Question

Consider the following two functions:

F=∑(2,3,6,7,9)
G=∑(5,7,9,13,15)
​
a) Show K-maps and minimal equations for each of the functions. How many total gates are required (not including inverters)? You can assume AND and OR gates with any fan-in you like.
b) Now consider that the functions are to be implemented as part of the same circuit. Show K-maps that reduce the total number of gates needed. How many total gates are required? Hint: consider product term sharing.

Answer 1

To find the minimal equations and number of gates required for the given functions F and G, create K-maps for each function. The minimal equation for function F is F = A'B + AC. The minimal equation for function G is G = A'C' + BC + AC'. A total of 8 gates (not including inverters) are required.

Step-by-step explanation:

To find the minimal equations and number of gates required for the given functions F and G, we need to first create K-maps for each function. For function F, the following K-map is formed:

0 1 0 1 1

0 0 0 1 1

From this K-map, we can write the minimal equation for function F as: F = A'B + AC.

Similarly, for function G, the following K-map is formed:

0 0 1 0 1

0 1 1 1 1

From this K-map, we can write the minimal equation for function G as: G = A'C' + BC + AC'.

Next, to calculate the number of gates required without inverters, we count the number of 1s in each K-map. For function F, there are 3 1s, and for function G, there are 5 1s. Therefore, a total of 3 + 5 = 8 gates (not including inverters) are required.