K-Map IF f(A,B,C)=AB+BC+AC

To simplify the given Boolean function f(A, B, C) = AB + BC + AC using a Karnaugh Map (K-Map), follow these steps:

1. Create a K-Map table with two rows and four columns. The rows represent the combinations of inputs A and B, while the columns represent the combination of input C.

C' C
A'B' A'B
A' B' AB
AB

2. Fill in the table with the corresponding function values. We know that f(A, B, C) = AB + BC + AC. Hence, we can mark the cells with 1's where the function evaluates to 1.

C' C
A'B' 1 1
A' B' 0 1
AB 1 1

3. Identify any adjacent cells in the K-Map that contain 1's, either horizontally or vertically. Group these cells together, ensuring that the group contains a power of 2 (1, 2, 4, 8, etc.) cells.

C' C
A'B' X X
A' B' 0 1
AB X X

4. Write down the minimum logical expression that represents the grouped cells. Each group corresponds to a product term.

Group 1: A'BC' (top row, left column)
Group 2: ABC (bottom row, left column)

5. Combine the product terms identified in Step 4 to form the simplified Boolean expression.

Simplified expression: f(A, B, C) = A'BC' + ABC