# How to Simplify a Function Using a K-Map

We will focus on the `Sum-of-Products (SOP)` method, which involves looking for `1s` in the map.

**Step 1: Create and Fill the Map**\
Draw the correct K-Map for your number of variables. Look at your function's truth table or list of minterms. Place a `1` in every cell that corresponds to an output of `1`. If there are "don't care" conditions, place an `X` in those cells. Leave all other cells blank (or you can think of them as `0`s).\
[![](https://learn.digilabdte.com/uploads/images/gallery/2025-09/scaled-1680-/image-1758288416340.png)](https://learn.digilabdte.com/uploads/images/gallery/2025-09/image-1758288416340.png)

**Step 2: Group the 1s**\
This is the most important step. You need to draw loops around groups of adjacent `1`s. Follow these rules:
- **Group Size:** Groups must contain a power-of-two number of cells (1, 2, 4, 8, or 16). You cannot have a group of 3, 5, or 6 cells.
- **Adjacency:** You can only group cells that are adjacent, either horizontally or vertically. Remember the "wrap-around" rule for the edges.
- **Make Groups as Large as Possible:** Always try to make the biggest groups you can. A single group of four is better than two separate groups of two.
- **Cover All 1s:** Every 1 on the map must be included in at least one group. A 1 can be part of multiple groups if it helps to make other groups larger.
- **Use Fewest Groups:** Your final goal is to cover all the 1s using the smallest number of groups possible.
- **Using "Don't Cares" (X):** You can include an X in a group if it helps you make a larger group of 1s. If an X doesn't help create a bigger group, just ignore it and treat it as a 0.\
[![](https://learn.digilabdte.com/uploads/images/gallery/2025-09/scaled-1680-/image-1758288467163.png)](https://learn.digilabdte.com/uploads/images/gallery/2025-09/image-1758288467163.png)

**Step 3: Write the Simplified Function**\
Each group you created will become one term in your final simplified function. To find the term for each group:
1. Look at the variables along the rows and columns for that group.
2. Find the variable(s) that do not change their value inside the group.
3. If a variable stays as `1` for the entire group, include it as is (e.g., `A`).
4. If a variable stays as `0` for the entire group, include it with a NOT (e.g., `A'`).
5. If a variable changes its value (it is both `0` and `1`) within the group, it is eliminated from that term.

The final simplified function is the `OR (sum)` of all the terms you derived from each group.