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GATE 1990 Computer Science questions
Recent questions tagged gate1990
10
votes
3
answers
1
GATE1990-1-iv-b
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.
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
1.8k
views
gate1990
descriptive
digital-logic
number-representation
floating-point-representation
12
votes
2
answers
2
GATE1990-1-viii
The condition for overflow in the addition of two $2's$ complement numbers in terms of the carry generated by the two most significant bits is ___________.
The condition for overflow in the addition of two $2's$ complement numbers in terms of the carry generated by the two most significant bits is ___________.
asked
Nov 27, 2016
in
Digital Logic
makhdoom ghaya
2.3k
views
gate1990
descriptive
digital-logic
number-representation
4
votes
2
answers
3
GATE1990-17c
Show that the elements of the lattice $(N, \leq)$, where $N$ is the set of positive intergers and $a \leq b$ if and only if $a$ divides $b$, satisfy the distributive property.
Show that the elements of the lattice $(N, \leq)$, where $N$ is the set of positive intergers and $a \leq b$ if and only if $a$ divides $b$, satisfy the distributive property.
asked
Nov 27, 2016
in
Set Theory & Algebra
makhdoom ghaya
715
views
gate1990
descriptive
set-theory&algebra
lattice
0
votes
0
answers
4
GATE1990-17b
Show, using resolution, that the following well-formed formula is valid for all interpretations: $\left(\forall x \forall y \left(f \left(x, y \right) \Leftarrow \neg y \left(y, x \right) = \left(\forall x \left(f \left(x, x \right)\right)$
Show, using resolution, that the following well-formed formula is valid for all interpretations: $\left(\forall x \forall y \left(f \left(x, y \right) \Leftarrow \neg y \left(y, x \right) = \left(\forall x \left(f \left(x, x \right)\right)$
asked
Nov 27, 2016
in
Mathematical Logic
makhdoom ghaya
241
views
gate1990
descriptive
first-order-logic
bad-question
20
votes
2
answers
5
GATE1990-17a
Express $T(n)$ in terms of the harmonic number $\displaystyle H_{n}= \sum_{i=1}^{n} \frac{1}{i},\quad n \geq 1$, where $T(n)$ satisfies the recurrence relation, $T(n)=\frac{n+1}{n} T(n - 1)+1$, for $n \geq \sum$ and $T(1) = 1$ What is the asymptotic behaviour of $T(n)$ as a function of $n$ ?
Express $T(n)$ in terms of the harmonic number $\displaystyle H_{n}= \sum_{i=1}^{n} \frac{1}{i},\quad n \geq 1$, where $T(n)$ satisfies the recurrence relation, $T(n)=\frac{n+1}{n} T(n - 1)+1$, for $n \geq \sum$ and $T(1) = 1$ What is the asymptotic behaviour of $T(n)$ as a function of $n$ ?
asked
Nov 27, 2016
in
Algorithms
makhdoom ghaya
2k
views
gate1990
descriptive
algorithms
recurrence
0
votes
0
answers
6
GATE1990-16b
Consider the grammar: $G_{2}$: Para $\rightarrow$ Sentence RP/Sentence RP $\rightarrow$ b Sentence RP | b Sentence Sentence $\rightarrow$ Word b Sentence| Word Word $\rightarrow$ letter *word | letter letter $\rightarrow$ id Where $id,,*,.b$ ar terminals ... how to use a stack algorithm to parse the following string$id*id.b id * id.$ The parse should generate a rightmost derivation.
Consider the grammar: $G_{2}$: Para $\rightarrow$ Sentence RP/Sentence RP $\rightarrow$ b Sentence RP | b Sentence Sentence $\rightarrow$ Word b Sentence| Word Word $\rightarrow$ letter *word | letter letter $\rightarrow$ id Where $id,,*,.b$ ar terminals Convert ... show how to use a stack algorithm to parse the following string$id*id.b id * id.$ The parse should generate a rightmost derivation.
