1. CEC 220 Digital Circuit Design Implicants Wed, Sept. 23 CEC 220 Digital Circuit Design Slide 1 of 10

2. Lecture Outline Wed, Sept. 23 CEC 220 Digital Circuit Design Implicants Prime Implicants Essential Prime Implicants Slide 2 of 10

3. Four Variable Karnaugh Maps Implicants and Prime Implicants Wed, Sept. 23 CEC 220 Digital Circuit Design Implicants  A single 1 or group of 1’s which can be combined to form a simpler term is called an implicant AB CD 00011110 00111 0111 111 1011 Slide 3 of 10

4. Four Variable Karnaugh Maps Implicants and Prime Implicants Wed, Sept. 23 CEC 220 Digital Circuit Design Prime Implicants  An Implicant which can NOT be combined into another block is called a prime implicant AB CD 00011110 00111 0111 111 1011 Slide 4 of 10

5. Four Variable Karnaugh Maps Implicants and Prime Implicants Wed, Sept. 23 CEC 220 Digital Circuit Design Prime Implicants  An Example AB CD 00011110 0011 01111 11111 1011 All Prime Implicants: Min SOP Expression: Not all Prime Implicants are essential!! Slide 5 of 10

6. Four Variable Karnaugh Maps Implicants and Prime Implicants Wed, Sept. 23 CEC 220 Digital Circuit Design Essential Prime Implicants  If a minterm is covered by only one prime implicant then that prime implicant is an essential prime implicant. AB CD 00011110 0011 01111 11111 1011 Essential Prime Implicants? Min SOP Expression: Essential Prime Implicants MUST be included in the min SOP expression Slide 6 of 10

7. Karnaugh Maps Flowchart for Determining the min SOP Expression Wed, Sept. 23 CEC 220 Digital Circuit Design All uncovered 1’s checked? Are the chosen 1 and its adjacent 1’s and X’s covered by a single term? Are the chosen 1 and its adjacent 1’s and X’s covered by a single term? Find a minimum set of prime implicants which cover the remaining 1’s on the map. Find a minimum set of prime implicants which cover the remaining 1’s on the map. That term is an essential prime implicant. Circle it. Find all adjacent 1’s and X’s. Choose a 1 which has not been covered. yes no Start Slide 7 of 10

8. Karnaugh Maps Flowchart for determining the minimum SOP Wed, Sept. 23 CEC 220 Digital Circuit Design An Example 1 1 1 Essential Prime Implicants: 1 1 1 1 1 1 Slide 8 of 10

9. Karnaugh Maps Flowchart for determining the minimum SOP Wed, Sept. 23 CEC 220 Digital Circuit Design An Example 1 1 1 1 Essential Prime Implicants: 1 111 Slide 9 of 10

10. Next Lecture Wed, Sept. 23 CEC 220 Digital Circuit Design Multi-Level Gate Circuits Slide 10 of 10