Gate (CS) 1992 Paper without Solution | GATE Computer Science Engineering(CSE) 2025 Mock Test Series - Computer Science Engineering (CSE) PDF Download

 Page 1


GATE CS - 1992
  
SECTION – A 
1. Fill in the blanks:
(i) The Boolean function in sum of products form where K-map is given below 
(figure) is:___________ 
(ii) Consider a 3-bit error detection and 1-bit error correction hamming code for 
4-bit date. The extra parity bits required would be ________ and the 3-bit 
error detection is possible because the code has a minimum distance of 
________ 
(iii) Many microprocessors have a specified lower limit on clock frequency (apart 
from the maximum clock frequency limit) because ______ 
(iv) Many of the advanced microprocessors prefetch instructions and store it in 
an instruction buffer to speed up processing. This speed up is achieved 
because _________ 
(v) A simple and reliable data transfer can be accomplished by using the 
‘handshake protocol’. It accomplishes reliable data transfer because for every 
data item sent by the transmitter __________. 
(vi) In an 11-bit computer instruction format, the size of address field is 4-bits. 
The computer uses expanding OP code technique and has 5 two-address 
instructions and 32 two-address instructions and the number of zero-address 
instructions it can support is _________ 
(vii) Macro expansion is done in pass one instead of pass two in a pass macro 
assembler because _________ 
(viii) The purpose of instruction location counter in an assembler is _______ 
(ix) Complexity of Kruskal’s algorithm for finding the minimum spanning tree of 
an undirected graph containing n vertices and m edges if the edges are 
sorted is __________ 
(x) Maximum number of edges in a planar graph with n vertices is ________ 
2. Choose the correct alternatives (more than one may be correct) and write the 
corresponding letters only: 
(i) The operation which is commutative but not associative is: 
(a) AND (b) OR (c) EX-OR  (d) NAND 
(ii) All digital circuits can be realized using only 
(a) Ex-OR gates   (b) Multiplexers 
(c) Half adders   (d) OR gates 
0 
A 
0 1 
0 
1 
B 
C 
1 
A 
Page 2


GATE CS - 1992
  
SECTION – A 
1. Fill in the blanks:
(i) The Boolean function in sum of products form where K-map is given below 
(figure) is:___________ 
(ii) Consider a 3-bit error detection and 1-bit error correction hamming code for 
4-bit date. The extra parity bits required would be ________ and the 3-bit 
error detection is possible because the code has a minimum distance of 
________ 
(iii) Many microprocessors have a specified lower limit on clock frequency (apart 
from the maximum clock frequency limit) because ______ 
(iv) Many of the advanced microprocessors prefetch instructions and store it in 
an instruction buffer to speed up processing. This speed up is achieved 
because _________ 
(v) A simple and reliable data transfer can be accomplished by using the 
‘handshake protocol’. It accomplishes reliable data transfer because for every 
data item sent by the transmitter __________. 
(vi) In an 11-bit computer instruction format, the size of address field is 4-bits. 
The computer uses expanding OP code technique and has 5 two-address 
instructions and 32 two-address instructions and the number of zero-address 
instructions it can support is _________ 
(vii) Macro expansion is done in pass one instead of pass two in a pass macro 
assembler because _________ 
(viii) The purpose of instruction location counter in an assembler is _______ 
(ix) Complexity of Kruskal’s algorithm for finding the minimum spanning tree of 
an undirected graph containing n vertices and m edges if the edges are 
sorted is __________ 
(x) Maximum number of edges in a planar graph with n vertices is ________ 
2. Choose the correct alternatives (more than one may be correct) and write the 
corresponding letters only: 
(i) The operation which is commutative but not associative is: 
(a) AND (b) OR (c) EX-OR  (d) NAND 
(ii) All digital circuits can be realized using only 
(a) Ex-OR gates   (b) Multiplexers 
(c) Half adders   (d) OR gates 
0 
A 
0 1 
0 
1 
B 
C 
1 
A 
GATE CS - 1992
  
