1. CEC 220 Digital Circuit Design More Karnaugh Maps Monday, February 02 CEC 220 Digital Circuit Design Slide 1 of 11

2. Lecture Outline Monday, February 02 CEC 220 Digital Circuit Design Four Variable Karnaugh Maps Five Variable Karnaugh Maps Slide 2 of 11

3. AB CD 00011110 001111 011 11111 101111 AB CD 00011110 001 011 11111 101 AB CD 00011110 00 01 1111 10 Four Variable Karnaugh Maps Monday, February 02 CEC 220 Digital Circuit Design Minterm locations for a 4-variable K-map AB CD 00011110 00 01 11 10 0 1 2 3 4 5 6 7 12 13 14 15 8 9 10 11 AB CD 00011110 00 01 11 10 Is this the minimum SOP form? Slide 3 of 11

4. AB CD 00011110 0011 01111 111 101 Four Variable Karnaugh Maps Monday, February 02 CEC 220 Digital Circuit Design Determine the minimum SOP Form of f AB CD 00011110 00 01 11 10 0 1 2 3 4 5 6 7 12 13 14 15 8 9 10 11 Slide 4 of 11

5. AB CD 00011110 0011 011 111111 101111 Four Variable Karnaugh Maps Monday, February 02 CEC 220 Digital Circuit Design Determine the minimum SOP Form of f AB CD 00011110 00 01 11 10 0 1 2 3 4 5 6 7 12 13 14 15 8 9 10 11 Slide 5 of 11

6. AB CD 00011110 00X 0111X1 1111 10X Four Variable Karnaugh Maps Monday, February 02 CEC 220 Digital Circuit Design Determine the minimum SOP Form of f AB CD 00011110 00 01 11 10 0 1 2 3 4 5 6 7 12 13 14 15 8 9 10 11 Slide 6 of 11

7. Four Variable Karnaugh Maps Monday, February 02 CEC 220 Digital Circuit Design Determine the minimum POS Form of f AB CD 00011110 001101 010000 111011 101001 AB CD 00011110 000010 011111 110100 100110 Slide 7 of 11

8. Four Variable Karnaugh Maps Monday, February 02 CEC 220 Digital Circuit Design The inputs A,B,C,D represent an 8-4-2-1 BCD digit. The output should be 1 iff the input is exactly divisible by three AB CD 00011110 0010X0 0100X1 1110XX 1001XX AB CD 00011110 00 01 11 10 0 1 2 3 4 5 6 7 12 13 14 15 8 9 10 11 Slide 8 of 11

9. Four Variable Karnaugh Maps Five Variable K-maps Monday, February 02 CEC 220 Digital Circuit Design Five Variable K-Maps (A, B, C, D, E)  Can also form groupings “vertically” BC DE 00011110 001 01111 111 10 BC DE 00011110 001 011 11 10 Slide 9 of 11

10. Karnaugh Maps An Example From CEC 222 Lab 4 Monday, February 02 CEC 220 Digital Circuit Design BI must be “0” for all invalid BCD codes D3D2D1D0BI 0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011 1100 1101 1110 1111 00011110 00 01 11 10 0 1 2 3 4 5 6 7 12 13 14 15 8 9 10 11 BI = Implement using NOR gates Slide 10 of 11 D3 D2 D1 D0

11. Next Lecture Monday, February 02 CEC 220 Digital Circuit Design Implicants Prime Implicants Essential Prime Implicants Slide 11 of 11