Designing a 3-Bit Parallel Full Adder Using AND, OR, and NOT Gates

A 3-bit parallel full adder is a crucial component in digital systems that can add two 3-bit binary numbers along with a carry-in bit. This article will guide you through the process of creating a 3-bit parallel full adder using basic logic gates: AND, OR, and NOT gates. We will cover the truth table, the sum and carry out expressions, and the circuit design.

Step 1: Truth Table

The truth table for a 3-bit parallel full adder consists of all possible combinations of the inputs.

A2A1A0B2B1B0CinS2S1S0Cout 00000000000 00000010010 00000100100 00000110110 11111111111

Total number of rows is 26 64 for three bits each of A and B plus the carry-in.

Step 2: Sum and Carry Out Expressions

The sum outputs and the carry outputs can be derived using the following expressions:

Sum Output S: S0 A0 ⊕ B0 ⊕ Cin S1 A1 ⊕ B1 ⊕ C1 S2 A2 ⊕ B2 ⊕ C2 Carry Output Cout: Cout C2 C0 A0 ∧ B0 ∨ Cin ∧ (A0 ⊕ B0) C1 A1 ∧ B1 ∨ C0 ∧ (A1 ⊕ B1) C2 A2 ∧ B2 ∨ C1 ∧ (A2 ⊕ B2)

Step 3: Logic Circuit Design

Now, we will design the circuit using AND, OR, and NOT gates based on the expressions derived.

Sum Outputs

The sum outputs can be implemented using XOR gates. Since XOR can be constructed using AND, OR, and NOT gates, the expressions are as follows:

S0 A0 !B0 !Cin | !A0 B0 !Cin | A0 B0 Cin | !A0 !B0 Cin

Carry Outputs

The carry outputs can be implemented using AND and OR gates based on the expressions derived. For example, for S0 and Cout, the circuit is designed as follows:

S0 A0 !B0 !Cin | !A0 B0 !Cin | A0 B0 Cin | !A0 !B0 Cin

Cout C2

C0 A0 B0 | Cin (A0 ⊕ B0)

C1 A1 B1 | C0 (A1 ⊕ B1)

C2 A2 B2 | C1 (A2 ⊕ B2)

Summary

In summary, to create a 3-bit parallel full adder using AND, OR, and NOT gates, you need to follow these steps:

Construct a truth table covering all combinations of inputs. Deduce the logical expressions for the sum and carry outputs based on the truth table. Design the circuit using AND, OR, and NOT gates to implement these expressions.

This structured approach allows you to build a functional 3-bit parallel full adder using basic logic gates.

Key Takeaways:

Understanding the truth table is essential for designing the adder. The sum and carry expressions are derived from the truth table. The circuit can be implemented using basic logic gates.

This article provides a comprehensive guide for creating a 3-bit parallel full adder, which is a fundamental component in digital electronics and computer architecture.