LESSON 04 – LOGIC GATES (XOR & XNOR) & CIRCUIT SIMPLIFICATION

LESSON NOTE 2 – CIRCUIT SIMPLIFICATION

We have already seen that we can have two equivalent circuits where one circuit is very simple and the other is relatively complex. Finding an equivalent simple circuit for a complex circuit is very important. We will call this process simplifying a circuit. Here are the steps:

1. Create the logic table for the circuit.

2. Compare that logic table to simple circuit logic tables (if match, then done).

3. Sometimes, a combination of logic tables is necessary.

The following table is useful for this task:

A	B	A AND B = Q	A OR B = Q	A NAND B = Q	A NOR B = Q	A XOR B = Q	A XNOR B = Q
0	0	0	0	1	1	0	1
0	1	0	1	1	0	1	0
1	0	0	1	1	0	1	0
1	1	1	1	0	0	0	1

Example – Simplify the following circuit:

Solution

Step 1 – Create logic table:

A	B	Q
0	0	1
0	1	0
1	0	0
1	1	0

Step 2 – Compare to simple logic tables.

We see that it is the same the logic table for A NOR B = Q. Therefore, a simpler circuit would be the following:

Example 2 – Simplify the following circuit:

Solution

Step 1 – Create logic table (challenging):

A	B	Q
0	0	0
0	1	1
1	0	1
1	1	0

Step 2 – Compare to simple logic tables.

We see that it is the same the logic table for A XOR B = Q. Therefore, a simpler circuit would be the following: