__Half Adder, Full Adder and Subtractor__

**To construct and verify the truth tables of**

__AIM:__1. Half Adder

2. Half Subtractor

3. Full Adder

4. Full Subtractor

using logic gates.

__APPARATUS REQUIRED____:__

1. Half/Full Adder/Subtractor trainer kit

2. Regulated power supply

3. Connecting wires.

4. Patch cords.

**Circuit diagram for Half adder:**

__Procedure:__

*Two input half adder:*- X1 and X2 are two logic bits, X1 is MSB and X2 is LSB.
- Connect the circuit as shown in figure 1.
- Connect X1 and X2 to the logic input switches.
- Set up data in X1 and X2 by means of the input switches and fill up the table 1.
- Verify the result with the theoretical values.

**Truth Table:**

**Circuit diagram for Half subtractor:**

__Procedure:__

*Two input half subtractor:*- X1 and X2 are two logic bits, X1 is MSB and X2 is LSB.
- Connect the circuit as shown in figure 2.
- Connect X1 and X2 to the logic input switches.
- Set up data in X1 and X2 by means of the input switches and fill up the table 2.
- Verify the result with the theoretical values.

**Truth Table:**

**Circuit diagram for Full adder:**

__Procedure:__**X1 and X2 are two logic inputs and Cin is the carry input to find the sum S and carry C outputs for all combinations of X1, X2, and Cin.**

*Three input full adder:*- Connect X1, X2 and Cin to three data input switches.
- Connect OR gate output and EX-OR gate output to output status.
- Connect the circuit as shown in figure 3.
- Set up data in X1, X2, and Cin by means of the input switches and fill up the table 3.
- Verify the result with the theoretical values.

**Truth Table:**

**Circuit diagram for Full subtractor:**

__Procedure:__**X1 and X2 are two logic inputs and Bin is the borrow input to find the difference D and borrow B outputs for all combinations of X1, X2, and Bin.**

*Three input full subtractor:*- Connect X1, X2 and Bin to three data input switches.
- Connect OR gate output and EX-OR gate output to output status.
- Connect the circuit as shown in figure 4.
- Set up data in X1, X2, and Bin by means of the input switches and fill up the table 4.
- Verify the result with the theoretical values.

**Truth Table:**

**Result**:

**NAND gate:**

**Realization of OR, AND, NOT, NOR gates by NAND gates**

**OR gate:**

**AND gate:**

**NOT gate:**

**NOR gate:**

**Procedure**:

- Connect the trainer as shown in figures.
- Verify the working of OR gate, AND gate, NOT gate, NAND gate and NOR gate with the help of truth tables given.

**Result**:

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