To demonstrate the implementation of basic Boolean logic functions (AND, OR, NOT) using universal gates (NAND and NOR) and verify their truth tables using 74LS00 (NAND) and 74LS02 (NOR) ICs.
74LS00 IC (Quad 2-input NAND gate)
74LS02 IC (Quad 2-input NOR gate)
Breadboard
Connecting wires
Power supply (5V DC)
Digital Triner with switches and LEDs
Universal gates are gates that can be used to implement any Boolean function without the need for any other gate type. The two universal gates are:
NAND Gate
NOR Gate
Using these gates, we can construct AND, OR, and NOT gates.
A NOT gate can be implemented using a NAND
Tie both inputs of the NAND gate together.
Y = (A.B)' = (A.A)' = A' (Using the Idempotent Law A⋅A=A)
An AND gate can be implemented using two NAND gates.
The output of the first NAND gate is (A⋅B)'
The second NAND gate acts as a NOT gate to invert the output of the first NAND gate:
Y = (A⋅B)' '= A⋅B (Using the Involution Law).
An OR gate can be implemented using three NAND gates.
First, implement NOT gates using NAND gates to get A' and B'
Then, use a NAND gate to compute (A'.B')'
(A' . B')' = A' ' + B' ' = A + B (Using De Morgan's Theorem:)
(Give Boolean Algebra justification of AND, OR, NOT gate implementation using NOR gates.)
Step 1: NOT Gate Using NAND
Connect the two inputs of a NAND gate (74LS00) together to form a NOT gate.
Connect the input to a toggle switch and the output to an LED.
Verify the truth table.
Logic Diagram:
A--+--| \
| |NAND)O--- A'
+--| /
Truth Table:
| A | A'|
|---+---|
| 0 | 1 |
| 1 | 0 |
ate can be implemented using a NAND gate by connecting both inputs together.
Step 2: AND Gate Using NAND
Use two NAND gates from the 74LS00 IC.
Connect the inputs A and B to the first NAND gate.
Connect the output of the first NAND gate to both inputs of the second NAND gate.
Connect the output to an LED.
Verify the truth table.
Logic Diagram:
A---| \ +--| \
|NAND1)O---| |NAND2)O---AB
B---| / +--| /
Truth Table:
| A | B | AB |
|---|---|----|
| 0 | 0 | 0 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
Step 3: OR Gate Using NAND
Use three NAND gates from the 74LS00 IC.
Connect the inputs A and B to two separate NAND gates configured as NOT gates.
Connect the outputs of these NOT gates to the inputs of the third NAND gate.
Connect the output to an LED.
Verify the truth table.
Logic Diagram:
A-+-| \
| |NAND1)O-+
+-| / +-| \
|NAND3)O---(A+B)
+-| \ +-| /
| |NAND2)O-+
B-+-| /
Truth Tabl:
| A | B | A+B |
|---|---|-----|
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 1 |
Step 1: NOT Gate Using NOR
Connect the two inputs of a NOR gate (74LS02) together to form a NOT gate.
Connect the input to a toggle switch and the output to an LED.
Verify the truth table.
Logic Diagram:
A--+-\ \
| )NOR)O--- A'
+-/ /
Truth Table:
| A | A'|
|---+---|
| 0 | 1 |
| 1 | 0 |
Step 2: OR Gate Using NOR
Use two NOR gates from the 74LS02 IC.
Connect the inputs A and B to the first NOR gate.
Connect the output of the first NOR gate to both inputs of the second NOR gate.
Connect the output to an LED.
Verify the truth table.
Logic Diagram:
A-\ \ +-\ \
)NOR1)O---| |NOR2)O--A+B
B-/ / +-/ /
Truth Table:
| A | B | A+B |
|---|---|-----|
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 1 |
Step 3: AND Gate Using NOR
Use three NOR gates from the 74LS02 IC.
Connect the inputs A and B to two separate NOR gates configured as NOT gates.
Connect the outputs of these NOT gates to the inputs of the third NOR gate.
Connect the output to an LED.
Verify the truth table.
Logic Diagram:
A-+-\ \
| )NOR1)O-+
+-/ / |
+-\ \
)NOR3)O---AB
+-/ /
+-\ \ |
| )NOR2)O-+
B-+-/ /
Truth Table:
| A | B | AB |
|---|---|----|
| 0 | 0 | 0 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
Record the output for each combination of inputs in the truth tables.
Verify that the outputs match the expected Boolean logic.
This experiment demonstrates the implementation of basic Boolean logic functions using universal gates (NAND and NOR). The 74LS00 and 74LS02 ICs were used to construct NOT, AND, and OR gates, and their truth tables were verified.
Always double-check your connections and ensure the power supply is set to 5V DC to avoid damaging the ICs.