# Electricity

## Boolean Algebra and its Application to Problem Solving and Logic Circuits

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## Lesson Plan 5

### Topic: Boolean Algebra To Building circuits.

**
Objectives
**

- ____ (a) The students will be able to apply simple ideas from Boolean algebra and write truth tables.
- ____ (b) From the truth tables the students will able to implement logic circuits.

**
Development
**

- ____ (a) Review simple statements and their connectives.
- ____ (b) Introduce the basic principles of boolean algebra.
- ____ ____ The Elements ( 0,1)
- ____ ____ the operations of addition, multiplication and negation
- ____ ____ The elements are used in the truth tables instead of true or false
- ____ (c) Discuss dualities that can be considered true or false, on or off, closed or opened
- ____ (d) Replace the operations (+, x) by or and and
- ____ (e) Review truth tables from the previous section with zero and one
- ____ (f) Introduce equations from these truth tables. ex. F = x + y. ( where x and y are inputs and F the output

**
Evaluation
**

(a) Provide drill and practice using zero and one in the truth tables

### Application of Boolean Algebra

- 1. The state of an electrical switch is either on or off. Use zero or one to represent these states.
- 2. Develop truth tables using the connectives.
- 3. Discuss the position of switches when opened or closed.

*(figure available in print form)*

- 4. Use equations to summarize the desired outcomes. Thus introducing the implementation of boolean algebra with logic gates.

*
Write equations of desired outcome
*

ex. F = X + y [use all connectors].

Write truth table table

Draw logic gates. | (e) And gates denoted by: |

*(figure available in print form)*

*(figure available in print form)*

**
Suggested problems
**

- 1. Write a truth table for the following;
- ____ (a) Nand F = (Xy).
- ____ (b) And F = (X + y)
- ____ (c) F=(X+y)
- 2. Construct a truth table for the gate shown.

*(figure available in print form)*

- 3. Design a truth table for a half subtractor
- ans. X y b d
- ____ 0 0 0 0
- ____ 0 1 1 1
- ____ 1 0 0 1
- ____ 1 1 0 0
- 4. Design a truth table for a full subtractor.
- ans X y z b d
- ____ 0 0 0 0 0
- ____ 0 0 1 1 1
- ____ 0 1 0 1 1
- ____ 0 1 1 1 0
- ____ 1 0 0 0 1
- ____ 1 0 1 0 0
- ____ 1 1 0 0 0
- ____ 1 1 1 1 1
- 4. Construct a truth table for

*(figure available in print form)*

- 5. Make a truth table to show that
- ____ CD=C+D
- 6. Given the following write an equation for
- ____ (a) X (b) Y (c) F
- ____ ans X = AB
- ____ Y=(AC)
- ____ F=X+Y+B

- 7. Write truth tables for F = AB + AC

- ____ draw the logic gate

- 8. Design a circuit such that a hall light can be controlled by both an upstairs and a down stairs switch.
- 9. Design a circuit such that a light can be controlled by each of three switches.
- 10. What is the Boolean expression for the AND OR logic diagram

*(figure available in print form)*

- ____ ans; AB + AC = F
- 11. What is the truth table for the design in 10
- ____ ans; input output input output

A B C F A B C F 0 0 0 0 1 0 0 0 0 0 1 0 1 0 1 1 0 1 0 1 1 1 0 0 0 1 1 1 1 1 1 1