(iii) Bit-slice processors 
(a) Can be cascaded to get any desired word length processor  
(b) speed of operation is independent of the word length configured  
(c) don’t contain anything equivalent of program counter in a ‘normal’ 
microprocessor 
(d) contain only the data path of a ‘normal’ CPU 
(iv) PCHL is an instruction in 8085 which transfers the contents of the register 
pair HL to PC. This is not a very commonly used instruction as it changes the 
flow of control in rather ‘unstructured’ fashion. This instruction can be useful 
in implementing.   
(a) if ……. then ….. else ….. construct (b) while …… construct 
(c) case …… construct (d) call …… construct  
(v) Start and stop bits do not contain an ‘information’ but are used in serial 
communication for  
(a) Error detection    (b) Error correction 
(c) Synchronization   
(d) Slowing down the communications  
(vi) Which of the following problems is not NP-hard? 
(a) Hamiltonian circuit problem 
(b) The 0/1 Knapsack problem  
(c) Finding bi-connected components of a graph  
(d) The graph colouring problem  
(vii) A 2-3 tree is tree such that  
(a) all internal nodes have either 2 or 3 children  
(b) all paths from root to the leaves have the same length 
The number of internal nodes of a 2-3 tree having 9 leaves could be 
(a) 4 (b) 5 (c) 6 (d) 7 
(viii) A non-planar graph with minimum number of vertices has 
(a) 9 edges, 6 vertices (b) 6 edges, 4 vertices 
(c) 10 edges, 5 vertices (d) 9 edges, 5 vertices 
(ix) Following algorithm(s) can be used to sort n integers in the range 
3
1 n ? ?
? ?
K in
0 (n) time 
(a) Heapsort (b) Quicksort (c) Mergesort (d) Radixsort 
Page 3


GATE CS - 1992
  
SECTION – A 
1. Fill in the blanks:
(i) The Boolean function in sum of products form where K-map is given below 
(figure) is:___________ 
(ii) Consider a 3-bit error detection and 1-bit error correction hamming code for 
4-bit date. The extra parity bits required would be ________ and the 3-bit 
error detection is possible because the code has a minimum distance of 
________ 
(iii) Many microprocessors have a specified lower limit on clock frequency (apart 
from the maximum clock frequency limit) because ______ 
(iv) Many of the advanced microprocessors prefetch instructions and store it in 
an instruction buffer to speed up processing. This speed up is achieved 
because _________ 
(v) A simple and reliable data transfer can be accomplished by using the 
‘handshake protocol’. It accomplishes reliable data transfer because for every 
data item sent by the transmitter __________. 
(vi) In an 11-bit computer instruction format, the size of address field is 4-bits. 
The computer uses expanding OP code technique and has 5 two-address 
instructions and 32 two-address instructions and the number of zero-address 
instructions it can support is _________ 
(vii) Macro expansion is done in pass one instead of pass two in a pass macro 
assembler because _________ 
(viii) The purpose of instruction location counter in an assembler is _______ 
(ix) Complexity of Kruskal’s algorithm for finding the minimum spanning tree of 
an undirected graph containing n vertices and m edges if the edges are 
sorted is __________ 
(x) Maximum number of edges in a planar graph with n vertices is ________ 
2. Choose the correct alternatives (more than one may be correct) and write the 
corresponding letters only: 
(i) The operation which is commutative but not associative is: 
(a) AND (b) OR (c) EX-OR  (d) NAND 
(ii) All digital circuits can be realized using only 
(a) Ex-OR gates   (b) Multiplexers 
(c) Half adders   (d) OR gates 
0 
A 
0 1 
0 
1 
B 
C 
1 
A 
GATE CS - 1992
  