asked
Nov 26, 2016
in
Compiler Design
makhdoom ghaya
270
views
gate1990
descriptive
compiler-design
grammar
unsolved
18
votes
1
answer
7
GATE1990-16a
Show that grammar $G1$ is ambiguous using parse trees: $G_{1}: S \rightarrow$ if S then S else S $S \rightarrow$ if S then S
Show that grammar $G1$ is ambiguous using parse trees: $G_{1}: S \rightarrow$ if S then S else S $S \rightarrow$ if S then S
asked
Nov 26, 2016
in
Compiler Design
makhdoom ghaya
3.3k
views
gate1990
descriptive
compiler-design
grammar
2
votes
0
answers
8
GATE1990-15b
Complete the following production rules which generate the language:$L= \left\{a^{n} b^{n} c^{n}\mid a, b, c \in \Sigma \right\}$ where variables $R$ and $Q$ are used to move back and forth over the current string generated $S \rightarrow aYc$ ... $Qc \rightarrow cQ$ $Q \rightarrow R'c$ $cR' \rightarrow ...$ $bR' \rightarrow ...$ $aR' \rightarrow a...$
Complete the following production rules which generate the language:$L= \left\{a^{n} b^{n} c^{n}\mid a, b, c \in \Sigma \right\}$ where variables $R$ and $Q$ are used to move back and forth over the current string generated $S \rightarrow aYc$ $Y \rightarrow a Yc\mid Q$ ... $Qc \rightarrow cQ$ $Q \rightarrow R'c$ $cR' \rightarrow ...$ $bR' \rightarrow ...$ $aR' \rightarrow a...$
asked
Nov 26, 2016
in
Theory of Computation
makhdoom ghaya
312
views
gate1990
descriptive
theory-of-computation
grammar
context-sensitive
non-gate
17
votes
2
answers
9
GATE1990-15a
Is the language generated by the grammar $G$ regular? If so, give a regular expression for it, else prove otherwise G: $S \rightarrow aB$ $B \rightarrow bC$ $C \rightarrow xB$ $C \rightarrow c$
Is the language generated by the grammar $G$ regular? If so, give a regular expression for it, else prove otherwise G: $S \rightarrow aB$ $B \rightarrow bC$ $C \rightarrow xB$ $C \rightarrow c$
asked
Nov 26, 2016
in
Theory of Computation
makhdoom ghaya
1.4k
views
gate1990
descriptive
theory-of-computation
regular-languages
regular-grammar
grammar
1
vote
0
answers
10
GATE1990-14
The following algorithm (written in pseudo-pascal) work on an undirected graph G program Explore (G) procedure Visit (u) begin if Adj (u) is not empty {comment:Adj (u) is the list of edges incident to u} then begin Select an edge from Adj (u); ... edges, given that each vertex can be accessed and removed from LIST in constant time. Also show that all edges of the graph are traversed.
The following algorithm (written in pseudo-pascal) work on an undirected graph G program Explore (G) procedure Visit (u) begin if Adj (u) is not empty {comment:Adj (u) is the list of edges incident to u} then begin Select an edge from Adj (u); Let edge ... edges, given that each vertex can be accessed and removed from LIST in constant time. Also show that all edges of the graph are traversed.
asked
Nov 26, 2016
in
Algorithms
makhdoom ghaya
348
views
gate1990
descriptive
graph-algorithms
unsolved
2
votes
1
answer
11
GATE1990-13b
Consider a hash table with chaining scheme for overflow handling: What is the worst-case timing complexity of inserting $n$ elements into such a table? For what type of instance does this hashing scheme take the worst-case time for insertion?
Consider a hash table with chaining scheme for overflow handling: What is the worst-case timing complexity of inserting $n$ elements into such a table? For what type of instance does this hashing scheme take the worst-case time for insertion?
asked
Nov 26, 2016
in
Algorithms
makhdoom ghaya
1k
views
gate1990
hashing
algorithms
8
votes
2
answers
12
GATE1990-13a
Consider the height-balanced tree $T_{t}$ with values stored at only the leaf nodes, shown in Fig.4. (i) Show how to merge to the tree, $T_{1}$ elements from tree $T_{2}$ shown in Fig.5 using node D of tree $T_{1}$. (ii) What is the time complexity of ... $T_{1}$ and $T_{2}$ are of height $h_{1}$ and $h_{2}$ respectively, assuming that rotation schemes are given. Give reasons.
Consider the height-balanced tree $T_{t}$ with values stored at only the leaf nodes, shown in Fig.4. (i) Show how to merge to the tree, $T_{1}$ elements from tree $T_{2}$ shown in Fig.5 using node D of tree $T_{1}$. (ii) What is the time complexity of a merge ... $T_{1}$ and $T_{2}$ are of height $h_{1}$ and $h_{2}$ respectively, assuming that rotation schemes are given. Give reasons.
asked
Nov 26, 2016
in
DS
makhdoom ghaya
1.7k
views
gate1990
descriptive
data-structures
trees
7
votes
1
answer
13
GATE1990-12b
Consider the following problem. Given $n$ positive integers $a_{1}, a_{2}\dots a_n,$ it is required to partition them in to two parts $A$ and $B$ such that $|\sum_{i \in A} a_{i} - \sum_{i \in B} a_{i}|$ is minimised Consider a greedy ... in that part whose sum in smaller at that step. Give an example with $n=5$ for which the solution produced by the greedy algorithm is not optimal.
