1. Logic Gates

2. AND Function
Text Description ⇒ Output Y is TRUE if inputs A AND B
are TRUE, else it is FALSE.
A
Logic Symbol ⇒ AND Y
B
INPUTS OUTPUT
A B Y
0 0 0
Truth Table ⇒ 0 1 0
1 0 0
1 1 1
AND Gate Truth Table
AND Symbol
Boolean Expression ⇒ Y = A x B = A • B = AB

3. OR Function
Text Description ⇒ Output Y is TRUE if input A OR B is
TRUE, else it is FALSE.
A
Logic Symbol ⇒ OR Y
B
INPUTS OUTPUT
A B Y
0 0 0
Truth Table ⇒ 0 1 1
1 0 1
1 1 1
OR Gate Truth Table
OR Symbol
Boolean Expression ⇒ Y = A + B

4. NOT Function (inverter)
Text Description ⇒ Output Y is TRUE if input A is FALSE,
else it is FALSE. Y is the inverse of A.
Logic Symbol ⇒ A NOT Y
INPUT OUTPUT
A Y
0 1
Truth Table ⇒ 1 0
NOT Gate Truth Table
NOT Alternative Notation
Bar
Boolean Expression ⇒ Y = A Y = A’
Y = !A

5. NAND Function
Output Y is FALSE if inputs A AND B
Text Description ⇒
are TRUE, else it is TRUE.
A bubble is an inverter
A This is an AND Gate with an inverted output
Logic Symbol ⇒ NAND Y
B
INPUTS OUTPUT
A B Y
0 0 1
Truth Table ⇒ 0 1 1
1 0 1
1 1 0
NAND Gate Truth Table
Boolean Expression ⇒ Y = A x B = AB

6. NOR Function
Output Y is FALSE if input A OR B is
Text Description ⇒
TRUE, else it is TRUE.
A bubble is an inverter.
A This is an OR Gate with its output inverted.
Logic Symbol ⇒ NOR Y
B
INPUTS OUTPUT
A B Y
0 0 1
Truth Table ⇒ 0 1 0
1 0 0
1 1 0
NOR Gate Truth Table
Boolean Expression ⇒ Y = A + B

7. Circuit-to-Truth Table
Example
A
AND
B
OR Y
NOT
C
AND
A B C Y
0 0 0
0 0 1
0 1 0
0 1 1
1 0 0
2# of Inputs = # of Combinations 1 0 1
1 1 0
23 = 8 1 1 1

8. Circuit-to-Truth Table
Example
0 0
A
0 AND
B
0
OR Y
1
NOT 0
0 AND
C
A B C Y
0 0 0 0
0 0 1
0 1 0
0 1 1
1 0 0
1 0 1
1 1 0
1 1 1

9. Circuit-to-Truth Table
Example
0 0
A
0 AND
B
1
OR Y
1
NOT 1
1 AND
C
A B C Y
0 0 0 0
0 0 1 1
0 1 0
0 1 1
1 0 0
1 0 1
1 1 0
1 1 1

10. Circuit-to-Truth Table
Example
0 0
A
1 AND
B
0
OR Y
1
NOT 0
0 AND
C
A B C Y
0 0 0 0
0 0 1 1
0 1 0 0
0 1 1
1 0 0
1 0 1
1 1 0
1 1 1

11. Circuit-to-Truth Table
Example
0 0
A
1 AND
B
1
OR Y
1
NOT 1
1 AND
C
A B C Y
0 0 0 0
0 0 1 1
0 1 0 0
0 1 1 1
1 0 0
1 0 1
1 1 0
1 1 1

12. Circuit-to-Truth Table
Example
1 0
A
0 AND
B
0
OR Y
0
NOT 0
0 AND
C
A B C Y
0 0 0 0
0 0 1 1
0 1 0 0
0 1 1 1
1 0 0 0
1 0 1
1 1 0
1 1 1

13. Circuit-to-Truth Table
Example
1 0
A
0 AND
B
0
OR Y
0
NOT 0
1 AND
C
A B C Y
0 0 0 0
0 0 1 1
0 1 0 0
0 1 1 1
1 0 0 0
1 0 1 0
1 1 0
1 1 1

14. Circuit-to-Truth Table
Example
1 1
A
1 AND
B
1
OR Y
0
NOT 0
0 AND
C
A B C Y
0 0 0 0
0 0 1 1
0 1 0 0
0 1 1 1
1 0 0 0
1 0 1 0
1 1 0 1
1 1 1

15. Circuit-to-Truth Table
Example
1 1
A
1 AND
B
1
OR Y
0
NOT 0
1 AND
C
A B C Y
0 0 0 0
0 0 1 1
0 1 0 0
0 1 1 1
1 0 0 0
1 0 1 0
1 1 0 1
1 1 1 1

16. Circuit-to-Boolean Equation
AB
A
AND
B
OR Y=AB + AC
A
}
}
NOT
AND
C
AC A B C Y
0 0 0 0
0 0 1 1
0 1 0 0
0 1 1 1
1 0 0 0
1 0 1 0
1 1 0 1
1 1 1 1

17. A - O - I Logic
A
AND
B
OR Y
NOT
AND
C
AND Gates
Other Logic Arrangements:
OR Gates NAND - NAND Logic
INVERTER Gates NOR - NOR Logic

18. NAND Gate – Special Application
S NAND T
S T
0 1 A
1 0 NAND Y
B
INPUTS OUTPUT
A B Y
0 0 1
Equivalent To An Inverter Gate 0
1
1
0
1
1
1 1 0

19. NOR Gate - Special
Application
S NOR T
S T
0 1 A
1 0 B
NOR Y
INPUTS OUTPUT
A B Y
0 0 1
0 1 0
1 0 0
Equivalent To An Inverter Gate 1 1 0