Practical No.4 Construct Exclusive Gates using Universal Gates
Practical No.4
Construct Exclusive Gates using Universal Gates
Aim
To construct EX-OR and EX-NOR gates using only NAND and NOR gates and verify their truth tables.
Simulator
Open
Before Starting
Step 1
Open Logic.ly.
You will see
Gates
Inputs
Outputs
Wire Tool
Step 2
Drag the following components.
For EX-OR using NAND
2 Input Switches (A and B)
4 NAND Gates
1 LED
Arrange them exactly like the circuit diagram.
Do NOT connect wires yet.
PART A
EX-OR using NAND Gates
The circuit uses 4 NAND gates.
We will connect one gate at a time.
STEP 1
Create Inputs
Drag
Input Switch → A
Input Switch → B
Rename them
A
B
STEP 2
Place Four NAND Gates
Place four NAND gates.
Rename them
NAND1
NAND2
NAND3
NAND4
This makes the circuit easy to understand.
STEP 3
Connect NAND1
Connect
A → NAND1 Input 1
B → NAND1 Input 2
Now NAND1 gives
(A.B)'
This output is called
X
Test
Change switches.
Observe
Output of NAND1 changes.
No need to complete the circuit yet.
STEP 4
Connect NAND2
Connect
A
↓
Input 1 of NAND2
Output of NAND1
↓
Input 2 of NAND2
Now NAND2 produces
A(A.B)'
Test
Toggle A and B.
Observe output.
STEP 5
Connect NAND3
Connect
B
↓
Input 2 of NAND3
Output of NAND1
↓
Input 1 of NAND3
Output becomes
B(A.B)'
Test
Again change switches.
Observe LED (or probe).
STEP 6
Connect NAND4
Connect
Output of NAND2
↓
Input 1
Output of NAND3
↓
Input 2
Output of NAND4
↓
LED
Circuit Completed
STEP 7
Verify Truth Table
| A | B | LED |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |
Ask students
Does LED glow only when inputs are different?
If YES
Circuit is correct.
Important Observation
Tell students
Same inputs
OFF
Different inputs
ON
This single sentence helps them remember XOR forever.
PART B
EX-NOR using NAND Gates
This circuit also uses NAND gates.
Step 1
Place
2 Inputs
5 NAND Gates
1 LED
Step 2
Create NOT Gates
A is connected to both inputs of NAND.
A
|\
| \
----
Output
A'
Do the same for B.
Output
B'
Step 3
Create
AB
using NAND arrangement shown in the manual.
Step 4
Create
A'B'
Step 5
Connect both outputs to the final NAND gate.
Output
AB + A'B'
This is EX-NOR.
Verify
| A | B | LED |
|---|---|---|
| 0 | 0 | 1 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
Ask
Does LED glow only when inputs are same?
If YES
Correct.
PART C
EX-OR using NOR Gates
Place
2 Inputs
4 NOR Gates
LED
Step 1
Connect
A
↓
NOR1
B
↓
NOR1
Output
(A+B)'
Step 2
Make
A'
using NOR.
Connect A to both inputs.
Step 3
Make
B'
using NOR.
Step 4
Connect outputs exactly as the manual.
Final output goes to LED.
Verify
| A | B | LED |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |
PART D
EX-NOR using NOR Gates
Place
2 Inputs
4 NOR Gates
LED
Follow the diagram.
Final output should be
| A | B | LED |
|---|---|---|
| 0 | 0 | 1 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
How to Test Every Circuit
Never test only one input.
Test all four combinations.
| A | B |
|---|---|
| 0 | 0 |
| 0 | 1 |
| 1 | 0 |
| 1 | 1 |
Observe LED.
Compare with truth table.
If every row matches,
Circuit is correct.
Viva Tips
Q1. Which gates are called universal gates?
Answer: NAND and NOR.
Q2. Why are they called universal gates?
Answer: Because any logic gate or Boolean function can be implemented using only NAND gates or only NOR gates.
Q3. When is XOR output HIGH?
Answer: When the two inputs are different.
Q4. When is XNOR output HIGH?
Answer: When the two inputs are the same.
Q5. How many NAND gates are required to construct a 2-input XOR gate?
Answer: 4 NAND gates.
Result (Write in Practical Journal)
The EX-OR and EX-NOR gates were successfully constructed using NAND and NOR universal gates in the Logic.ly simulator. The observed outputs matched the expected truth tables for all input combinations.
Interpretation of Results
The simulator verified that NAND and NOR gates are universal gates because they can be used to implement EX-OR and EX-NOR gates without using any dedicated XOR/XNOR gate. The output for each input combination matched the theoretical truth table.
Conclusion and Recommendation
The practical demonstrated that complex logic functions can be implemented using only universal gates. Students should practice wiring the circuits repeatedly and verify all four input combinations to strengthen their understanding of digital logic design.