Question

Simplify the following expression in sum-of-products form using a 3-variable

Karnaugh map. g(x,y,z)=Sm(1,4,5,6)

Given the function, (a) plot it as a 3-variable Karnaugh map, then (b) use that
plot to express the function as a minterm list in the form Sm( ).

Simplify the following expression in product-of-sums form using a 4-variable
Karnaugh map

Answer 1

To simplify the expression g(x,y,z)=Sm(1,4,5,6) using a 3-variable Karnaugh map, create the map, mark the given minterms, and group the adjacent 1s to form a sum-of-products expression.

Step-by-step explanation:

To simplify the expression g(x,y,z) = Sm(1,4,5,6) using a 3-variable Karnaugh map, follow these steps:

1. 
   
3. Create a 3-variable Karnaugh map with variables x, y, and z.
4. 
   
6. In the Karnaugh map, mark the cells corresponding to the given minterms 1, 4, 5, and 6 as 1s.
7. 
   
9. Group the adjacent 1s in the map to form a sum-of-products expression.
10. 
    
12. Convert the grouped 1s into a minterm list in the form Sm().

For the 4-variable Karnaugh map in the second part of the question, a similar process can be followed to simplify the expression in product-of-sums form.