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TOPIC_CLASSIFICATION

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The expression large frac x y x y 2 is equal to The maximum of x and y The minimum of x and y 1 None of the above

Absolute Value

If x is real and mid x 2 2x 3 mid 11 then possible values of mid x 3 x 2 x mid include 2 4 2 14 4 52 14 52

Absolute Value

If mid 4X 7 mid 5 then the values of 2 mid X mid mid X mid is quad 2 left dfrac 1 3 right left dfrac 1 2 right 3 left dfrac 3 2 right 9 left dfrac 2 3 right 9

Absolute Value

An Abstract Data Type ADT is same as an abstract class a data type that cannot be instantiated a data type for which only the operations defined on it can be used but none else all of the above

Abstract Data Type

The number of full and half adders required to add 16 bit numbers is 8 half adders 8 full adders 1 half adder 15 full adders 16 half adders 0 full adders 4 half adders 12 full adders

Adder

Fill in the blanks In the two bit full adder subtractor unit shown in below figure when the switch is in position 2 ___________ using _________ arithmetic

Adder

Consider the ALU shown below If the operands are in 2 u2019s complement representation which of the following operations can be performed by suitably setting the control lines K and C_0 only and u2013 denote addition and subtraction respectively A B and A u2013 B but not A 1 A B and A 1 but not A u2013 B A B but not A u2013 B or A 1 A B and A u2013 B and A 1

Adder

Consider an eight bit ripple carry adder for computing the sum of A and B where A and B are integers represented in 2 s complement form If the decimal value of A is one the decimal value of B that leads to the longest latency for the sum to stabilize is ___________

Adder

An N bit carry lookahead adder where N is a multiple of 4 employs ICs 74181 4 bit ALU and 74182 4 bit carry lookahead generator The minimum addition time using the best architecture for this adder is proportional to N proportional to log N a constant None of the above

Adder

A 4 bit carry look ahead adder which adds two 4 bit numbers is designed using AND OR NOT NAND NOR gates only Assuming that all the inputs are available in both complemented and uncomplemented forms and the delay of each gate is one time unit what is the overall propagation delay of the adder Assume that the carry network has been implemented using two level AND OR logic 4 time units 6 time units 10 time units 12 time units

Adder

Consider a carry look ahead adder for adding two n bit integers built using gates of fan in at most two The time to perform addition using this adder is Theta 1 Theta log n Theta sqrt n Theta n

Adder

Aliasing in the context of programming languages refers to multiple variables having the same memory location multiple variables having the same value multiple variables having the same identifier multiple uses of the same variable

Aliasing

The maximum gate delay for any output to appear in an array multiplier for multiplying two n bit numbers is O n 2 O n O log n O 1

Array Multiplier

Consider an array multiplier for multiplying two n bit numbers If each gate in the circuit has a unit delay the total delay of the multiplier is Theta 1 Theta log n Theta n Theta n 2

Array Multiplier

The procedure given below is required to find and replace certain characters inside an input character string supplied in array A The characters to be replaced are supplied in array oldc while their respective replacement characters are supplied in array newc Array A has a fixed length of five characters while arrays oldc and newc contain three characters each However the procedure is flawed void find_and_replace char A char oldc char newc for int i 0 i lt 5 i for int j 0 j lt 3 j if A i oldc j A i newc j The procedure is tested with the following four test cases oldc u201cabc u201d newc u201cdab u201d oldc u201ccde u201d newc u201cbcd u201d oldc u201cbca u201d newc u201ccda u201d oldc u201cabc u201d newc u201cbac u201d The tester now tests the program on all input strings of length five consisting of characters u2018 a u2019 u2018 b u2019 u2018 c u2019 u2018 d u2019 and u2018 e u2019 with duplicates allowed If the tester carries out this testing with the four test cases given above how many test cases will be able to capture the flaw Only one Only two Only three All four

