# chap07 - Last updated ECEn/CS 224 Chapter 7 Homework...

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Unformatted text preview: Last updated: 10/1/2006 ECEn/CS 224 Chapter 7 Homework Solutions 7.1 Using a KMap, prove the SOP form of the consensus theorem (see section 3.5.5). Does the KMap help illustrate why the third term is redundant? The consensus theorem is: AC + A’B + BC = AC + A’B A BC 0 1 00 01 1 11 1 1 10 1 From the KMap, we can see that BC is redundant. It is not required to cover all of the “1”s. 7.2. Draw the KMap for a 4-input XOR function. Can you see why it cannot be reduced? AB CD 00 01 11 10 00 1 1 01 1 1 11 1 1 10 1 1 It is clear from its KMap that the XOR function cannot be reduced because no groupings can be made to combine terms. BC AB A’B Last updated: 10/1/2006 7.4. Find the minimum SOP solution to the following problem: F(A,B,C,D) = Σ m(0,2,5,7,8,10,13,15). If multiple minimum solutions exist, show all of them. AB CD 00 01 11 10 00 1 1 01 1 1 11 1 1 10 1 1 F = B’D’ + BD = B ≡ D 7.5. Find the minimum POS solution to the following problem: F(A,B,C,D) = Π M(1,3,4,6,9,11,12,14). If multiple minimum solutions exist, show all of them. M(1,3,4,6,9,11,12,14)....
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chap07 - Last updated ECEn/CS 224 Chapter 7 Homework...

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