# Recent questions tagged gate1994

1
Design a 3-bit counter using D-flip flops such that not more than one flip-flop changes state between any two consecutive states.
2
A priority encoder accepts three input signals $\text{(A, B and C)}$ and produces a two-bit output $(X_1, X_0 )$ corresponding to the highest priority active input signal. Assume $A$ has the highest priority followed by $B$ and $C$ has the lowest priority. If none of the inputs are active the output should be $00$, design the priority encoder using $4:1$ multiplexers as the main components.
3
Consider the resource allocation graph in the figure. Find if the system is in a deadlock state Otherwise, find a safe sequence
4
Draw a precedence graph for the following sequential code. The statements are numbered from $S_1$ to $S_6$ $S_1$ read n $S_2$ i := 1 $S_3$ if i > n next $S_4$ a(i) := i+1 $S_5$ i := i+1 $S_6$ next : write a(i) Can this graph be converted to a concurrent program using parbegin-parend construct only?
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A queue $Q$ containing $n$ items and an empty stack $S$ are given. It is required to transfer all the items from the queue to the stack, so that the item at the front of queue is on the TOP of the stack, and the order of all other items are ... operations which can be performed on the queue and stack are Delete, Insert, Push and Pop. Do not assume any implementation of the queue or stack.
6
An array $A$ contains $n$ integers in non-decreasing order, $A[1] \leq A[2] \leq \cdots \leq A[n]$. Describe, using Pascal like pseudo code, a linear time algorithm to find $i, j,$ such that $A[i]+A[j]=a$ given integer $M$, if such $i, j$ exist.
7
An independent set in a graph is a subset of vertices such that no two vertices in the subset are connected by an edge. An incomplete scheme for a greedy algorithm to find a maximum independent set in a tree is given below: V: Set of all vertices in the tree; ... ; Output(I); Complete the algorithm by specifying the property of vertex $u$ in each case. What is the time complexity of the algorithm?
8
Suppose we have a computer with single register and only three instructions given below: ... T \rightarrow (E)\mid id$}\\ \end{array}$ Write a syntax directed translation to generate code using this grammar for the computer described above.
1 vote
9
Consider the program below: Program main: var r:integer; procedure two: begin write (r); end procedure one: var r:integer; begin r:=5; two; end begin r:=2; two; one; two; end What is printed by the above program if Static scoping is assumed for all variables; Dynamic scoping is assumed for all variables. Give reasons for your answer.
10
Consider the following recursive function: function fib (n:integer);integer; begin if (n=0) or (n=1) then fib := 1 else fib := fib(n-1) + fib(n-2) end; The above function is run on a computer with a stack of $64$ bytes. Assuming that only return ... value and an address takes $2$ bytes each, estimate the maximum value of $n$ for which the stack will not overflow. Give reasons for your answer.
11
A grammar $G$ is in Chomsky-Normal Form (CNF) if all its productions are of the form $A \to BC$ or $A \to a$, where $A,B$ and $C$, are non-terminals and $a$ is a terminal. Suppose $G$ is a CFG in CNF and $w$ is a string in $L(G)$ of length $n$, then how long is a derivation of $w$ in $G$?
12
(a) Given a set: $S = \left\{x \mid \text{ there is an x-block of 5's in the decimal expansion of } \pi\right\}$ (Note: $x$-$block$ is a maximal block of $x$ successive $5$'s) Which of the following statements is true with respect to $S$? No ... b) Given that a language $L_1$ is regular and and that the language $L_1 \cup L_2$ is regular, is the language $L_2$ always regular? Prove your answer.
13
State whether the following statements are True or False with reasons for your answer A subroutine cannot always be used to replace a macro in an assembly language program. A symbol declared as ‘external’ in an assembly language program is assigned an address outside the program by the assembler itself.
14
State whether the following statements are True or False with reasons for your answer: Coroutine is just another name for a subroutine. A two pass assembler uses its machine opcode table in the first pass of assembly.
15
Every element $a$ of some ring $(R, +, o)$ satisfies the equation $a\;o\;a=a$. Decide whether or not the ring is commutative.
16
Use the patterns given to prove that $\sum\limits_{i=0}^{n-1} (2i+1) = n^2$ (You are not permitted to employ induction) Use the result obtained in (a) to prove that $\sum\limits_{i=1}^{n} i = \frac{n(n+1)}{2}$
17
Consider $B^+$ - tree of order $d$ shown in figure. (A $B^+$ - tree of order $d$ contains between $d$ and $2d$ keys in each node) Draw the resulting $B^+$ - tree after $100$ is inserted in the figure below. For a $B^+$ - tree of order $d$ with $n$ leaf nodes, the number of nodes accessed during a search is $O(-)$.
18
Consider the following relational schema: COURSES (cno, cname) STUDENTS (rollno, sname, age, year) REGISTERED_FOR (cno, rollno) The underlined attributes indicate the primary keys for the relations. The year' attribute for the STUDENTS relation indicates the year in which the ... who have registered for cno 322. Write a SQL query to print the age and year of the youngest student in each year.
19
Assume that a CPU has only two registers $R_1$ and $R_2$ and that only the following instruction is available $XOR \: R_i, R_j;\{R_j \leftarrow R_i \oplus R_j, \text{ for } i, j =1, 2\}$ Using this XOR instruction, find an instruction sequence in order to ... registers $R_1$ and $R_2$ The line p of the circuit shown in figure has stuck at 1 fault. Determine an input test to detect the fault.
20
Find the contents of the flip-flop $Q_2, Q_1$ and $Q_0$ in the circuit of figure, after giving four clock pulses to the clock terminal. Assume $Q_2Q_1Q_0=000$ initially.
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Following $7$ ... (assuming that at most $1$ bit could be corrupted). If the message contains an error find the bit which is erroneous and gives correct message.
23
A rooted tree with $12$ nodes has its nodes numbered $1$ to $12$ in pre-order. When the tree is traversed in post-order, the nodes are visited in the order $3, 5, 4, 2, 7, 8, 6, 10, 11, 12, 9, 1$. Reconstruct the original tree from this information, that is, find the parent of each node, and show the tree diagrammatically.
24
An array $A$ contains $n$ integers in locations $A[0], A[1], \dots A[n-1]$. It is required to shift the elements of the array cyclically to the left by $K$ places, where $1\leq K \leq n-1$. An incomplete algorithm for doing this in linear time, without using another array is given below. Complete ... A[j]:=____; j:=(j+K) mod n; if j<min then min:=j; end; A[(n+i-K)mod n]:=____; i:=______; end;
25
What function of $x$, $n$ is computed by this program? Function what(x, n:integer): integer: Var value : integer begin value := 1 if n > 0 then begin if n mod 2 =1 then value := value * x; value := value * what(x*x, n div 2); end; what := value; end;
26
A $3-\text{ary}$ tree is a tree in which every internal node has exactly three children. Use induction to prove that the number of leaves in a $3-\text{ary}$ tree with $n$ internal nodes is $2(n-1)$.
27
Let $*$ be a Boolean operation defined as $A*B = AB + \overline{A}\;\overline{B}$. If $C=A*B$ then evaluate and fill in the blanks: $A*A=$____ $C*A=$____ Solve the following boolean equations for the values of $A, B$ and $C$: $AB+\overline{A}C=1$ $AC+B=0$
Let $p$ and $q$ be propositions. Using only the Truth Table, decide whether $p \Longleftrightarrow q$ does not imply $p \to \lnot q$ is True or False.
Find the inverse of the matrix $\begin{bmatrix} 1 & 0 & 1 \\ -1 & 1 & 1 \\ 0 & 1 & 0 \end{bmatrix}$