's and produces an output stream of 0's and 1's. Initially it replicates the input on its output until two consecutive 0's are encountered on the input. From then onward, it produces an output stream, which is ... to be used to design the circuit. Give the minimized sum-of-product expression for J and K inputs of one of its state flip-flops
asked Feb 12, 2018 in Digital Logic jothee 1.4k views
4 votes
1 answer
15
Consider the synchronous sequential circuit in the below figure Given that the initial state of the circuit is S$_4$, identify the set of states, which are not reachable.
asked Feb 10, 2018 in Digital Logic jothee 1k views
3 votes
1 answer
16
Consider the set X={a,b,c,d,e} under partial ordering R={(a,a),(a,b),(a,c),(a,d),(a,e),(b,b),(b,c),(b,e),(c,c),(c,e),(d,d),(d,e),(e,e)}. The Hasse diagram of the partial order (X,R) is shown below. The Hasse diagram of the partial ... i take the pair (b,d) it has LUB as e but no GLB since it is directed... may be the hasse diagram was undirected then it is already a lattice right correct me
asked Oct 26, 2017 in Digital Logic A_i_$_h 335 views
15 votes
1 answer
17
Without any additional circuitry an $8:1 $ MUX can be used to obtain Some but not all Boolean functions of $3$ variables All function of $3$ variables but none of $4$ variables All functions of $3$ variables and some but not all of $4$ variables All functions of $4$ variables
asked Jun 20, 2017 in Digital Logic sourav. 3k views
25 votes
4 answers
18
The next state table of a $2-$bit saturating up-counter is given below. $\begin{array}{cc|cc} Q_1 & Q_0 & Q_1^+ & Q_0^+ \\ \hline 0 & 0 & 0 & 1 \\ 0 & 1 & 1 & 0 \\ 1 & 0 & 1 & 1 \\ 1 & 1 & 1 & 1 \end{array}$ The counter is built as a synchronous sequential circuit ... $T_1 = Q_1+Q_0, \quad T_0= \bar{Q_1} \bar{Q_0}$ $T_1 = \bar{Q_1}Q_0, \quad T_0= Q_1 + Q_0$
asked Feb 14, 2017 in Digital Logic khushtak 5.6k views
28 votes
5 answers
19
If $w, x, y, z$ are Boolean variables, then which one of the following is INCORRECT? $wx+w(x+y)+x(x +y) = x+wy$ $\overline{w \bar{x}(y+\bar{z})} + \bar{w}x = \bar{w} + x + \bar{y}z$ $(w \bar{x}(y+x\bar{z}) + \bar{w} \bar{x}) y = x \bar{y}$ $(w+y)(wxy+wyz) = wxy+wyz$
asked Feb 14, 2017 in Digital Logic khushtak 5.7k views
29 votes
4 answers
20
Given the following binary number in $32$-bit (single precision) $IEEE-754$ format : $\large 00111110011011010000000000000000$ The decimal value closest to this floating-point number is : $1.45*10^1$ $1.45*10^{-1}$ $2.27*10^{-1}$ $2.27*10^1$
asked Feb 14, 2017 in Digital Logic khushtak 11.2k views
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