1. Steering Gates, Timing Diagrams & Combinational Logic Technician Series Steering 1.1 ©Paul Godin Created Jan 2014

2. Timing Diagrams Steering 1.2

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. Steering 1.3

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 Steering 1.4

5. Timing Diagram sample: OR ABAB Z ABZABZ 000 0 0 00 001 1 1 11 11 001 Steering 1.5

6. Complete the Timing Diagram: Exercise 1 ABAB Z ABZABZ Steering 1.6

7. Complete the Timing Diagram: Exercise 2 ABAB Z ABZABZ Steering 1.7

8. Steering or Control Gates Steering 1.8

9. Introduction ◊An application for a logic circuit is to control one digital signal with another digital signal. ◊The AND and the OR gates can function as signal Control, or Steering Gates. Steering 1.9

10. 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 Steering 1.10

11. Steering Gates 0 1 Control Output 1 0 Signal 0Control Signal Output 0 0 Animated Steering 1.11

12. Exercise: Control Gates Worksheet (AND, OR) ControlSignalYStatus 00 01 10 11 ControlSignalZZ’Status 00 01 10 11 Control Signal Y Z Z’ Steering 1.12

13. Combinational Logic Steering 1.13

14. 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 Steering 1.14

15. Combinational Logic Example 1 The circuit below is a combinational logic circuit. A B C Y Steering 1.15

16. 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 Steering 1.16

17. Combinational Logic Example 1 It can be described using a Boolean equation: A B C Y (A ● B) + C = Y A ● B Steering 1.17

18. 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 Steering 1.18

19. 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 Steering 1.19

20. 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 Steering 1.20

21. 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 Steering 1.21

22. 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. Steering 1.22

23. Example 1: Circuit to Boolean Step 1: AB Step 2: AB Step 3: AB+C Steering 1.23

24. Circuit to Boolean Exercise 1: Step 1: Step 2: Convert the following circuit to its Boolean Expression Steering 1.24

25. Circuit to Boolean Exercise 2: Step 1: Step 2: Convert the following circuit to its Boolean Expression Step 3: Step 4: Steering 1.25

26. Circuit to Boolean Exercise 3: Step 1: Step 2: Convert the following circuit to its Boolean Expression Step 3: Steering 1.26

27. Circuit to Boolean Exercise 4: Convert the following circuit to its Boolean Expression Steering 1.27

28. 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 Steering 1.28

29. 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 Steering 1.29

30. 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 Steering 1.30

31. Step 6: Common the B and the C inputs BC Boolean to Circuit Conversion Example A B C ABC (ABC) + BC = Y Done Steering 1.31

32. Boolean to Circuit Exercise 1: Draw the circuit whose expression is: (AB)+(CD) Steering 1.32

33. Boolean to Circuit Exercise 2: Draw the circuit whose expression is: (A+B)(BC) Steering 1.33

34. Boolean to Circuit Exercise 3: Draw the circuit whose expression is: (AB) + (AC) Steering 1.34

35. END ©Paul R. Godin prgodin ° @ gmail.com The Resistor and his Ohmies Steering 1.35