Question

From the following function: F = ABĆD + ABCD + ABĆD + ABCD

a) Obtain the minimum expression in sum of products using Karnaugh Maps.

Answer 1

The function F = AB¯CD + ABCD + AB¯D + ABCD is minimized to AB using Karnaugh Maps by grouping common terms and eliminating variables that change within the groups.

Step-by-step explanation:

To minimize the given logical function F = AB¯CD + ABCD + AB¯D + ABCD using Karnaugh Maps (K-maps), we follow a step-by-step process:

1. Create a 4-variable K-map since there are four variables (A, B, C, D) in the function.
2. Place 1 in the K-map cells corresponding to the minterms of the function. For AB¯CD (minterm is A=1, B=1, C=0, D=1), ABCD (minterm is A=1, B=1, C=1, D=1), AB¯D (minterm is A=1, B=1, C=0, D=0), and another ABCD (which is already accounted for).
3. Group the adjacent 1s in the K-map into the largest possible rectangles with 1, 2, 4, 8, and so on cells in each group.
4. Write the minimized expression by identifying the variable states that don't change within each group.

Through the K-map simplification, we note that the terms AB¯CD and AB¯D can be combined because they differ only by their D term. Similarly, since ABCD appears twice, it is evident that it covers two cells in the K-map. After grouping, the minimized expression is deduced to be AB which summarizes the K-map process for sum of products reduction.