Arrays

The procedure given below is required to find and replace certain characters inside an input character string supplied in array A The characters to be replaced are supplied in array oldc while their respective replacement characters are supplied in array newc Array A has a fixed length of five characters while arrays oldc and newc contain three characters each However the procedure is flawed void find_and_replace char A char oldc char newc for int i 0 i lt 5 i for int j 0 j lt 3 j if A i oldc j A i newc j The procedure is tested with the following four test cases oldc u201cabc u201d newc u201cdab u201d oldc u201ccde u201d newc u201cbcd u201d oldc u201cbca u201d newc u201ccda u201d oldc u201cabc u201d newc u201cbac u201d If array A is made to hold the string u201c abcde u201d which of the above four test cases will be successful in exposing the flaw in this procedure None 2 only 3 and 4 only 4 only

Arrays

Suppose you are given arrays p 1 N and q 1 N both uninitialized that is each location may contain an arbitrary value and a variable count initialized to 0 Consider the following procedures set and is _set set i count count 1 q count i p i count is_set i if p i u2264 0 or p i gt count return false if q p i u2260 i return false return true Suppose we make the following sequence of calls set 7 set 3 set 9 After these sequence of calls what is the value of count and what do q 1 q 2 q 3 p 7 p 3 and p 9 contain Complete the following statement The first count elements of __________contain values i such that set _________________ has been called Show that if set i has not been called for some i then regardless of what p i contains is _set i will return false

Arrays

Let A be a two dimensional array declared as follows A array 1 u2026 10 1 u2026 15 of integer Assuming that each integer takes one memory location the array is stored in row major order and the first element of the array is stored at location 100 what is the address of the element A i j 15i j 84 15j i 84 10i j 89 10j i 89

Arrays

In a compact single dimensional array representation for lower triangular matrices i e all the elements above the diagonal are zero of size n imes n non zero elements i e elements of lower triangle of each row are stored one after another starting from the first row the index of the i j th element of the lower triangular matrix in this new representation is i j i j 1 j 1 frac i i 1 2 i frac j j 1 2

Arrays

Consider the C function given below Assume that the array listA contains n gt 0 elements sorted in ascending order int ProcessArray int listA int x int n int i j k i 0 j n 1 do k i j 2 if x lt listA k j k 1 if listA k lt x i k 1 while i lt j if listA k x return k else return 1 Which one of the following statements about the function ProcessArray is CORRECT It will run into an infinite loop when x is not in listA It is an implementation of binary search It will always find the maximum element in listA It will return u2212 1 even when x is present in listA

Arrays

Consider an array A 1 n It consists of a permutation of numbers 1 n Now compute another array B 1 n as follows B A i i for all i Which of the following is true B will be a sorted array B is a permutation of array A Doing the same transformation twice will not give the same array B is not a permutation of array A None of the above

Arrays

An n imes n array v is defined as follows v left i j right i j for all i j i leq n 1 leq j leq n The sum of the elements of the array v is 0 n 1 n 2 3n 2 n 2 frac left n 1 right 2

Arrays

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

Arrays

An array A contains n geq 1 positive integers in the locations A 1 A 2 dots A n The following program fragment prints the length of a shortest sequence of consecutive elements of A A i A i 1 dots A j such that the sum of their values is geq M a given positive number It prints u2018 n 1 u2019 if no such sequence exists Complete the program by filling in the boxes In each case use the simplest possible expression Write only the line number and the contents of the box begin i 1 j 1 sum u25fb min n finish false while not finish do if u25fb then if j n then finish true else begin j j 1 sum u25fb end else begin if j i lt min then min j i sum sum u2013A i i i 1 end writeln min 1 end

