1. Karnaugh map minimization Basic Terms (1) minterm 0000 0 1 1 1 1 1 1 1 1 0 1 1 maxterm - a single 1 - a single 0 1. implicant 0000 0 1 1 1 1 1 1 1 1 01 1 - any group of adjacent 1’s (or 0’s) of the size 1, 2, 4, 8, 16,... 2. prime implicant 0000 0 1 1 1 1 1 1 1 1 01 1 3. an implicant that is not contained within any larger implicant

2. Karnaugh map minimization Basic Terms (2) 1 * - 1 (minterm) that is included in only one prime implicant 0000 0 1*1* 1 1*1* 1 1 1 1 1*1* 0 1*1* 1 4. essential prime implicant 0000 0 1*1* 1 1*1* 1 1 1 1 1*1* 01*1* 1 5. secondary prime implicant 0000 0 1*1* 1 1*1* 1 1 1 1 1*1* 01*1* 1 6. 0 * - 0 (maxterm) that is included in only one prime implicant prime implicant that contains 1 * (or 0 * ) prime implicant that does not contain any 1 * (or 0 * )

3. Karnaugh map minimization Algorithm (1) 1. Fill Karnaugh map based on the function description 2. Decide about your goal if your goal is the minimum sum-of-products form you will be covering 1’s if your goal is the minimum product-of-sums form you will be covering 0’s 3. Find ALL prime implicants (covering 1’s or 0’s depending on step 2) 4. Find ALL 1 * s or 0 * s (depending on step 2), i.e., 1’s (0’s) belonging to only one prime implicant 5. Find ALL essential prime implicants, i.e., prime implicants containing 1 * s ( or 0 * s ) 6. Identify the remaining prime implicants as secondary prime implicants

4. 7. Find ALL 1’s (0’s) not covered by essential prime implicants 8. Cover 1’s (0’s) found in step 7 using the minimum number of the largest secondary prime implicants Karnaugh map minimization Algorithm (2) 9. Write the minimized equation of the function F or F (depending on step 2) in the sum-of-products form ALL essential prime implicants first secondary prime implicants SELECTED in step 8 next 10. Document all your steps You should be able to verify each step independently of other steps If your goal is the product-of-sums form AND you have chosen to cover 0’s in step 2, apply the DeMorgan’s theorem to the equation obtained in step 9 to obtain the equation for F.