Boolean Algebra

2,206 views

Published on

Published in: Technology
0 Comments
3 Likes
Statistics
Notes
  • Be the first to comment

No Downloads
Views
Total views
2,206
On SlideShare
0
From Embeds
0
Number of Embeds
13
Actions
Shares
0
Downloads
127
Comments
0
Likes
3
Embeds 0
No embeds

No notes for slide

Boolean Algebra

  1. 1. Understanding Boolean Algebra Software Developers View of Hardware
  2. 2. What is Boolean Algebra?  Is used to describe logical propositions where the outcome is either true or false.
  3. 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. 4. The Process
  5. 5. Step 1  Find the output for Q.  Q = C.D
  6. 6. Step 2  Find the output for D.  D = A+B
  7. 7. Step 3  Find the output for C.  C = NOT B
  8. 8. Step 4  Combine the equation.  Q = (NOT B).(A+B)
  9. 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. 10. Activity 1  Construct a truth table for the following circuit using Boolean algebra:
  11. 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. 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. 13. Answer
  14. 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. 15. Answer
  16. 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. 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. 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.

×