Arrays

A Young tableau is a 2D array of integers increasing from left to right and from top to bottom Any unfilled entries are marked with infty and hence there cannot be any entry to the right of or below a infty The following Young tableau consists of unique entries 1 2 5 14 3 4 6 23 10 12 18 25 31 infty infty infty When an element is removed from a Young tableau other elements should be moved into its place so that the resulting table is still a Young tableau unfilled entries may be filled with a infty The minimum number of entries other than 1 to be shifted to remove 1 from the given Young tableau is _____

Arrays

A program P reads in 500 integers in the range 0 100 representing the scores of 500 students It then prints the frequency of each score above 50 What would be the best way for P to store the frequencies An array of 50 numbers An array of 100 numbers An array of 500 numbers A dynamically allocated array of 550 numbers

Arrays

The order of an internal node in a B tree index is the maximum number of children it can have Suppose that a child pointer takes 6 bytes the search field value takes 14 bytes and the block size is 512 bytes What is the order of the internal node 24 25 26 27

B Tree

The order of a leaf node in a B tree is the maximum number of value data record pointer pairs it can hold Given that the block size is 1K bytes data record pointer is 7 bytes long the value field is 9 bytes long and a block pointer is 6 bytes long what is the order of the leaf node 63 64 67 68

B Tree

In a database file structure the search key field is 9 bytes long the block size is 512 bytes a record pointer is 7 bytes and a block pointer is 6 bytes The largest possible order of a non leaf node in a B tree implementing this file structure is 23 24 34 44

B Tree

Consider the B tree in the adjoining figure where each node has at most two keys and three links Now the key K 50 is deleted from the B tree resulting after the two insertions made earlier Consider the following statements about the B tree resulting after this deletion The height of the tree remains the same The node k20 disregarding the links is present in the tree The root node remains unchanged disregarding the links 1 Which one of the following options is true Statements i and ii are true Statements ii and iii are true Statements iii and i are true All the statements are false

B Tree

Consider the B tree in the adjoining figure where each node has at most two keys and three links Keys K 15 and then K 25 are inserted into this tree in that order Exactly how many of the following nodes disregarding the links will be present in the tree after the two insertions 1 2 3 4

B Tree

Consider a table T in a relational database with a key field K A B tree of order p is used as an access structure on K where p denotes the maximum number of tree pointers in a B tree index node Assume that K is 10 bytes long disk block size is 512 bytes each data pointer PD is 8 bytes long and each block pointer PB is 5 bytes long In order for each B tree node to fit in a single disk block the maximum value of p is 20 22 23 32

B Tree

Consider a B tree with degree m that is the number of children c of any internal note except the root is such that m leq c leq 2m 1 Derive the maximum and minimum number of records in the leaf nodes for such a B tree with height h h geq 1 Assume that the root of a tree is at height 0

B Tree

A B Tree used as an index for a large database table has four levels including the root node If a new key is inserted in this index then the maximum number of nodes that could be newly created in the process are 5 4 3 2

B Tree

A B tree index is to be built on the Name attribute of the relation STUDENT Assume that all the student names are of length 8 bytes disk blocks are of size 512 bytes and index pointers are of size 4 bytes Given the scenario what would be the best choice of the degree i e number of pointers per node of the B tree 16 42 43 44

B Tree

Which of the following is correct B trees are for storing data on disk and B trees are for main memory Range queries are faster on B trees B trees are for primary indexes and B trees are for secondary indexes The height of a B tree is independent of the number of records

B Tree

The following table refers to search items for a key in B trees and B trees B u2212tree B u2212tree Successful search Unsuccessful search Successful search Unsuccessful search X1 X2 X3 X4 A successful search means that the key exists in the database and unsuccessful means that it is not present in the database Each of the entries X_1 X_2 X_3 and X_4 can have a value of either Constant or Variable Constant means that the search time is the same independent of the specific key value where variable means that it is dependent on the specific key value chosen for the search Give the correct values for the entries X_1 X_2 X_3 and X_4 for example X_1 ext Constant X_2 ext Constant X_3 ext Constant X_4 ext Constant Relation R A B has the following view defined on it CREATE VIEW V AS SELECT R1 A R2 B FROM R AS R1 R as R2 WHERE R1 B R2 A The current contents of relation R are shown below What are the contents of the view V A B 1 2 2 4 6 6 9 2 3 4 5 7 8 10 The tuples 2 11 and 11 6 are now inserted into R What are the additional tuples that are inserted in V

