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). 
 
 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. 
 
 
 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: 
 
 Look at the variables along the rows and columns for that group. 
 Find the variable(s) that do not change their value inside the group. 
 If a variable stays as 1 for the entire group, include it as is (e.g., A ). 
 If a variable stays as 0 for the entire group, include it with a NOT (e.g., A' ). 
 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.