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Homework #1
January 8, 2008
1
Homework #1
due January 23 at noon
ECE 15a
Winter 2008
1. Expand the following into a polynomial having as few terms as possible:
(2p) (a) (ab’+bc)(a’b’+ac+bc)
(3p) (b) (x+y)(x’+y)(x+y’)(x’+y’)
2. Factor the following into linear factors:
(1p) (a) x’y+zw’
(2p) (b) ax’+ay(x+z)
(2p) (c) a’bc+ad
3. Using Venn diagrams, show that if A and B are sets, then
(5p)(a) (A’+B)’ = AB’
(5p) (b) X(Y+Z) = XY + XZ
4. Simplify the following:
(5p) (a)
(a’+b’+c)(a’b+ac’)’
(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’yz’)
(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 01/13/2010 for the course ECE 15A taught by Professor M during the Winter '08 term at UCSB.
 Winter '08
 M

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