B Tree

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

B Tree

B trees are preferred to binary trees in databases because Disk capacities are greater than memory capacities Disk access is much slower than memory access Disk data transfer rates are much less than memory data transfer rates Disks are more reliable than memory

B Tree

A B tree of order d is a tree in which each internal node has between d and 2 d key values An internal node with M key values has M 1 children The root if it is an internal node has between 1 and 2d key values The distance of a node from the root is the length of the path from the root to the node All leaves are at the same distance from the root The height of the tree is the distance of a leaf from the root What is the total number of key values in the internal nodes of a B tree with l leaves l geq 2 What is the maximum number of internal nodes in a B tree of order 4 with 52 leaves What is the minimum number of leaves in a B tree of order d and height h h geq 1

B Tree

Suppose a fair six sided die is rolled once If the value on the die is 1 2 or 3 the die is rolled a second time What is the probability that the sum total of values that turn up is at least 6 dfrac 10 21 dfrac 5 12 dfrac 2 3 dfrac 1 6

Bayes Theorem

Box P has 2 red balls and 3 blue balls and box Q has 3 red balls and 1 blue ball A ball is selected as follows i select a box ii choose a ball from the selected box such that each ball in the box is equally likely to be chosen The probabilities of selecting boxes P and Q are dfrac 1 3 and dfrac 2 3 respectively Given that a ball selected in the above process is a red ball the probability that it came from the box P is dfrac 4 19 dfrac 5 19 dfrac 2 9 dfrac 19 30

Bayes Theorem

An automobile plant contracted to buy shock absorbers from two suppliers X and Y X supplies 60 and Y supplies 40 of the shock absorbers All shock absorbers are subjected to a quality test The ones that pass the quality test are considered reliable Of X u2019s shock absorbers 96 are reliable Of Y u2019s shock absorbers 72 are reliable The probability that a randomly chosen shock absorber which is found to be reliable is made by Y is A 0 288 B 0 334 C 0 667 D 0 720

Bayes Theorem

The number of possible commutative binary operations that can be defined on a set of n elements for a given n is ___________

Binary Operation

The binary operator u2260 is defined by the following truth table p q p u2260 q 0 0 0 0 1 1 1 0 1 1 1 0 Which one of the following is true about the binary operator u2260 Both commutative and associative Commutative but not associative Not commutative but associative Neither commutative nor associative

Binary Operation

On the set N of non negative integers the binary operation ______ is associative and non commutative

Binary Operation

Let be the binary operator defined as X Y X Y where X and Y are Boolean variables Consider the following two statements S1 P Q R P Q R S2 Q R R Q Which are the following is are true for the Boolean variables P Q and R Only S1 is true Only S2 is true Both S1 and S2 are true Neither S1 nor S2 are true

Binary Operation

For the set N of natural numbers and a binary operation f N x N u2192 N an element z u220a N is called an identity for f if f a z a f z a for all a u220a N Which of the following binary operations have an identity f x y x y 3 f x y max x y f x y xy I and II only II and III only I and III only None of these

Binary Operation

Consider the set a b c with binary operators and defined as follows a b c a b a c b a b c c a c b a b c a a b c b b c a c c c b For example a c c c a a c b c and b c a Given the following set of equations a x a y c b x c y c The number of solution s i e pair s x y that satisfy the equations is 0 1 2 3

Binary Operation

A logical binary relation odot is defined as follows A B A odot B True True True True False True False True False False False True Let sim be the unary negation NOT operator with higher precedence then odot Which one of the following is equivalent to A wedge B sim A odot B sim A odot sim B sim sim A odot sim B sim sim A odot B

