1. Basic Gates 1.1 Basic Digital Logic: AND, OR and NOT gates ©Paul Godin Created August 2007 Last Update Sept 2013

2. Basic Gates 1.2 Digital Logic: Introduction ◊The foundation of digital systems is the ability to make logic-based decisions on input states. ◊Boolean Algebra is a relatively simple mathematic form based on logic functions comprising of two states: true (logic 1) or false (logic 0). It is used to describe output states based on a set of input states. ◊Boolean mathematics has been around for over a hundred years but much of it is well suited to digital systems. Boolean logic is used in internet search engines.

3. Basic Gates 1.3 Truth Tables Truth tables describe the function of a digital device. They show the output states based on input states. InputOutput 000 011 101 111 Every possible input combination

4. Basic Gates 1.4 Basic Digital Logic Functions Digital logic is based on 3 primary functions (the Basic Gates): AND OR NOT

5. Basic Gates 1.5 The AND Operation AND All inputs must be True for the output to be True. ◊Other ways to describe AND: ◊If all inputs are 1 the output is 1 ◊If any input is 0, the output is 0 ◊“If this input AND this input are 1, the output is 1”

6. Basic Gates 1.6 AND Logic Symbol Inputs Output If all inputs are 1, the output is 1 If any input is 0, the output is 0

7. Basic Gates 1.7 AND Logic Symbol InputsOutput Determine the output 0 0

8. Basic Gates 1.8 AND Logic Symbol InputsOutput Determine the output 0 1

9. Basic Gates 1.9 AND Logic Symbol InputsOutput Determine the output 1 1

10. Basic Gates 1.10 AND Truth Table InputOutput 000 010 100 111 AND

11. Basic Gates 1.11 AND Gates It is possible to have AND gates with more than 2 inputs. The same logic rule applies – all inputs must be 1 for the output to be 1.

12. Basic Gates 1.12 AND Gates ◊IEEE symbol for an AND gate ◊Boolean equations for an AND gate: A●B = x AB = x & The AND operation operates similarly to multiplication.

13. Basic Gates 1.13 The OR Operation OR If any input is True, the output is True Other ways to describe OR: ◊if any input is 1, the output is 1 ◊if all inputs are 0, the output is 0 ◊“If this input OR this input is 1, the output is 1”

14. Basic Gates 1.14 OR Logic Symbol Inputs Output If any input is 1, the output is 1 If all inputs are 0, the output is 0

15. Basic Gates 1.15 OR Logic Symbol InputsOutput Determine the output 0 0

16. Basic Gates 1.16 OR Logic Symbol InputsOutput Determine the output 0 1

17. Basic Gates 1.17 OR Logic Symbol InputsOutput Determine the output 1 1

18. Basic Gates 1.18 OR Truth Table InputOutput 000 011 101 111 OR

19. Basic Gates 1.19 OR Gates It is possible to have OR gates with more than 2 inputs. The same logic rule applies – If any input is 1, the output is 1.

20. Basic Gates 1.20 OR Gates ◊IEEE symbol for an OR gate ◊Boolean equation for an OR gate: A+B = x ≥1 The OR operation operates similarly to Addition.

21. Basic Gates 1.21 The NOT Operation NOT The output is the opposite state of the input. ◊Other ways to describe NOT: ◊If any input is 1, the output is 0 ◊If any input is 0, the output is 1 The NOT function is often called INVERTER or COMPLIMENTARY.

22. Basic Gates 1.22 NOT Logic Symbol Input Output If the input is 1, the output is 0 If the input is 0, the output is 1 Note: The “bubble” on the output is considered the NOT function.

23. Basic Gates 1.23 NOT Logic Symbol Input Output Determine the output 0

24. Basic Gates 1.24 NOT Logic Symbol Input Output Determine the output 1

25. Basic Gates 1.25 NOT Truth Table InputOutput 01 10 NOT

26. Basic Gates 1.26 NOT Gates ◊IEEE symbol for a NOT gate: ◊Boolean for a NOT function: A = x (overbar symbol) A’ = x (prime symbol) 1 Note: The triangle symbol on the output is considered the NOT function

27. Basic Gates 1.27 Alternate Symbols ◊The NOT is the “bubble” on the gate. ◊Alternate symbols for the NOT gate: 1

28. Basic Gates 1.28 Review 1 ◊There are 3 basic gates: ◊AND, where all inputs must be high for a high output ◊OR, where any input must be high for a high output ◊NOT, where the output is the opposite (compliment) of the input

29. Basic Gates 1.29 Review 2 AND Logic Symbol OR Logic Symbol NOT (or Inverter) Logic Symbol

30. Basic Gates 1.30 Review 3 A ● B = Y AB = Y A + B = Y A = Y A’ = Y A AND B = Y A OR B = Y NOT A = Y

31. Basic Gates 1.31 Exercise 1 What is the outcome of the following: 1 1 0 1 0 1 1

32. Basic Gates 1.32 Exercise 2 Complete the sentences: ◊If all inputs of an OR gate are low, the output is_________ ◊If any input of an AND gate is low, the output is _________ ◊The output of a NOT gate is always the ___________ of the input.

33. Basic Gates 1.33 Exercise 3 Complete the tables InputOutput 00 01 10 11 ≥1 InputOutput 00 01 10 11 &

34. Basic Gates 1.34 Exercise 4 Draw the logic equivalent of the AND and the OR gates using switches.

35. Basic Gates 1.35 Exercise 5 A vehicle has 2 proximity sensors and one motor. When triggered, the sensors produce a logic 1. The motor goes forward with a logic 0 and stops with a logic 1. If both sensors sense an object, stop. If only one, or none of the sensors sense an object, go forward. Draw the sensors, motor and the logic needed. (Hint: do a truth table)

36. Basic Gates 1.36 End ©Paul R. Godin prgodin ° @ gmail.com