Question

Consider the Boolean function of three variables written as a sum of minterm products: F=A Bˉ Cˉ +AB Cˉ + Aˉ BC+ABC a. Reduce this function by using a Karnaugh map b. Use Logisim to create the circuit for the reduced function. What function is this circuit performing? c. By taking Fˉ from your answer in part (a), use Logisim to create the circuit using only NAND gates. d. Using the Karnaugh map, write out the Boolean function for Fˉ

by referring to the zeros within the map.

Answer 1

To reduce the Boolean function F=A Bˉ Cˉ +AB Cˉ + Aˉ BC+ABC, use a Karnaugh map to group adjacent 1s and simplify the terms. The simplified Boolean function is A Bˉ + AB Cˉ + Aˉ BC + ABC.

Step-by-step explanation:

Reducing a Boolean function using a Karnaugh map involves grouping adjacent 1s in the map to form larger groups called prime implicants. The prime implicants are then used to simplify the Boolean function. In this case, the Boolean function F=A Bˉ Cˉ +AB Cˉ + Aˉ BC+ABC can be reduced to F=A Bˉ + AB Cˉ + Aˉ BC.

1. In the Karnaugh map, the 1s are grouped as follows:
   
2. The simplified Boolean function is obtained by combining the terms corresponding to the grouped 1s.