Binary Operation

A binary operation oplus on a set of integers is defined as x oplus y x 2 y 2 Which one of the following statements is TRUE about oplus A Commutative but not associative B Both commutative and associative C Associative but not commutative D Neither commutative nor associative

Binary Operation

When searching for the key value 60 in a binary search tree nodes containing the key values 10 20 40 50 70 80 90 are traversed not necessarily in the order given How many different orders are possible in which these key values can occur on the search path from the root to the node containing the value 60 35 64 128 5040

Binary Search Tree

The numbers 1 2 dots n are inserted in a binary search tree in some order In the resulting tree the right subtree of the root contains p nodes The first number to be inserted in the tree must be p p 1 n p n p 1

Binary Search Tree

The following numbers are inserted into an empty binary search tree in the given order 10 1 3 5 15 12 16 What is the height of the binary search tree the height is the maximum distance of a leaf node from the root 2 3 4 6

Binary Search Tree

Suppose the numbers 7 5 1 8 3 6 0 9 4 2 are inserted in that order into an initially empty binary search tree The binary search tree uses the usual ordering on natural numbers What is the in order traversal sequence of the resultant tree 7 5 1 0 3 2 4 6 8 9 0 2 4 3 1 6 5 9 8 7 0 1 2 3 4 5 6 7 8 9 9 8 6 4 2 3 0 1 5 7

Binary Search Tree

Suppose that we have numbers between 1 and 100 in a binary search tree and want to search for the number 55 Which of the following sequences CANNOT be the sequence of nodes examined 10 75 64 43 60 57 55 90 12 68 34 62 45 55 9 85 47 68 43 57 55 79 14 72 56 16 53 55

Binary Search Tree

Let T n be the number of different binary search trees on n distinct elements Then T n sum_ k 1 n T k 1 T x where x is n k 1 n k n k 1 n k 2

Binary Search Tree

A program takes as input a balanced binary search tree with n leaf nodes and computes the value of a function g x for each node x If the cost of computing g x is Large min left substack ext number of leaf nodes ext in left subtree of x substack ext number of leaf nodes ext in right subtree of x right Then the worst case time complexity of the program is Theta n Theta n log n Theta n 2 Theta n 2 log n

Binary Search Tree

A data structure is required for storing a set of integers such that each of the following operations can be done in O log n time where n is the number of elements in the set Deletion of the smallest element Insertion of an element if it is not already present in the set Which of the following data structures can be used for this purpose A heap can be used but not a balanced binary search tree A balanced binary search tree can be used but not a heap Both balanced binary search tree and heap can be used Neither balanced search tree nor heap can be used

Binary Search Tree

A binary search tree is used to locate the number 43 Which of the following probe sequences are possible and which are not Explain a 61 52 14 17 40 43 b 2 3 50 40 60 43 c 10 65 31 48 37 43 d 81 61 52 14 41 43 e 17 77 27 66 18 43

Binary Search Tree

A binary search tree is generated by inserting in order the following integers 50 15 62 5 20 58 91 3 8 37 60 24 The number of nodes in the left subtree and right subtree of the root respectively is 4 7 7 4 8 3 3 8

Binary Search Tree

A binary search tree contains the numbers 1 2 3 4 5 6 7 8 When the tree is traversed in pre order and the values in each node printed out the sequence of values obtained is 5 3 1 2 4 6 8 7 If the tree is traversed in post order the sequence obtained would be 8 7 6 5 4 3 2 1 1 2 3 4 8 7 6 5 2 1 4 3 6 7 8 5 2 1 4 3 7 8 6 5

Binary Search Tree

A Binary Search Tree BST stores values in the range 37 to 573 Consider the following sequence of keys 81 537 102 439 285 376 305 52 97 121 195 242 381 472 142 248 520 386 345 270 307 550 149 507 395 463 402 270 Suppose the BST has been unsuccessfully searched for key 273 Which all of the above sequences list nodes in the order in which we could have encountered them in the search II and III only I and III only III and IV only III only

