Convert the following to canonical forms(i) F(x,y,z,w)= (1,3,7,9,11,12

1.	Convert the following to canonical forms(i) F(x,y,z,w)= (1,3,7,9,11,12)
Answer» Explanation: Canonical PRODUCT of SUM: F(A,B,C,D)=(A+B+C+D)⋅(A+B+C+D¯¯¯¯)⋅(A+B+C¯¯¯¯+D)⋅(A+B+C¯¯¯¯+D¯¯¯¯) ⋅(A+B¯¯¯¯+C+D)⋅(A+B¯¯¯¯+C+D¯¯¯¯)⋅(A¯¯¯¯+B¯¯¯¯+C+D) we can write LIKE this also F(A,B,C,D)=∑(5,7,8,9,10,11,13,14,15) Canonical Sum of Product: F(A,B,C,D)=A¯¯¯¯BC¯¯¯¯D+A¯¯¯¯BCD+A⋅B¯¯¯¯⋅C¯¯¯¯⋅D¯¯¯¯+AB¯¯¯¯⋅C¯¯¯¯D+AB¯¯¯¯CD¯¯¯¯+AB¯¯¯¯CD+ABC¯¯¯¯D+ABCD¯¯¯¯+ABCD (b)F(X,y,z)=∑(1,3,7) Canonical Sum of Product: F(x,y,z)=x¯¯¯⋅y¯¯¯⋅z+x¯¯¯⋅y⋅z+x⋅y⋅z we can write like this F(x,y,z)=∏(0,2,4,5,6) Canonical Product of Sum: F(x,y,z)=(x+y+z)⋅(x+y¯¯¯+z)⋅(x¯¯¯+y+z)⋅(x¯¯¯+y+z¯¯¯)⋅(x¯¯¯+y¯¯¯+z)

Convert the following to canonical forms(i) F(x,y,z,w)= (1,3,7,9,11,12)

Answer»

Explanation:

Canonical PRODUCT of SUM:

F(A,B,C,D)=(A+B+C+D)⋅(A+B+C+D¯¯¯¯)⋅(A+B+C¯¯¯¯+D)⋅(A+B+C¯¯¯¯+D¯¯¯¯)

⋅(A+B¯¯¯¯+C+D)⋅(A+B¯¯¯¯+C+D¯¯¯¯)⋅(A¯¯¯¯+B¯¯¯¯+C+D)

we can write LIKE this also F(A,B,C,D)=∑(5,7,8,9,10,11,13,14,15)

Canonical Sum of Product:

F(A,B,C,D)=A¯¯¯¯BC¯¯¯¯D+A¯¯¯¯BCD+A⋅B¯¯¯¯⋅C¯¯¯¯⋅D¯¯¯¯+AB¯¯¯¯⋅C¯¯¯¯D+AB¯¯¯¯CD¯¯¯¯+AB¯¯¯¯CD+ABC¯¯¯¯D+ABCD¯¯¯¯+ABCD

(b)F(X,y,z)=∑(1,3,7)

Canonical Sum of Product:

F(x,y,z)=x¯¯¯⋅y¯¯¯⋅z+x¯¯¯⋅y⋅z+x⋅y⋅z

we can write like this F(x,y,z)=∏(0,2,4,5,6)

Canonical Product of Sum:

F(x,y,z)=(x+y+z)⋅(x+y¯¯¯+z)⋅(x¯¯¯+y+z)⋅(x¯¯¯+y+z¯¯¯)⋅(x¯¯¯+y¯¯¯+z)