1. Agenda Lecture Content: Combinatorial Circuits Boolean Algebras
Exercise & Review

2. Combinatorial Circuits

3. Combinatorial Circuits
Computers / Electronic devices circuits:
Input: 0 or 1
Output: 0 or 1
Circuits can be constructed using any basic element that has two different states.
Combinatorial circuits have no memory  previous inputs and the states of the system do not affect the output of a combinatorial circuit.
Combinatorial circuits can be constructed using solid-state devices, called gates.

4. Gates
Input and output of electronic devices: {0,1}
Gates: the basic elements of a circuit
Utilize gates to design circuits that perform a variety of task

5. Gates
Inverter
OR gate
AND gate
XOR gate
NAND gate
NOR gate
Multiple input gate

6. Gates
x  y
x  y
x  y  z  …
x  y  z  …

7. Logic Table of Gates

8. Combinatorial Circuits

9. How to draw the inputs

10. Interconnecting Combinatorial Circuits

11. Combinatorial Circuits and Boolean Expression
Combinatorial circuits can be represented by a Boolean expression.
y = (x1  x2)  x3 is a Boolean expression expression

12. Combinatorial Circuits and Boolean Expression
Find the combinatorial circuits for the following boolean expressions:
y = (x1  (x2  x3 ))  x2

13. Combinatorial Circuits and Boolean Expression

14. Logic Table

15. Write the Boolean Expression

16. Equivalent Combinatorial Circuits
Two combinatorial circuits are equivalent, if they have identical outputs for given identical inputs (they have identical logic tables).

17. Equivalent Combinatorial Circuits