1. Basic Digital Logic: AND, OR and NOT gates Technician Series
©Paul Godin
Last Update Dec 2014

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. Truth Tables
Truth tables describe the function of a digital device. They show the output states based on input states.
Input
Output 1
Every possible input combination

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

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

7. AND Logic Symbol
Inputs
Output
Determine the output

8. AND Logic Symbol
Inputs
Output 1
Determine the output

9. AND Logic Symbol 1
Inputs
Output 1
Determine the output

10. AND Truth Table
Input
Output 1
AND

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. The AND operation operates similarly to multiplication.
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. If any input is True, the output is True
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. OR Logic Symbol Output Inputs If any input is 1, the output is 1
If all inputs are 0, the output is 0

15. OR Logic Symbol
Inputs
Output
Determine the output

16. OR Logic Symbol
Inputs
Output 1
Determine the output

17. OR Logic Symbol 1
Inputs
Output 1
Determine the output

18. OR Truth Table
Input
Output 1 OR

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. The OR operation operates similarly to Addition.
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. 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. NOT Logic Symbol Input Output If the input is 1, the output is 0
Note: The “bubble” on the output is considered the NOT function.

23. NOT Logic Symbol
Output
Input
Determine the output

24. NOT Logic Symbol 1
Output
Input
Determine the output

25. NOT Truth Table
Input
Output 1
NOT

26. Note: The triangle symbol on the output is considered the NOT function
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. 1 Alternate Symbols The NOT is the “bubble” on the gate.
Alternate symbols for the NOT gate: 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. Review 2 AND Logic Symbol OR Logic Symbol
NOT (or Inverter) Logic Symbol

30. Review 3 A AND B = Y A OR B = Y NOT A = Y A ● B = Y AB = Y A + B = Y

31. Exercise 1
What is the outcome of the following: 1 1 1 1 1

32. Exercise 2 If all inputs of an OR gate are low, the output is_________
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. Exercise 3
Draw the logic equivalent of the AND and the OR gates using switches.

34. Is it a boy or a girl?
Yes!
End
©Paul R. Godin
gmail.com