Binary Search Tree

Insert the following keys one by one into a binary search tree in the order specified 15 32 20 9 3 25 12 1 Show the final binary search tree after the insertions Draw the binary search tree after deleting 15 from it Complete the statements S1 S2 and S3 in the following function so that the function computes the depth of a binary tree rooted at t ypedef struct tnode int key struct tnode left right Tree int depth Tree t int x y it t NULL return 0 x depth t gt left S1 ___________ S2 if x gt y return __________ S3 else return _______

Binary Search Tree

What is the number of binary trees with 3 nodes which when traversed in post order give the sequence A B C Draw all these binary trees

Binary Tree

State whether the following statements are TRUE or FALSE It is possible to construct a binary tree uniquely whose pre order and post order traversals are given

Binary Tree

State whether the following statements are TRUE or FALSE If the number of leaves in a tree is not a power of 2 then the tree is not a binary tree

Binary Tree

Prove by the principal of mathematical induction that for any binary tree in which every non leaf node has 2 descendants the number of leaves in the tree is one more than the number of non leaf nodes

Binary Tree

In the balanced binary tree in the below figure how many nodes will become unbalanced when a node is inserted as a child of the node u201cg u201d 1 3 7 8

Binary Tree

If the binary tree in figure is traversed in inorder then the order in which the nodes will be visited is ______

Binary Tree

Construct a binary tree whose preorder traversal is K L N M P R Q S T and inorder traversal is N L K P R M S Q T

Binary Tree

Consider the binary tree in the figure below Outline a procedure in Pseudo code to delete an arbitrary node from such a binary tree with n nodes that preserves the structures What is the worst case time complexity of your procedure

Binary Tree

Consider the binary tree in the figure below Give different steps for deleting the node with key 5 so that the structure is preserved

Binary Tree

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

Binary Tree

A binary tree T has n leaf nodes The number of nodes of degree 2 in T is log_2 n n 1 n 2 n

Binary Tree

A binary search tree contains the value 1 2 3 4 5 6 7 8 The tree is traversed in pre order and the values are printed out Which of the following sequences is a valid output 5 3 1 2 4 7 8 6 5 3 1 2 6 4 8 7 5 3 2 4 1 6 7 8 5 3 1 2 4 7 6 8

Binary Tree

Which of the following sequences denotes the post order traversal sequence of the below tree f e g c d b a g c b d a f e g c d b f e a f e d g c b a

Binary Tree

The weighted external path length of the binary tree in figure is ______

Binary Tree

Consider the binary tree in the figure below a What structure is represented by the binary tree

Binary Tree

When a coin is tossed the probability of getting a Head is p 0 lt p lt 1 Let N be the random variable denoting the number of tosses till the first Head appears including the toss where the Head appears Assuming that successive tosses are independent the expected value of N is dfrac 1 p dfrac 1 1 p dfrac 1 p 2 dfrac 1 1 p 2

Binomial Distribution

For each element in a set of size 2n an unbiased coin is tossed The 2n coin tosses are independent An element is chosen if the corresponding coin toss was a head The probability that exactly n elements are chosen is frac 2n mathrm C _n 4 n frac 2n mathrm C _n 2 n frac 1 2n mathrm C _n frac 1 2

Binomial Distribution

An unbiased coin is tossed repeatedly until the outcome of two successive tosses is the same Assuming that the trials are independent the expected number of tosses is 3 4 5 6

Binomial Distribution

A random bit string of length n is constructed by tossing a fair coin n times and setting a bit to 0 or 1 depending on outcomes head and tail respectively The probability that two such randomly generated strings are not identical is frac 1 2 n 1 frac 1 n frac 1 n 1 frac 1 2 n

