hw2_2012 - + a b c d . a b c d a a a a a a a b c d b a b b...

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Homework #2 due January 30 at noon ECE 15a Winter 2012 On your homework, please, write your discussion section day and time. For problems 1-4, assume the 2-value Boolean algebra over the set B={0,1} with + and . operators defined as: + 0 1 . 0 1 0 0 1 0 0 0 1 1 1 1 0 1 Demonstrate, that each of the statements 1 – 4 is valid using (a) truth tables (b) Venn diagrams. (10p) 1. (a+b)’=a’b’ (10p) 2. a(a+b)=a (10p) 3. If a+x=b+x and a+x’=b+x’, then a=b. (10p) 4. If ab’=0 then a+bc=b(a+c) for every element c in B. (15p) 5. Show that the set {a,b,c,d} with operations (+) and (.) defined below is a Boolean algebra.
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Unformatted text preview: + a b c d . a b c d a a a a a a a b c d b a b b a b b b c c c a b c d c c c c c d a a d d d d c c d For problems 6 and 7, use Boolean algebra postulates and theorems. Supply reasons for each step. Use postulate and theorem numbers from lecture #3 notation. (15p) 6. Simplify the following expressions into a minimum sum of products: (a) 5p (((x+y)’+z)’w)’ (b) 5p (a+b)’cd’+a+b (c) 5p ((a+b)’+c’d)’ (15p) 7. Simplify each of the following expressions into a minimum product of sum form: (a) 5p ab+abc’+ac’d (b) 5p a+bc+def (c) 5p ab + bc + ac...
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This note was uploaded on 04/04/2012 for the course ECE 15A taught by Professor M during the Spring '08 term at UCSB.

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