Homework #1
January 17, 2007
1
Homework #1
due January 22 at noon
ECE 15a
Winter 2007
1. Expand the following into a polynomial having as few terms as possible:
(2p) (a) (x+y’x)(x+yz)
(3p) (b) (x+y)(x’+y)(x+y’)(x’+y’)
2. Factor the following into linear factors:
(1p) (a) xy+zw
(2p) (b) x+y(z+w)
(2p) (c) abc+a’d
3. Using Venn diagrams, show that if A and B are sets, then
(5p)(a)
(A+B)’ = A’B’
(5p) (b) X(Y+Z) = XY + XZ
4. Simplify the following:
(5p) (a)
(a+b’+c)’(ab+a’c’)
(5p) (b) (x’y+xy+x’y)(x’y+zw)
(5p) (c) abx’+abx+x’abx
(5p) (d) (xy+xy’+x’y)(x+y+z+x’y’z’)
(10p) 5. Write out the proof of Theorems 1 and 2 (See lecture #2), based on the fact that
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This note was uploaded on 01/20/2011 for the course ECE 15A taught by Professor M during the Winter '08 term at UCSB.
 Winter '08
 M

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