Let the cost of an expression be the total number of gates plus the total number of inputs of the circuit implementing the expression. Assume that AND gates and OR gates of any number of inputs can be used in the implementation. In addition, assume that the complement of each input variable are also available (i.e., you don't need to use any NOT gate). Consider the function: f(a,b,c,d) = ∑ m(4,7,8,11) + D(12,15).
a. Use K-map to find a minimum-cost SOP realization for f. What is the cost of this expression?
b. Use K-map to find a minimum-cost POS realization for f. What is the cost of this expression?
c. Implement f using two 2-input OR gates and two 3-input AND gates. What is the cost of this implementation? Hint: Use Boolean algebra to manipulate the expression in part (a). You may need to consider a multilevel implementation of the expression in part (a).