Consider the following problem. Given $n$ positive integers $a_{1}, a_{2}\dots a_n,$ it is required to partition them in to two parts $A$ and $B$ such that $|\sum_{i \in A} a_{i} - \sum_{i \in B} a_{i}|$ is minimised Consider a greedy algorithm ... in that part whose sum in smaller at that step. Give an example with $n=5$ for which the solution produced by the greedy algorithm is not optimal.
asked
Nov 25, 2016
in
Algorithms
makhdoom ghaya
895
views
gate1990
descriptive
algorithms
algorithm-design-techniques
0
votes
0
answers
14
GATE1990-12a
Consider the following instance of the $0 -1$ Knapsack problem: $\max 6X_{1} + 11X_{2} + 16X_{3} + 21X_{4} + 26X_{5}$ Subject to $4X_{1} + 8X_{2} + 12X_{3} + 16X_{4} + 20 X_{5} < 32$ and $X_{i}=0$ or $1$ ... the nodes in the tree in the order in which they are expanded and for each node show the bound on the partial solutions and the decision which leads to that node.
Consider the following instance of the $0 -1$ Knapsack problem: $\max 6X_{1} + 11X_{2} + 16X_{3} + 21X_{4} + 26X_{5}$ Subject to $4X_{1} + 8X_{2} + 12X_{3} + 16X_{4} + 20 X_{5} < 32$ and $X_{i}=0$ or $1$ for $i=1,\dots,5$. ... . Number the nodes in the tree in the order in which they are expanded and for each node show the bound on the partial solutions and the decision which leads to that node.
asked
Nov 25, 2016
in
Algorithms
makhdoom ghaya
385
views
gate1990
descriptive
algorithms
branch-and-bound
unsolved
7
votes
3
answers
15
GATE1990-11b
The following program computes values of a mathematical function $f(x)$. Determine the form of $f(x)$. main () { int m, n; float x, y, t; scanf ("%f%d", &x, &n); t = 1; y = 0; m = 1; do { t *= (-x/m); y += t; } while (m++ < n); printf ("The value of y is %f", y); }
The following program computes values of a mathematical function $f(x)$. Determine the form of $f(x)$. main () { int m, n; float x, y, t; scanf ("%f%d", &x, &n); t = 1; y = 0; m = 1; do { t *= (-x/m); y += t; } while (m++ < n); printf ("The value of y is %f", y); }
asked
Nov 25, 2016
in
Algorithms
makhdoom ghaya
992
views
gate1990
descriptive
algorithms
identify-function
0
votes
2
answers
16
GATE1990-11a
What does the following program output? program module (input, output); var a:array [1...5] of integer; i, j: integer; procedure unknown (var b: integer, var c: integer); var i:integer; begin for i := 1 to 5 do a[i] := i; b:= 0; c := 0 for i := 1 to 5 do write (a[i]); writeln(); a[3 ... b); b := 5; c := 6; end; begin i:=1; j:=3; unknown (a[i], a[j]); for i:=1 to 5 do write (a[i]); end;
What does the following program output? program module (input, output); var a:array [1...5] of integer; i, j: integer; procedure unknown (var b: integer, var c: integer); var i:integer; begin for i := 1 to 5 do a[i] := i; b:= 0; c := 0 for i := 1 to 5 do write (a[i]); writeln(); a[3]:=11; ... (c,b); b := 5; c := 6; end; begin i:=1; j:=3; unknown (a[i], a[j]); for i:=1 to 5 do write (a[i]); end;
asked
Nov 25, 2016
in
Compiler Design
makhdoom ghaya
692
views
gate1990
descriptive
compiler-design
runtime-environments
parameter-passing
15
votes
4
answers
17
GATE1990-10b
One giga bytes of data are to be organized as an indexed-sequential file with a uniform blocking factor 8. Assuming a block size of 1 Kilo bytes and a block refrencing pointer size of $32$ bits, find out the number of levels of indexing that would be ... the size of the master index. The referencing capability (fanout ratio) per block of index storage may be considered to be $32$.
