CS302 Digital Logic Design Assignment 3 Solution Spring 2013

Question 1                                                                                                                                          [15 Marks]

Using Quine-McCluskey method reduce the expression given below by following all the steps.

 

Answer:

                                   

Minterm A B C D
1 0 0 0 1
3 0 0 1 1
4 0 1 0 0
5 0 1 0 1
10 1 0 1 0
12 1 1 0 0
13 1 1 0 1
15 1 1 1 1

                                            Table of Minterm

 

Minterm A B C D
1

4

0

0

0

1

0

0

1

0

5

3

10

12

0

0

1

1

1

0

0

1

0

1

1

0

1

1

0

0

13 1 1 0 1
15 1 1 1 1

                                 Table no 4: rearrange variables

 

 

Minterm A B C D
1, 3 0 0 * 1
1, 5 0 * 0 1
4, 5 0 1 1 *
4, 12 * 1 0 0
5, 13 0 1 * 1
12, 13 1 1 0 *
13, 15 1 1 * 1
5, 13 * 1 0 1

                               Table No 3: single variable removed

 

Minterm A B C D
1, 3, 5 0 * * 1
4, 5, 12, 13 * 1 0 *
12, 13, 15 1 1 * *

                                      Table no 4 Double variable removed

 

 

  1 3 4 5 10 12 13 15
$ X   x        
    $ x   X x  
AB           $ x X

                                        Table 5 simplification

 

 

Question 2                                                                                                                                          [5Marks]

If the waveforms in the figure given below are applied to an active-LOW input S-R latch, draw the resulting Q output waveform in relation to the inputs. Assume that Q starts at LOW.

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