1. Understanding Boolean
Algebra
Software Developers View of
Hardware

2. What is Boolean Algebra?
 Is used to describe logical propositions
where the outcome is either true or
false.

3. Algebra Notation
Logic Gate Meaning Notation
NOT NOT A A
OR A OR B A+B
AND A AND B A.B
XOR A XOR B A⊕B

4. The Process

5. Step 1
 Find the output for Q.
 Q = C.D

6. Step 2
 Find the output for D.
 D = A+B

7. Step 3
 Find the output for C.
 C = NOT B

8. Step 4
 Combine the equation.
 Q = (NOT B).(A+B)

9. Step 5
 Test via a truth table.
A B C B A+B Q
0 0 0 1 0 0
0 0 1 1 0 0
0 1 0 0 1 0
0 1 1 0 1 0
1 0 0 1 1 1
1 0 1 1 1 1
1 1 0 0 1 0
1 1 1 0 1 0

10. Activity 1
 Construct a truth table for the following
circuit using Boolean algebra:

11. Answer
A B C=A D=C.B Q=B+D
0 0 1 0 0
0 1 1 1 1
1 0 0 0 0
1 1 0 0 1

12. Activity 2
 Construct a circuit that will output 1
only when A=0 and B=1.
A B Q
0 0 0
0 1 1
1 0 0
1 1 0

13. Answer

14. Activity 3
 We can solve a problem if we are given a truth table
rather than a written description. Here is another
truth table, create a circuit from it.
A B Q
0 0 1
0 1 0
1 0 1
1 1 1

15. Answer

16. Activity 5
 You have a buzzer in your car that sounds
when your keys are in the ignition and the
door is open (Door Open = 0).Create the
following:
 Algebra Notation
 Truth Table
 Circuit

17. Activity 6
 You have a buzzer in your car that sounds
when your keys are in the ignition and the
door is open (Door Open = 0).Create the
following:
 Algebra Notation
 Truth Table
 Circuit

18. Situations
1.You have a buzzer in your car that sounds when your keys are in
the ignition and the door is open.
2.You have a fire alarm installed in your house. This alarm will
sound if it senses heat or smoke.
3.There is a federal election coming up. People are allowed to vote
if they are a Canadian citizen and they are 18.
4.Mr. Carranza is giving his students an assignment. To complete
the assignment the students must do a presentation or write an
essay.
5.Stephanie is applying to a university Applied Mathematics
program. She must have OACs in Algebra, Calculus and
Physics or Chemistry.