One giga bytes of data are to be organized as an indexed-sequential file with a uniform blocking factor 8. Assuming a block size of 1 Kilo bytes and a block refrencing pointer size of $32$ bits, find out the number of levels of indexing that would be required ... also the size of the master index. The referencing capability (fanout ratio) per block of index storage may be considered to be $32$.
asked
Nov 24, 2016
in
Databases
makhdoom ghaya
2.9k
views
gate1990
descriptive
databases
indexing
20
votes
1
answer
18
GATE1990-10-a
Consider the following relational database: employees (eno, ename, address, basic-salary) projects (pno, pname, nos-of-staffs-allotted) working (pno, eno, pjob) The queries regarding data in the above database are formulated below in SQL. Describe in ... *) FROM projects)) SELECT pname FROM projects WHERE pno IN (SELECT pno FROM projects MINUS SELECT DISTINCT pno FROM working);
Consider the following relational database: employees (eno, ename, address, basic-salary) projects (pno, pname, nos-of-staffs-allotted) working (pno, eno, pjob) The queries regarding data in the above database are formulated below in SQL. Describe in ENGLISH sentences ... (*) FROM projects)) SELECT pname FROM projects WHERE pno IN (SELECT pno FROM projects MINUS SELECT DISTINCT pno FROM working);
asked
Nov 24, 2016
in
Databases
makhdoom ghaya
1.2k
views
gate1990
descriptive
databases
sql
15
votes
1
answer
19
GATE1990-9b
Assuming the current disk cylinder to be $50$ and the sequence for the cylinders to be $1, 36, 49, 65, 53, 12, 3, 20, 55, 16, 65$ and $78$ find the sequence of servicing using Shortest seek time first (SSTF) and Elevator disk scheduling policies.
Assuming the current disk cylinder to be $50$ and the sequence for the cylinders to be $1, 36, 49, 65, 53, 12, 3, 20, 55, 16, 65$ and $78$ find the sequence of servicing using Shortest seek time first (SSTF) and Elevator disk scheduling policies.
asked
Nov 24, 2016
in
Operating System
makhdoom ghaya
1.7k
views
gate1990
descriptive
operating-system
disk-scheduling
1
vote
0
answers
20
GATE1990-9a
Assume that an instruction test-and-set (TS) has been provided in a machine whose function is as follows: 'the left most bit of the one byte operand is checked and accordingly the condition code (CC) is set to $1$ or $0$. After checking and setting the condition code, implement a critical region using this instruction.
Assume that an instruction test-and-set (TS) has been provided in a machine whose function is as follows: 'the left most bit of the one byte operand is checked and accordingly the condition code (CC) is set to $1$ or $0$. After checking and setting the condition code, implement a critical region using this instruction.
asked
Nov 24, 2016
in
Operating System
makhdoom ghaya
465
views
descriptive
gate1990
operating-system
process-synchronization
critical-section
unsolved
4
votes
1
answer
21
GATE1990-8b
State the Booth's algorithm for multiplication of two numbers. Draw a block diagram for the implementation of the Booth's algorithm for determining the product of two 8-bit signed numbers.
State the Booth's algorithm for multiplication of two numbers. Draw a block diagram for the implementation of the Booth's algorithm for determining the product of two 8-bit signed numbers.
asked
Nov 24, 2016
in
Digital Logic
makhdoom ghaya
1k
views
gate1990
descriptive
digital-logic
booths-algorithm
5
votes
1
answer
22
GATE1990-8a
A single bus CPU consists of four general purpose register, namely, $R0 ....... R3, ALU, MAR, MDR, PC, SP$ and $IR$ (Instruction Register). Assuming suitable microinstructions, write a microroutine for the instruction, $ADD R0, R1$
A single bus CPU consists of four general purpose register, namely, $R0 ....... R3, ALU, MAR, MDR, PC, SP$ and $IR$ (Instruction Register). Assuming suitable microinstructions, write a microroutine for the instruction, $ADD R0, R1$
asked
Nov 24, 2016
in
CO and Architecture
makhdoom ghaya
759
views
gate1990
descriptive
co-and-architecture
microprogramming
13
votes
2
answers
23
GATE1990-7-c
A certain moving arm disk-storage device has the following specifications: Number of tracks per surface=$404$ Track storage capacity=$130030$ bytes. Disk speed=$3600$ rpm Average seek time=$30$ m secs. Estimate the average latency, the disk storage capacity and the data transfer rate.