(iii) Bit-slice processors 
(a) Can be cascaded to get any desired word length processor  
(b) speed of operation is independent of the word length configured  
(c) don’t contain anything equivalent of program counter in a ‘normal’ 
microprocessor 
(d) contain only the data path of a ‘normal’ CPU 
(iv) PCHL is an instruction in 8085 which transfers the contents of the register 
pair HL to PC. This is not a very commonly used instruction as it changes the 
flow of control in rather ‘unstructured’ fashion. This instruction can be useful 
in implementing.   
(a) if ……. then ….. else ….. construct (b) while …… construct 
(c) case …… construct (d) call …… construct  
(v) Start and stop bits do not contain an ‘information’ but are used in serial 
communication for  
(a) Error detection    (b) Error correction 
(c) Synchronization   
(d) Slowing down the communications  
(vi) Which of the following problems is not NP-hard? 
(a) Hamiltonian circuit problem 
(b) The 0/1 Knapsack problem  
(c) Finding bi-connected components of a graph  
(d) The graph colouring problem  
(vii) A 2-3 tree is tree such that  
(a) all internal nodes have either 2 or 3 children  
(b) all paths from root to the leaves have the same length 
The number of internal nodes of a 2-3 tree having 9 leaves could be 
(a) 4 (b) 5 (c) 6 (d) 7 
(viii) A non-planar graph with minimum number of vertices has 
(a) 9 edges, 6 vertices (b) 6 edges, 4 vertices 
(c) 10 edges, 5 vertices (d) 9 edges, 5 vertices 
(ix) Following algorithm(s) can be used to sort n integers in the range 
3
1 n ? ?
? ?
K in
0 (n) time 
(a) Heapsort (b) Quicksort (c) Mergesort (d) Radixsort 
GATE CS - 1992
  
(x) At a particular time of computation the value of a counting semaphore is 7. 
Then 20 P operations and 15 V operations were completed on this 
semaphore. The resulting value of the semaphore is: 
(a) 42 (b) 2 (c) 7 (d) 12 
(xi) A computer system has 6 tape drives, with n process completing for them. 
Each process may need 3 tape drives. The maximum value of n for which the 
system is guaranteed to be deadlock free is: 
(a) 2 (b) 3 (c) 4 (d) 1 
(xii) Which of the following is an example of a spooled device?  
(a) The terminal used to the input data for a program being executed. 
(b) The secondary memory device in a virtual memory system 
(c) A line printer used to print the output of a number of jobs.  
(d) None of the above 
(xiii) For a context-free grammar, FOLLOW(A) is the set of terminals that can 
appear immediately to the right of non-terminal A in some “sentential” form. 
We define two sets LFOLLOW(A) and RFOLLOW(A) by replacing the word 
“sentential” by “left sentential” and “right most sentential” respectively in the 
definition of FOLLOW(A). 
Which of the following statements is/are true? 
(a) FOLLOW(A) and FOLLOW (A) may be different. 
(b) FOLLOW(A) and FOLLOW (A) are always the same. 
(c) All the three sets are identical. 
(d) All the three sets are different. 
(xiv) Consider the SLR(1) and LALR (1) parsing tables for a context free 
grammar. Which of the following statements is/are true? 
(a) The go to part of both tables may be different. 
(b) The shift entries are identical in both the tables. 
(c) The reduce entries in the tables may be different.  
(d) The error entries in the tables may be different. 
(xv) Which of the following predicate calculus statements is/are valid: 
(a) ( ) ( ) ( ) ( ) ( ) ( ) ( ) { }
x P x x Q x x P x Q x ? ? ? ? ? ?
(b) ( ) ( ) ( ) ( ) ( ) ( ) ( ) { }
x P x x Q x x P x Q x ? ? ? ? ? ?
(c) ( ) ( ) ( ) { } ( ) ( ) ( ) ( ) x P x Q x x P x x Q x ? ? ? ? ? ?
(d) ( ) ( ) ( ) { } ( ) ( ) ( ) ( ) ~ x P x Q x x P x x Q x ? ? ? ? ? ?
Page 4


