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Understanding Boolean Algebra
Understanding Boolean Algebra
Software Developers View of Hardware
Software Developers View of Hardware
What is Boolean Algebra?What is Boolean Algebra?
Is used to describe logical propositions where the outcome is either true or false.
Is used to describe logical propositions where the outcome is either true or false.
Algebra NotationAlgebra NotationLogic 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
The ProcessThe Process
Step 1Step 1
Find the output for Q.
Q = C.D
Find the output for Q.
Q = C.D
Step 2Step 2
Find the output for D.
D = A+B
Find the output for D.
D = A+B
Step 3Step 3
Find the output for C.
C = NOT B
Find the output for C.
C = NOT B
Step 4Step 4
Combine the equation.
Q = (NOT B).(A+B)
Combine the equation.
Q = (NOT B).(A+B)
Step 5Step 5 Test via a truth table. Test via a truth table.
A B C B A+B Q0 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
Activity 1Activity 1
Construct a truth table for the following circuit using Boolean algebra:
Construct a truth table for the following circuit using Boolean algebra:
AnswerAnswer
A B C=A D=C.B Q=B+D0 0 1 0 0
0 1 1 1 1
1 0 0 0 0
1 1 0 0 1
Activity 2Activity 2
Construct a circuit that will output 1 only when A=0 and B=1.
Construct a circuit that will output 1 only when A=0 and B=1.
A B Q0 0 0
0 1 1
1 0 0
1 1 0
AnswerAnswer
Activity 3Activity 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.
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 Q0 0 1
0 1 0
1 0 1
1 1 1
AnswerAnswer
Activity 5Activity 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
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
Activity 6Activity 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
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
SituationsSituations
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.
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.
