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hw1_solution

# hw1_solution - ECEN 248 Fall 2011 Homework 1 Solutions 2.1...

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Unformatted text preview: ECEN 248 Fall 2011 Homework 1 Solutions 2.1 Prove: x + yz = (x + y)∙(x + z) 1 2.2 Prove: (x + y)∙(x + ) = x 1 0 2.3 Prove: 1 1 2.7 a) whether Compare truth tables: LHS RHS 0 0 0 0 0 0 0 1 1 1 0 1 0 1 1 0 1 1 1 1 1 0 0 1 1 1 0 1 1 1 1 1 0 1 1 1 1 1 0 0 LHS = RHS. The expression is valid. b) whether valid. Compare truth tables: LHS RHS 0 0 0 1 1 0 0 1 0 0 0 1 0 0 0 0 1 1 1 1 1 0 0 1 1 1 0 1 0 0 1 1 0 1 1 1 1 1 1 1 LHS = RHS. The expression is valid. c) whether Compare truth tables: is valid. is is valid. ECEN 248 Fall 2011 LHS RHS 0 0 0 0 0 0 0 1 1 0 One counter example is enough for disproval. The expression is invalid. 2.8 figure 2.19a x2 A C f x3 B D x1 Expression: Waveform: 2.9 figure 2.19b ECEN 248 Fall 2011 Expression: Waveform: 2.10 prove ∑ 1,2,3,4,5,6,7 ...
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