GATE CS - 1992
  
SECTION – A 
1. Fill in the blanks:
(i) The Boolean function in sum of products form where K-map is given below 
(figure) is:___________ 
(ii) Consider a 3-bit error detection and 1-bit error correction hamming code for 
4-bit date. The extra parity bits required would be ________ and the 3-bit 
error detection is possible because the code has a minimum distance of 
________ 
(iii) Many microprocessors have a specified lower limit on clock frequency (apart 
from the maximum clock frequency limit) because ______ 
(iv) Many of the advanced microprocessors prefetch instructions and store it in 
an instruction buffer to speed up processing. This speed up is achieved 
because _________ 
(v) A simple and reliable data transfer can be accomplished by using the 
‘handshake protocol’. It accomplishes reliable data transfer because for every 
data item sent by the transmitter __________. 
(vi) In an 11-bit computer instruction format, the size of address field is 4-bits. 
The computer uses expanding OP code technique and has 5 two-address 
instructions and 32 two-address instructions and the number of zero-address 
instructions it can support is _________ 
(vii) Macro expansion is done in pass one instead of pass two in a pass macro 
assembler because _________ 
(viii) The purpose of instruction location counter in an assembler is _______ 
(ix) Complexity of Kruskal’s algorithm for finding the minimum spanning tree of 
an undirected graph containing n vertices and m edges if the edges are 
sorted is __________ 
(x) Maximum number of edges in a planar graph with n vertices is ________ 
2. Choose the correct alternatives (more than one may be correct) and write the 
corresponding letters only: 
(i) The operation which is commutative but not associative is: 
(a) AND (b) OR (c) EX-OR  (d) NAND 
(ii) All digital circuits can be realized using only 
(a) Ex-OR gates   (b) Multiplexers 
(c) Half adders   (d) OR gates 
0 
A 
0 1 
0 
1 
B 
C 
1 
A 
GATE CS - 1992
  
(iii) Bit-slice processors 
(a) Can be cascaded to get any desired word length processor  
(b) speed of operation is independent of the word length configured  
(c) don’t contain anything equivalent of program counter in a ‘normal’ 
microprocessor 
(d) contain only the data path of a ‘normal’ CPU 
(iv) PCHL is an instruction in 8085 which transfers the contents of the register 
pair HL to PC. This is not a very commonly used instruction as it changes the 
flow of control in rather ‘unstructured’ fashion. This instruction can be useful 
in implementing.   
(a) if ……. then ….. else ….. construct (b) while …… construct 
(c) case …… construct (d) call …… construct  
(v) Start and stop bits do not contain an ‘information’ but are used in serial 
communication for  
(a) Error detection    (b) Error correction 
(c) Synchronization   
(d) Slowing down the communications  
(vi) Which of the following problems is not NP-hard? 
(a) Hamiltonian circuit problem 
(b) The 0/1 Knapsack problem  
(c) Finding bi-connected components of a graph  
(d) The graph colouring problem  
(vii) A 2-3 tree is tree such that  
(a) all internal nodes have either 2 or 3 children  
(b) all paths from root to the leaves have the same length 
The number of internal nodes of a 2-3 tree having 9 leaves could be 
(a) 4 (b) 5 (c) 6 (d) 7 
(viii) A non-planar graph with minimum number of vertices has 
(a) 9 edges, 6 vertices (b) 6 edges, 4 vertices 
(c) 10 edges, 5 vertices (d) 9 edges, 5 vertices 
(ix) Following algorithm(s) can be used to sort n integers in the range 
3
1 n ? ?
? ?
K in
0 (n) time 
(a) Heapsort (b) Quicksort (c) Mergesort (d) Radixsort 
GATE CS - 1992
  
(x) At a particular time of computation the value of a counting semaphore is 7. 
Then 20 P operations and 15 V operations were completed on this 
semaphore. The resulting value of the semaphore is: 
(a) 42 (b) 2 (c) 7 (d) 12 
(xi) A computer system has 6 tape drives, with n process completing for them. 
Each process may need 3 tape drives. The maximum value of n for which the 
system is guaranteed to be deadlock free is: 
(a) 2 (b) 3 (c) 4 (d) 1 
(xii) Which of the following is an example of a spooled device?  
(a) The terminal used to the input data for a program being executed. 
(b) The secondary memory device in a virtual memory system 
(c) A line printer used to print the output of a number of jobs.  
(d) None of the above 
(xiii) For a context-free grammar, FOLLOW(A) is the set of terminals that can 
appear immediately to the right of non-terminal A in some “sentential” form. 
We define two sets LFOLLOW(A) and RFOLLOW(A) by replacing the word 
“sentential” by “left sentential” and “right most sentential” respectively in the 
definition of FOLLOW(A). 
Which of the following statements is/are true? 
(a) FOLLOW(A) and FOLLOW (A) may be different. 
(b) FOLLOW(A) and FOLLOW (A) are always the same. 
(c) All the three sets are identical. 
(d) All the three sets are different. 
(xiv) Consider the SLR(1) and LALR (1) parsing tables for a context free 
grammar. Which of the following statements is/are true? 
(a) The go to part of both tables may be different. 
(b) The shift entries are identical in both the tables. 
(c) The reduce entries in the tables may be different.  
(d) The error entries in the tables may be different. 
(xv) Which of the following predicate calculus statements is/are valid: 
(a) ( ) ( ) ( ) ( ) ( ) ( ) ( ) { }
x P x x Q x x P x Q x ? ? ? ? ? ?
(b) ( ) ( ) ( ) ( ) ( ) ( ) ( ) { }
x P x x Q x x P x Q x ? ? ? ? ? ?
(c) ( ) ( ) ( ) { } ( ) ( ) ( ) ( ) x P x Q x x P x x Q x ? ? ? ? ? ?
(d) ( ) ( ) ( ) { } ( ) ( ) ( ) ( ) ~ x P x Q x x P x x Q x ? ? ? ? ? ?
GATE CS - 1992
  
