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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
exclusiveOR. The output of an exclusiveOR function is true only if exactly one of the inputs is true.
Show the truth table of a twoinput exclusiveOR 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 SumofProducts (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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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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