1. Circuits & Boolean Expressions

2. Example # 1: Unsimplified Circuit
Develop a circuit and truth table from a Boolean expression
Boolean Expression: X = A B C + A B C
Simplify the Expression:
X = A B C + A B C
B C ( A + A )
B C ( 1 )
B C A
ABC
ABC+ABC
ABC BC BC
Unsimplified Circuit

3. _ Example # 1: Unsimplified X = A B C + A B C Example # 1: Simplified__
Example # 1: Simplified
X = B C
A B C X
A B C X
A B C _
A B C

4. Example # 2
Develop a truth table and Boolean Expression from a circuit: A B C X 1 A A AB B
ABC C C
Boolean Expression:
X = A B C + C
Simplified: X = A B + C Rule: AB + C = A + C

5. Develop a logic circuit and Boolean expression from a truth table
Example # 3:
Develop a logic circuit and Boolean expression from a truth table
Boolean Expression:
X = A B C + A B C + A B C
Simplify:
A B ( C + C ) + A B C
A B + A B C 1
A B C X A AB
AB +ABC B AB
ABC