(xvi) Which of the following is/are tautology  
(a) a b b c ? ? ? (b) a b b c ? ? ? 
(c) ( ) a b b c ? ? ? (d) ( ) a b b c ? ? ?
(xvii) Which of the following regular expression identifies are true? 
(a) ( ) * * r r =   (b) ( ) ( ) * * * r s r s = +
(c) ( )* * * r s r s + = +   (d) * * * * r s r s = +
(xviii) If G is a context-free grammar and w is a string of length l in L(G), how 
long is a derivation of w in G, if G is Chomsky normal form?  
(a) 2l (b) 2l + 1 (c) 2l - 1  (d) l 
(xix) Context-free languages are 
(a) closed under union (b) closed under complementation 
(c) closed under intersection  (d) closed under Kleene closure  
(xx) In which of the cases stated below is the following statement true? 
“For every non-deterministic machine 
1
M there exists an equivalent 
deterministic machine 
2
M recognizing the same language“. 
(a) 
1
M is non-deterministic finite automaton  
(b) 
1
M is a non-deterministic PDA 
(c) 
1
M is a non-deterministic Turing machine 
(d) For no machine 
1
M use the above statement true 
3. Write short answers to the following:
(i) Which of the following macros can put a macro assembler into an infinite
loop? 
.MACRI M1,X .MACRO M2, X 
..IF EQ,X .IF EQ, X 
M1 X+1 M2X 
.ENDC .ENDC 
.IF NE, X .IF NE, X 
WORD X .WORD X + 1 
.ENDC .ENDC 
.ENDM .ENDM 
Give an example of a call that does so. 
(ii) Mention the pass number for each of the following activities that occur in a 
two pass assembler 
Page 5


GATE CS - 1992
  
SECTION – A 
1. Fill in the blanks:
(i) The Boolean function in sum of products form where K-map is given below 
(figure) is:___________ 
(ii) Consider a 3-bit error detection and 1-bit error correction hamming code for 
4-bit date. The extra parity bits required would be ________ and the 3-bit 
error detection is possible because the code has a minimum distance of 
________ 
(iii) Many microprocessors have a specified lower limit on clock frequency (apart 
from the maximum clock frequency limit) because ______ 
(iv) Many of the advanced microprocessors prefetch instructions and store it in 
an instruction buffer to speed up processing. This speed up is achieved 
because _________ 
(v) A simple and reliable data transfer can be accomplished by using the 
‘handshake protocol’. It accomplishes reliable data transfer because for every 
data item sent by the transmitter __________. 
(vi) In an 11-bit computer instruction format, the size of address field is 4-bits. 
The computer uses expanding OP code technique and has 5 two-address 
instructions and 32 two-address instructions and the number of zero-address 
instructions it can support is _________ 
(vii) Macro expansion is done in pass one instead of pass two in a pass macro 
assembler because _________ 
(viii) The purpose of instruction location counter in an assembler is _______ 
(ix) Complexity of Kruskal’s algorithm for finding the minimum spanning tree of 
an undirected graph containing n vertices and m edges if the edges are 
sorted is __________ 
(x) Maximum number of edges in a planar graph with n vertices is ________ 
2. Choose the correct alternatives (more than one may be correct) and write the 
corresponding letters only: 
(i) The operation which is commutative but not associative is: 
(a) AND (b) OR (c) EX-OR  (d) NAND 
(ii) All digital circuits can be realized using only 
(a) Ex-OR gates   (b) Multiplexers 
(c) Half adders   (d) OR gates 
0 
A 
0 1 
0 
1 
B 
C 
1 
A 
GATE CS - 1992
  
