ELEN500 Homework 4

xyz	f1 f2		wxyz	f1 f2
-----	-----		-----	-----
0-0-	10		000-	11
-10-	10	into:	-10-	10
1-11	11		1-11	11
00--	01		0-1-	01
0-1-	01

Solution:

Move 1
0-0- | 10	reduced in input x to	000- | 10
Move 2
00-- | 01	reduced in input y to	000- | 01
Move 3	(could pick either of the above rows)
000- | 01	expanded in the output to	000- | 11

then the redundant row 000- | 10 can be eliminated.

First select only the rows with output h equal to 1.

vwxyz	h
---------	-----
1-0-1	1
001--	1
01--0	1
1010-	1

Next select only the rows with containg the cell 0-10- in the input.

vwxyz	h
---------	---
001--	1
01--0	1

remove the input columns other than w and z(the dashes in 0-10-) to get the cofactor:

wz	h
----	---
0-	1
10	1

2b) Is this cofactor a tautology? No, because the input combination 11 is not covered.
Or the shortcut shows the sum of the coverred cells is 3 minuterms and we need at least 4 minterms coverred for a two input cofactor to be a tautology.

b) For which variables, if any, is the function monotonically increasing? y and z

c) For which variables, if any, is the function monotonically decreasing? w and x

d) For which variables, if any, is the function non-monotonic? None