A certain moving arm disk-storage device has the following specifications: Number of tracks per surface=$404$ Track storage capacity=$130030$ bytes. Disk speed=$3600$ rpm Average seek time=$30$ m secs. Estimate the average latency, the disk storage capacity and the data transfer rate.
asked
Nov 24, 2016
in
Operating System
makhdoom ghaya
3.5k
views
descriptive
operating-system
disks
gate1990
45
votes
6
answers
24
GATE1990-7-b
In a two-level virtual memory, the memory access time for main memory, $t_{M}=10^{-8}$ sec, and the memory access time for the secondary memory, $t_D=10^{-3}$ sec. What must be the hit ratio, $H$ such that the access efficiency is within $80$ percent of its maximum value?
In a two-level virtual memory, the memory access time for main memory, $t_{M}=10^{-8}$ sec, and the memory access time for the secondary memory, $t_D=10^{-3}$ sec. What must be the hit ratio, $H$ such that the access efficiency is within $80$ percent of its maximum value?
asked
Nov 24, 2016
in
Operating System
makhdoom ghaya
9.8k
views
gate1990
descriptive
operating-system
virtual-memory
31
votes
1
answer
25
GATE1990-7a
A block-set associative cache memory consists of $128$ blocks divided into four block sets. The main memory consists of $16, 384$ blocks and each block contains $256$ eight bit words. How many bits are required for addressing the main memory? How many bits are needed to represent the TAG, SET and WORD fields?
A block-set associative cache memory consists of $128$ blocks divided into four block sets. The main memory consists of $16, 384$ blocks and each block contains $256$ eight bit words. How many bits are required for addressing the main memory? How many bits are needed to represent the TAG, SET and WORD fields?
asked
Nov 24, 2016
in
CO and Architecture
makhdoom ghaya
10.4k
views
gate1990
descriptive
co-and-architecture
cache-memory
17
votes
4
answers
26
GATE1990-5-c
For the synchronous counter shown in Fig.3, write the truth table of $Q_{0}, Q_{1}$,and $Q_{2}$ after each pulse, starting from $Q_{0}=Q_{1}=Q_{2}=0$ and determine the counting sequence and also the modulus of the counter.
For the synchronous counter shown in Fig.3, write the truth table of $Q_{0}, Q_{1}$,and $Q_{2}$ after each pulse, starting from $Q_{0}=Q_{1}=Q_{2}=0$ and determine the counting sequence and also the modulus of the counter.
asked
Nov 24, 2016
in
Digital Logic
makhdoom ghaya
2.4k
views
gate1990
descriptive
digital-logic
flip-flop
16
votes
5
answers
27
GATE1990-5-b
Show with the help of a block diagram how the Boolean function : $f=AB+BC+CA$ can be realised using only a $4:1$ multiplexer.
Show with the help of a block diagram how the Boolean function : $f=AB+BC+CA$ can be realised using only a $4:1$ multiplexer.
asked
Nov 24, 2016
in
Digital Logic
makhdoom ghaya
2k
views
gate1990
descriptive
digital-logic
multiplexer
17
votes
3
answers
28
GATE1990-5-a
Find the minimum product of sums of the following expression $f=ABC + \bar{A}\bar{B}\bar{C}$
Find the minimum product of sums of the following expression $f=ABC + \bar{A}\bar{B}\bar{C}$
asked
Nov 24, 2016
in
Digital Logic
makhdoom ghaya
2.7k
views
gate1990
digital-logic
canonical-normal-form
descriptive
11
votes
2
answers
29
GATE1990-4-v
State whether the following statements are TRUE or FALSE with reason: The Link-load-and-go loading scheme required less storage space than the link-and-go loading scheme.
State whether the following statements are TRUE or FALSE with reason: The Link-load-and-go loading scheme required less storage space than the link-and-go loading scheme.
asked
Nov 24, 2016
in
Compiler Design
makhdoom ghaya
2.7k
views
gate1990
true-false
compiler-design
runtime-environments
4
votes
0
answers
30
GATE1990-4-iv
State whether the following statements are TRUE or FALSE with reason: Transferring data in blocks from the main memory to the cache memory enables an interleaved main memory unit to operate at its maximum speed.
State whether the following statements are TRUE or FALSE with reason: Transferring data in blocks from the main memory to the cache memory enables an interleaved main memory unit to operate at its maximum speed.
asked
Nov 24, 2016
in
CO and Architecture
makhdoom ghaya
1.7k
views
gate1990
true-false
co-and-architecture
cache-memory
memory-interfacing
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