(iii) Bit-slice processors 
(a) Can be cascaded to get any desired word length processor  
(b) speed of operation is independent of the word length configured  
(c) don’t contain anything equivalent of program counter in a ‘normal’ 
microprocessor 
(d) contain only the data path of a ‘normal’ CPU 
(iv) PCHL is an instruction in 8085 which transfers the contents of the register 
pair HL to PC. This is not a very commonly used instruction as it changes the 
flow of control in rather ‘unstructured’ fashion. This instruction can be useful 
in implementing.   
(a) if ……. then ….. else ….. construct (b) while …… construct 
(c) case …… construct (d) call …… construct  
(v) Start and stop bits do not contain an ‘information’ but are used in serial 
communication for  
(a) Error detection    (b) Error correction 
(c) Synchronization   
(d) Slowing down the communications  
(vi) Which of the following problems is not NP-hard? 
(a) Hamiltonian circuit problem 
(b) The 0/1 Knapsack problem  
(c) Finding bi-connected components of a graph  
(d) The graph colouring problem  
(vii) A 2-3 tree is tree such that  
(a) all internal nodes have either 2 or 3 children  
(b) all paths from root to the leaves have the same length 
The number of internal nodes of a 2-3 tree having 9 leaves could be 
(a) 4 (b) 5 (c) 6 (d) 7 
(viii) A non-planar graph with minimum number of vertices has 
(a) 9 edges, 6 vertices (b) 6 edges, 4 vertices 
(c) 10 edges, 5 vertices (d) 9 edges, 5 vertices 
(ix) Following algorithm(s) can be used to sort n integers in the range 
3
1 n ? ?
? ?
K in
0 (n) time 
(a) Heapsort (b) Quicksort (c) Mergesort (d) Radixsort 
GATE CS - 1992
  
(x) At a particular time of computation the value of a counting semaphore is 7. 
Then 20 P operations and 15 V operations were completed on this 
semaphore. The resulting value of the semaphore is: 
(a) 42 (b) 2 (c) 7 (d) 12 
(xi) A computer system has 6 tape drives, with n process completing for them. 
Each process may need 3 tape drives. The maximum value of n for which the 
system is guaranteed to be deadlock free is: 
(a) 2 (b) 3 (c) 4 (d) 1 
(xii) Which of the following is an example of a spooled device?  
(a) The terminal used to the input data for a program being executed. 
(b) The secondary memory device in a virtual memory system 
(c) A line printer used to print the output of a number of jobs.  
(d) None of the above 
(xiii) For a context-free grammar, FOLLOW(A) is the set of terminals that can 
appear immediately to the right of non-terminal A in some “sentential” form. 
We define two sets LFOLLOW(A) and RFOLLOW(A) by replacing the word 
“sentential” by “left sentential” and “right most sentential” respectively in the 
definition of FOLLOW(A). 
Which of the following statements is/are true? 
(a) FOLLOW(A) and FOLLOW (A) may be different. 
(b) FOLLOW(A) and FOLLOW (A) are always the same. 
(c) All the three sets are identical. 
(d) All the three sets are different. 
(xiv) Consider the SLR(1) and LALR (1) parsing tables for a context free 
grammar. Which of the following statements is/are true? 
(a) The go to part of both tables may be different. 
(b) The shift entries are identical in both the tables. 
(c) The reduce entries in the tables may be different.  
(d) The error entries in the tables may be different. 
(xv) Which of the following predicate calculus statements is/are valid: 
(a) ( ) ( ) ( ) ( ) ( ) ( ) ( ) { }
x P x x Q x x P x Q x ? ? ? ? ? ?
(b) ( ) ( ) ( ) ( ) ( ) ( ) ( ) { }
x P x x Q x x P x Q x ? ? ? ? ? ?
(c) ( ) ( ) ( ) { } ( ) ( ) ( ) ( ) x P x Q x x P x x Q x ? ? ? ? ? ?
(d) ( ) ( ) ( ) { } ( ) ( ) ( ) ( ) ~ x P x Q x x P x x Q x ? ? ? ? ? ?
GATE CS - 1992
  
