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# Boolean Algebra

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### 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