1. Basic Gates 2.1 Basic Digital Logic: Application of Digital Gates using AND / OR / NOT ©Paul Godin Created August 2007 Last Update Sept 2013 Basic Gates 2

2. Basic Gates 2.2 Timing Diagrams

3. Basic Gates 2.3 Timing ◊Timing diagrams are the best means of comparing the input and output logic values of a digital circuit over time, such as would be found in a functioning circuit. ◊The output of digital circuit analysis tools such as oscilloscopes and logic analyzers essentially display timing diagrams.

4. Basic Gates 2.4 Timing Diagram sample: AND ABAB Y A The output Y is determined by looking at the input A and B states and comparing them to the truth table for the gate. Logic 0 B Y Logic 1

5. Basic Gates 2.5 Timing Diagram sample: OR ABAB Z ABZABZ 000 0 0 00 001 1 1 11 11 001

6. Basic Gates 2.6 Complete the Timing Diagram: Exercise 1 ABAB Z ABZABZ

7. Basic Gates 2.7 Complete the Timing Diagram: Exercise 2 ABAB Z ABZABZ

8. Basic Gates 2.8 Steering Gates ◊Digital gates can be used to control the flow of one digital signal with another. 1 1 Control Output 1 0 Signal 1Control Signal Output Animated

9. Basic Gates 2.9 Steering Gates 0 1 Control Output 1 0 Signal 0Control Signal Output 0 0 Animated

10. Basic Gates 2.10 Combinational Logic

11. Basic Gates 2.11 Combinational Logic ◊Combinational logic describes digital logic circuits that are based on arrays of logic gates. Combinational logic circuits have no retention of states. ◊Combinational logic circuits can be described with: ◊English Terms ◊Boolean equations ◊Truth Tables ◊Logic diagrams ◊Timing Diagrams

12. Basic Gates 2.12 Combinational Logic Example 1 The circuit below is a combinational logic circuit. A B C Y

13. Basic Gates 2.13 Combinational Logic Example 1 It can be described in English terms: A B C Y A AND B, OR C equals output Y A AND B

14. Basic Gates 2.14 Combinational Logic Example 1 It can be described using a Boolean equation: A B C Y (A ● B) + C = Y A ● B

15. Basic Gates 2.15 Combinational Logic Example 1 It can be described using a Truth Table: A B C Y ABCY 0000 0011 0100 0111 1000 1011 1101 1111 (A ● B) + C = Y Only instances where the output of the AND gate = 1 If C is 1, Y is 1

16. Basic Gates 2.16 Combinational Logic Example 1 It can be described using a Timing Diagram: A B C Y (A ● B) + C = Y A B C Y ABCY 0000 0011 0100 0111 1000 1011 1101 1111

17. Basic Gates 2.17 Combinational Logic Example 2 This is a combinational Logic equation: It can be described as “NOT A AND B AND C equals Y”. It can be drawn this way: A ● B ● C = Y A B C Y A

18. Basic Gates 2.18 Combinational Logic Example 2 The Truth Table and Timing diagram describes its function A ● B ● C = Y A B C Y A AA’BCY 01000 01010 01100 01111 10000 10010 10100 10110 A B C Y

19. Basic Gates 2.19 Boolean from a Circuit Diagram ◊A step-by-step process is used to determine the Boolean equation from a circuit diagram. ◊Begin at the inputs and include the logic expressions while working toward the outputs.

20. Basic Gates 2.20 Example 1: Circuit to Boolean Step 1: AB Step 2: AB Step 3: AB+C

21. Basic Gates 2.21 Circuit to Boolean Exercise 1: Step 1: Step 2: Convert the following circuit to its Boolean Expression

22. Basic Gates 2.22 Circuit to Boolean Exercise 2: Step 1: Step 2: Convert the following circuit to its Boolean Expression Step 3: Step 4:

23. Basic Gates 2.23 Circuit to Boolean Exercise 3: Step 1: Step 2: Convert the following circuit to its Boolean Expression Step 3:

24. Basic Gates 2.24 Circuit to Boolean Exercise 4: Convert the following circuit to its Boolean Expression

25. Basic Gates 2.25 Boolean to Circuit Conversion Example ◊Take a step-by-step approach when converting from Boolean to a circuit. Work outward from the expression that brings together groupings found within the expression. ◊Example: Convert (ABC) + BC = Y Step 1: ABC is OR’d with BC Y ABC BC

26. Basic Gates 2.26 Step 2: One side, ABC BC Boolean to Circuit Conversion Example A B C Step 3: Other side, BC B C ABC (ABC) + BC = Y Step 4: Put it all together

27. Basic Gates 2.27 Step 5: Tidy up the circuit (inputs on left, outputs on right) BC Boolean to Circuit Conversion Example A B C B C ABC (ABC) + BC = Y

28. Basic Gates 2.28 Step 6: Common the B and the C inputs BC Boolean to Circuit Conversion Example A B C ABC (ABC) + BC = Y Done

29. Basic Gates 2.29 Boolean to Circuit Exercise 1: Draw the circuit whose expression is: (AB)+(CD)

30. Basic Gates 2.30 Boolean to Circuit Exercise 2: Draw the circuit whose expression is: (A+B)(BC)

31. Basic Gates 2.31 Boolean to Circuit Exercise 3: Draw the circuit whose expression is: (AB) + (AC)

32. Basic Gates 2.32 END ©Paul R. Godin prgodin ° @ gmail.com