(xvi) Which of the following is/are tautology  
(a) a b b c ? ? ? (b) a b b c ? ? ? 
(c) ( ) a b b c ? ? ? (d) ( ) a b b c ? ? ?
(xvii) Which of the following regular expression identifies are true? 
(a) ( ) * * r r =   (b) ( ) ( ) * * * r s r s = +
(c) ( )* * * r s r s + = +   (d) * * * * r s r s = +
(xviii) If G is a context-free grammar and w is a string of length l in L(G), how 
long is a derivation of w in G, if G is Chomsky normal form?  
(a) 2l (b) 2l + 1 (c) 2l - 1  (d) l 
(xix) Context-free languages are 
(a) closed under union (b) closed under complementation 
(c) closed under intersection  (d) closed under Kleene closure  
(xx) In which of the cases stated below is the following statement true? 
“For every non-deterministic machine 
1
M there exists an equivalent 
deterministic machine 
2
M recognizing the same language“. 
(a) 
1
M is non-deterministic finite automaton  
(b) 
1
M is a non-deterministic PDA 
(c) 
1
M is a non-deterministic Turing machine 
(d) For no machine 
1
M use the above statement true 
3. Write short answers to the following:
(i) Which of the following macros can put a macro assembler into an infinite
loop? 
.MACRI M1,X .MACRO M2, X 
..IF EQ,X .IF EQ, X 
M1 X+1 M2X 
.ENDC .ENDC 
.IF NE, X .IF NE, X 
WORD X .WORD X + 1 
.ENDC .ENDC 
.ENDM .ENDM 
Give an example of a call that does so. 
(ii) Mention the pass number for each of the following activities that occur in a 
two pass assembler 
GATE CS - 1992
  
(a) object code generation  (b) literals added literal table 
(c) listing printed  
(d) address resolution of local symbols 
(iii) How many edges are there in a forest with p components having n vertices in 
all? 
(iv) Assume that the last element of the set is used as partition element in 
Quicksort. If n distinct elements from the set [1…..n] are to be sorted, give 
an input for which Quicksort takes maximum time. 
(v) Which page replacement policy sometimes leads to more page faults when 
size of memory is increased? 
SECTION – B 
4. (a) Consider addition in two’s complement arithmetic. A carry from the most
significant but does not always correspond to an overflow. Explain what is 
the condition for overflow in two’s complement arithmetic.  
(b) A priority encoder accepts three input signals (A, B and C) and produce a 
two-bit output ( )
1 0
, X X 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.   
(c) Design a 3-bit counter using D-flip flops such that not more than one flip-flop 
changes state between any two consecutive states. 
5. (a) The access times of the main memory and the Cache memory, in a computer
system, are 500 n sec and 50 n sec, respectively. It is estimated that 80% of 
the main memory request are for read the rest for write. The hit ratio for the 
read access only is 0.9 and a write-through policy (where both main and 
cache memories are updated simultaneously) is used. Determine the average 
time of the main memory.  
(b) Three devices A, B and C are corrected to the bus of a computer, 
input/output transfers for all three devices use interrupt control. Three 
interrupt request lines INTR1, INTR2 and INTR3 are available with priority of 
INTR
1
 > priority of INTR
2
 > priority of INTR
3
. 
Draw a schematic of the priority logic, using an interrupt mask register, in 
which Priority of A > Priority of B > Priority of C. 
6. A microprocessor is capable of addressing 1 megabyte of memory with a 20-bit
address bus. The system to be designed requires 256 K bytes of RAM, 256 K
bytes of EPROM, 16 I/O devices (memory mapped I/O) and 1 K byte of EERAM
(electrically erasable RAM).