Abstract
- Karnaugh Map is a truth table arranged in a grid structure, providing a visual way to simplify Sum-of-Products (SOP). The rows and columns of the grid are labeled with the input variables using Gray Code. Each cell in the grid represents the truth value of a specific combination of input variables.
- We group the
1in the Karnaugh Map using Karnaugh Map Group to find the simplified boolean function
Important
Good for Circuit Design up to 4 variables.
Save hardware cost
Since we can simplify the boolean function, we can reduce the number of Logic Gates needed to implement it by removing those that are redundant and don’t affect the truth values of any rows in the truth table.
Karnaugh Map Group
- Group Shape: rectangles or squares that are either horizontal or vertical (no diagonals).
- Group Size:
1s, where the value of should be as large as possible - Number of Groups: as few groups as possible (covering all 1s with no redundancy)
- Can Overlap: Yes
- Can wrap around the table: Yes
Simplify Boolean function
We group the cells with
1in a Karnaugh Map to show us that some of the inputs don’t affect the output truth value in certain input combinations. This allows us to eliminate those variables and simplify the Boolean function.