Lecture 3

1. Lecture 3 Karnaugh Map Chapter 2 Jack Ou, Ph.D.

2. Home Alarm Logic

3. Home Alarm Truth Table

4. Sum of Products Equation • Parts • 12 inverters • 3 2-input AND gates for each 4-input AND gate. Therefore, 24 2-input AND gates. • 7 2-input OR gates.

5. NAND Based Logic Gates

6. Delay Calculations • Parts • 12 inverters (1 TTL delay) • 3 2-input AND gates for each 4-input AND gate. Therefore, 24 2-input AND gates. • Each AND gate: 2 TTL delay • For each 4-input ANDN gate: 4 TTL delay • 7 2-input OR gates. • 2 TTL delay for each OR gate • 7 2-input OR gates (6 TTL delay) • Total delay: 6 TTL delay+4 TTL delay+1 TTL delay=11 TTL delay

7. Simplification Technique #1: Ordered the Truth Table using Gray Code Discontinuity disappears!

8. Use Don’t Cares to Simplify the Truth Table

9. Simplified SoP • Parts: • Inverters: 4 inverters (1 TTL delay) • 4 3-input AND gates • Each 3-input AND gate requires 2 2-input AND gate: • 2 x4=8 2-input AND gate (4 TTL delay) • 3 2-input OR gate (4 TTL delay) • Maximum 9 TTL delay (4+4+1)

10. Move Don’t Care Bits Closer Together • Parts: • 1 inverter (1 delay) • 2 AND gates (2 delays) • 1 OR gate (2 delay) • 5 delay

11. Steps for Creating a Karnaugh Map • Create an Equivalent Karnaugh Map • Each circle must be around a power of two number of bits • It is not a problem if circles overlap

12. Equivalent Karnaugh Map

13. Example 1

14. Example 2

15. Example 3

16. Home Alarm Example