Binomial Distribution

The total number of Boolean functions which can be realised with four variables is 4 17 256 65 536

Boolean Algebra

The simultaneous equations on the Boolean variables x y z and w x y z 1 xy 0 xz w 1 xy bar z bar w 0 have the following solution for x y z and w respectively 0 1 0 0 1 1 0 1 1 0 1 1 1 0 0 0

Boolean Algebra

Let x_ 1 u2295 x_ 2 u2295 x_ 3 u2295 x_ 4 0 where x_ 1 x_ 2 x_ 3 x_ 4 are Boolean variables and u2295 is the XOR operator Which one of the following must always be TRUE x_ 1 x_ 2 x_ 3 x_ 4 0 x_ 1 x_ 3 x_ 2 0 bar x _ 1 u2295 bar x _ 3 bar x _ 2 u2295 bar x _ 4 x_ 1 x_ 2 x_ 3 x_ 4 0

Boolean Algebra

For x in 0 1 let lnot x denote the negation of x that is lnot x begin cases 1 amp mbox iff x 0 0 amp mbox iff x 1 end cases If x in 0 1 n then lnot x denotes the component wise negation of x that is lnot x _i biggl lnot x_i mid i in 1 n biggr Consider a circuit C computing a function f 0 1 n o 0 1 using AND land OR lor and NOT lnot gates Let D be the circuit obtained from C by replacing each AND gate by an OR gate and replacing each OR gate by an AND Suppose D computes the function g Which of the following is true for all inputs x g x lnot f x g x f x land f lnot x g x f x lor f lnot x g x lnot f lnot x None of the above

Boolean Algebra

What values of A B C and D satisfy the following simultaneous Boolean equations overline A AB 0 AB AC AB A overline C CD overline C D A 1 B 0 C 0 D 1 A 1 B 1 C 0 D 0 A 1 B 0 C 1 D 1 A 1 B 0 C 0 D 0

Boolean Expressions

The truth table X Y X Y 0 0 0 0 1 0 1 0 1 1 1 1 represents the Boolean function X X Y X oplus Y Y

Boolean Expressions

The function AB C A BC ABC A B C AB C is equivalent to AC AB A C AB AC A C A B AC AB A B AC AB

Boolean Expressions

The Boolean expression A oplus B oplus A is equivalent to AB bar A bar B bar A B A bar B B bar A

Boolean Expressions

Let f w x y z sum left 0 4 5 7 8 9 13 15 right Which of the following expressions are NOT equivalent to f P x y z w xy wy z xz Q w y z wx y xz R w y z wx y xyz xy z S x y z wx y w y P only Q and S R and S S only

Boolean Expressions

Let f A B A B Simplified expression for function f f x y y z is x z xyz xy z None of the above

Boolean Expressions

Let be defined as x y bar x y Let z x y Value of z x is bar x y x 0 1

Boolean Expressions

If P Q R are Boolean variables then P bar Q P bar Q P R bar P bar R bar Q simplifies to P bar Q P bar R P bar Q R P bar R Q

Boolean Expressions

Find values of Boolean variables A B C which satisfy the following equations A B 1 AC BC A C 1 AB 0

Boolean Expressions

Define the connective for the Boolean variables X and Y as X Y XY X Y Let Z X Y Consider the following expressions P Q and R P X Y Z Q Y X Z R X Y Z 1 Which of the following is TRUE Only P and Q are valid Only Q and R are valid Only P and R are valid All P Q R are valid

Boolean Expressions

Consider the following state diagram and its realization by a JK flip flop The combinational circuit generates J and K in terms of x y and Q The Boolean expressions for J and K are overline x oplus y and overline x oplus y overline x oplus y and x oplus y x oplus y and overline x oplus y x oplus y and x oplus y

Boolean Expressions

A Boolean function x u2019y u2019 xy x u2019y is equivalent to x y x y x y x y

Boolean Expressions

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

Boolean Expressions