CS302 Digital Logic Design Assignment 3 Solution Spring June 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.