Question

F(w,x,y,z)= w’x’y’z’+w’x’yz’+w’xy’z+w’xyz+w’xyz’+wx’y’z’+wx’yz’ Using function above create a logic circuite for it. And estimate the cost (4 input AND gate = $1.57, two input AND gate $1.20 4 input OR gate $1.60, 2 input OR gate is $.80 a NOT gate coat $.50) create a Kmap and simplify above function then create a logic circuit for that function compare it with original function and estimate the cost now. How much you saved building this circuit?

Answer 1

To answer the student's question, we must create a logic circuit from the given function, estimate the cost of building it using given prices, simplify the function using a Karnaugh map, and then create and cost the simplified circuit to compare savings.

Step-by-step explanation:

The student is asking to create a logic circuit based on the given Boolean function, to estimate the cost of the circuit based on provided component prices, and then to simplify the function using a Karnaugh map before creating a simplified logic circuit and comparing costs.

For the original logic circuit, each term in the given function would require an AND gate, and all these outputs would then feed into an OR gate. To simplify the function, one would draw a Karnaugh map with the given minterms, identify possible simplifications, and create a new logic circuit based on the simplified function. Simplifying the function generally leads to fewer gates and thus reduces the cost.

Costs for the original circuit would involve calculating the cost for each AND gate needed (4-input AND gates for terms with four literals, 2-input AND gates for terms with two literals) and the cost for the OR gate(s) where all the AND gates outputs are combined. The NOT gates needed for the negated inputs must also be taken into account. After simplifying the function with a Karnaugh map, the number of gates typically reduces, leading to cost savings.