Solutions_HW1

Solutions_HW1 - Remo Pillat 06/10/2006 CDA 3103 Summer 2006...

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1 Remo Pillat 06/10/2006 CDA 3103 – Summer 2006 Assignment 1 - Solutions Question 1 (10 points) One logic function that is used for variety of purposes (e.g. adding, and parity checking), is the exclusive-OR. The output of an exclusive-OR function is true only if exactly one of the inputs is true. Show the truth table of a two-input exclusive-OR function, and implement it using AND gates, OR gates and inverters. Answer: The truth table of the XOR is implicitly given by the description in the question. If you look at the truth table and apply the canonical form of the Sum-of-Products (SOP), you can easily see, that XOR can be represented by AND, OR and NOT. X YX Y ⊕= + ii The implementation with logic gates follows: XY X Y X Y X Y 0 0 0 0 1 1 1 0 1 1 1 0 X Y X Y
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2 Question 2 (10 points) Prove DeMorgan’s theorems using perfect induction. Answer: You probably exercised mathematical induction in linear algebra in order to establish that a given statement is true for all natural numbers. Perfect induction is a special case of induction where the statement is proven by presenting all possible inputs and establishing that our statement holds under all conditions. In terms of proving a logical law, it is enough to present the complete truth table and
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Solutions_HW1 - Remo Pillat 06/10/2006 CDA 3103 Summer 2006...

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