Practical No. 8
Title: To Study and Verify Combinational Logic Circuits

Aim
To understand the design and operation of a Full Adder circuit and to verify its truth table and logical expressions.

Introduction
The Full Adder is a fundamental combinational logic circuit used to add three single-bit binary numbers. Unlike the Half Adder, it can process an input carry bit (Carry-in, Cin) from a previous stage of addition, in addition to the two input bits (A and B).

This capability makes the Full Adder a crucial component for constructing multi-bit adders, essential for the arithmetic logic units in all CPUs. A precise understanding of the Full Adder’s functionality is vital for comprehending how digital computers perform arithmetic operations.

Procedure / Example

Full Adder Design:

• Inputs: A, B, Cin (Carry-in from a previous stage)
• Outputs: Sum (S), Carry-out (Cout)

Truth Table:

A	B	Cin	Sum (S)	Cout
0	0	0	0	0
0	0	1	1	0
0	1	0	1	0
0	1	1	0	1
1	0	0	1	0
1	0	1	0	1
1	1	0	0	1
1	1	1	1	1

Logical Expressions:

• Sum (S): S = A XOR B XOR Cin
• Carry-out (Cout): Cout = (A AND B) OR (Cin AND (A XOR B))
• Equivalent form: Cout = (A AND B) OR (A AND Cin) OR (B AND Cin)

Circuit Diagram:
A Full Adder can be constructed using two Half Adders and an OR gate:

1.     First Half Adder adds A and B → produces partial sum and carry

2.     Second Half Adder adds partial sum with Cin → produces final Sum

3.     Carries from both Half Adders go to an OR gate → produces Cout

(Draw the logic circuit diagram here, showing inputs A, B, Cin, two Half Adders, and an OR gate producing Cout)

Example: Verification

Input: A = 1, B = 1, Cin = 0

• Sum (S) = 1 XOR 1 XOR 0 = 0 XOR 0 = 0
• Carry-out (Cout) = (1 AND 1) OR (0 AND (1 XOR 1)) = 1 OR 0 = 1

Binary Addition: 1 + 1 + 0 = 10 (Sum = 0, Carry-out = 1) ✔

Exercises

1.     Draw the Logic Circuit Diagram

• Draw the complete Full Adder circuit using standard gate symbols. Label inputs (A, B, Cin) and outputs (Sum, Cout). You may use two Half Adders and an OR gate.

2.     Verify the Truth Table

A	B	Cin	Sum (S)	Cout
0	0	0
0	0	1
0	1	0
0	1	1
1	0	0
1	0	1
1	1	0
1	1	1

Result / Conclusion
This practical successfully demonstrated the fundamental operation of a Full Adder, a key combinational logic circuit. By deriving its truth table, logical expressions, and understanding its circuit implementation, students gained a clear understanding of how three single-bit binary numbers are added. The Full Adder serves as a foundational component for constructing more complex arithmetic units in computer processing.