Question

Minimize the following functions using K-maps.

a) f(a,b,c)=∑m(0,2,4,6) Give the minimal SOP only. Draw the K-map, identify the groups and give the product term that corresponds to each group.

b) f(a,b,c)=∑m(0,1,2,3) Give the minimal POS only. Draw the K-map, identify the groups and give the product term that corresponds to each group.

Answer 1

To minimize the functions using K-maps, create the K-map, group the adjacent 1s or 0s, write down product terms, and combine them using the OR or AND operator.

Step-by-step explanation:

To minimize the functions using K-maps, you first need to create the K-map for each function. For function a), the K-map would have 3 variables, with 2 rows and 4 columns. Place 1s in the cells corresponding to the minterms given (0, 2, 4, 6). Group together adjacent 1s in powers of 2 (1,2,4,8). Write down the product term for each group, and combine them using OR operator to get the minimal SOP. For function b), the K-map would 3 variables, with 2 rows and 2 columns. Place 0s in the cells corresponding to the minterms given (0, 1, 2, 3). Group together adjacent 0s in powers of 2 (1,2,4,8). Write down the product term for each group, and combine them using AND operator to get the minimal POS.