ECE 102 - Homework 6

Due  10/05/2017   (Updated 10/03)

1.    Find the minimum product of sums of each of the following:
       a) f(A,B,C,D) = Π M(0,1,2,8,9,12,13,14)  • Π D(3,6,7,11)
       b) f(A,B,C,D)= Σ m (1,3,4,10,11)
       c) f(A,B,C,D)= Σ m(0,1,5,8,12,14,15) +  Σ d(2,7,4,10,13)
       d) f(A,B,C,D)= Π M(0,1,3,5,10,11) • Π D(6,14)
   
   
2. Find the minimum  sum of products of each of the following:
       a) f(A,B,C,D) = Σ m(0,1,2,4,6,7,8,9,13,15)
       b) f(A,B,C,D)= Σ m(0,1,5,12,14,15) +  Σ d(2,7,8,13)
       c) f(A,B,C,D)= Π M(3,8,9, 14)• Π D(0,1,4,5,10,11)
   
   
3. Plot the function F(A,B,C,D) = CD+B'C'D'+A'C'D+AB'D'+AC'D+A'BCD' on a K-map.
   Find the minimum POS and minimum SOPs. Identify the essential prime implicants in each case.
4. Given F(A,B,C,D,E) = Π M(1,3,6,9,11,19,20,24,25,26,27,28,29,30) Π D(0,2,13),
   find two minimum sum-of-product expansions for F. Underline the essential prime implicants in your answer 
   
   
5. Find a minimum two-level multiple-output AND-OR gate circuit to realize the following functions(eight gates).   
   F(A,B,C,D)= Σ m (9,11,13,14)
   G(A,B,C,D)= Σ m (9,10,12,13,14) 
   H(A,B,C,D)= Σ m (10,11,12,13)


6. Implement each of the following functions using using only two-input gates. The multi-level circuit should have AND and OR gates alternating at adjacent levels.   
   a) Z= AB+CD'E'
   b) X = ABC'+AD +A'CD'+A'E'F'  (last gate should be an AND gate)
   c) Part (b) with last gate as an OR gate

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