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Digital Logic and Design – CS302

	Assignment No. 1 Semester Spring 2013 Digital Logic and Design – CS302	Total Marks:   20 Due Date: 2nd May 2013
Objective: The assignment has been designed to develop the understanding related to the followings, Binary conversion and addition BCD conversion and addition Instructions: Please read the following instructions carefully before solving & submitting assignment: It should be clear that your assignment will not get any credit (zero marks) due to followings, 1.      The assignment is submitted after due date. 2.      The submitted assignment does not open or file is corrupt. 3.      The assignment not submitted in MS Word file format. 4.      The assignment is copied (from other student or copied from handouts or internet). 5.      Student ID is not mentioned in the assignment file or name of file is other than student ID. GOOD LUCK
Question 1                                                                                                                                          [5 Marks] Convert the decimal numbers “129” and “478” into their equivalents in the followings: a.      Binary b.      BCD (Show complete conversion steps) Question 2                                                                                                                                          [5Marks] a.      Perform binary addition of “129”  and “478” b.      Perform BCD addition of “129”  and “478” (Show complete addition steps) Question 3                                                                                                                                          [10Marks] Fill the empty columns in the table by performing each operation against each row.                                                                                                                                                                                                                          A B C X = NOT(A XOR B) Y = B XOR C X AND Y 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1

CS402_3_SOL

Solution

Qustion 1 

a)

b)

Question 2

reflexive, Symmetric, Transitive and anti-symmetric

Q#01:  Let X = { 1, 5, 9} , Y =  { 3, 4, 7}

            Define f : X →Y by  f(1) = 4,  f(5) = 7, f(9) = 4

(i)                 Is f one-one?

(ii)               Is f onto?

(iii)             Does inverse of f exist?                                                       

Q#02: Let A = {a, b, c} and R = {(a, c), (b, b), (c, a)} be a relation on A.

 Determine whether R is reflexive, Symmetric, Transitive and anti-symmetric, or not. 

                                                                                                           

Q#03: Find the 36th term of the arithmetic sequence whose 3rd term is 7 and 8th term is 17.

Please provide solution.

NFA/FA

Q. No. 1 Construct Non-Deterministic Finite Automaton (NFA) from the concatenation of the following two languages:                                         

                                                           

a. Language of all strings defined over Σ = {0, 1} whose length is even and number of 1’s are odd.

b. Language of all strings defined over Σ = {0, 1} whose second last letter is 1.

Hint: First construct FA for the given languages and then construct NFA from their concatenation.                                                                                 

Q. No. 2 Construct a Finite Automaton (FA) for the language of all strings defined over Σ = {0, 1} that ends with substring “01” and have odd length.

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