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

Karnaugh map minimization Basic Terms (2) 1 * - 1 (minterm) that is included in only one prime implicant *1* 1 1*1* *1* 0 1*1* 1 4. essential prime implicant *1* 1 1*1* *1* 01*1* 1 5. secondary prime implicant *1* 1 1*1* *1* 01*1* * - 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 * )

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

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.