ELEN500 Homework 5 Solution

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1. Do problem 2 on page 207 at the end of Chapter 5.
Find a sequence of moves that transforms:
xyzf1 f2 xyzf1 f2
---------- ----------
00-10 -0111
-1011 into: -1001
1-110 0-010
-0101 11-11
11-01
11- | 01 expand the output cube to get 11- | 11.

xyzf1 f2
----------
00-10
-1011
1-110
-0101
11-11 *
1-1 | 10 reduce the cube in y to get 101 | 10.
xyzf1 f2
----------
00-10
-1011
10110 *
-0101
11-11
101 | 10 expand the cube in x to get -01 | 10.
xyzf1 f2
----------
00-10
-1011
-0110 *
-0101
11-11
-01 | 10 expand the cube in outputs to get -01 | 11. (contains -01 | 01).
xyzf1 f2
----------
00-10
-1011
-0111 *
11-11
00- | 10 reduce the cube in z to get 000 | 10.
xyzf1 f2
----------
00010 *
-1011
-0111
11-11
000 | 10 expand the cube in y to get 0-0 | 10.
xyzf1 f2
----------
0-010 *
-1011
-0111
11-11
-10 | 11 reduce the cube in the output to get -10 | 01.
xyzf1 f2
----------
0-010
-1001 *
-0111
11-11
2. Do problem 5 on page 208 at the end of Chapter 5.
Find the cofactor of :
vwxyzfgh
--------------
1-0-1101
001--001
-111-110
01--0111
110-0010
1010-101

with respect to the cube --110 | 110
vwfg
--------------
-111
0111

Note: this cofactor is not a tautology, so the cube --110 | 110 is not a part of any valid move.
3. For f(w,x,y,z) = x'yz + w'y + wx'z
a) is the function UNATE? No
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? x
d) For which variables, if any, is the function non-monotonic? w