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# hw3 - 4(5 pts Use Karnaugh map to ﬁnd minimal SOP...

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Homework three EECS 203 Due 24 April 2009 Please keep track of how long you spend doing this homework assignment. Speciﬁcally, how much time is needed to do the problems after studying enough to understand the concepts? 1. (0 pts.) Do Mano 5.3, and 5.6. 2. (5 pts.) Name a function for which a SOP implementation requires an exponential number of literals in terms of the number of input variables, i.e., given f ( i n - 1 , i n - 2 , ··· , i 1 , i 0 ) ﬁnd an f for which the required number of literals, l , is related to the the number of inputs, n , in the following way l ( n ) 2 n Hint: Try ﬁnding a Karnaugh map that absolutely must have a large number of small prime implicants. 3. (5 pts.) Are the number of literals in an implicant directly or inversely correlated with the implicant’s size on a Karnaugh map?
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Unformatted text preview: 4. (5 pts.) Use Karnaugh map to ﬁnd minimal SOP expressions for the following function: (a) f ( a , b , c , d ) = ∏ ( 4 , 8 , 10 , 13 ) + d ( 5 , 14 ) 5. (5 pts.) Use a Karnaugh map to ﬁnd minimal POS expressions for the following functions: (a) f ( a , b , c , d ) = ∑ ( , 3 , 5 , 7 , 8 , 13 ) + d ( 9 , 10 , 11 , 12 , 15 ) 6. (10 pts.) For the circuit in the following ﬁgure, create a truth table to represent how the value of Q changes based on inputs a and b , as well as the previous value of Q . AND OR a b Q 7. (10 pts.) Use basic gates to design a clocked Set-Reset latch with active-low S and R inputs, and an active-high clock. 8. (0 pts.) How much time did you spend on this assignment? 1...
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