Full Adder (FA)

What Is an Full Adder?

A full adder is a fundamental digital circuit used in computer architecture and digital logic design. Let’s break down its key aspects:

But in binary logic, what does a carry mean? Well, let’s see this in the following example:

Notice that when you add 0 and 0 or 1 and 0, the result can be represented with just one bit. However, when you add 1 and 1, you require two bits, and one of them serves as the carry.

Now, why is a carry input necessary in full adders? Consider scenarios where you want to sum inputs with numbers greater than 1 bit. For instance, when adding two 4-bit binary numbers, you need to combine multiple adders and provide a carry input between them. This carry input indicates that the previous (less significant) operation resulted in a carry.

Outputs:

A full adder produces two binary outputs:

• Sum s: represents the result of adding a, b, and cIn.
• Carry-out cOut: indicates whether there is a carry to the next higher order of magnitude.

Truth Table:

The truth table for a full adder operator (FA) defines the relationship between inputs and outputs.

Given a full adder with inputs: a, b, and cIn, the logical expressions for sum and cOut are as follows:

Modeling

The Swan model of the full adder circuit is composed of the boolean operators XOR, OR, and AND seen previously:

Model Simulation

1. Test harness
   In order to observe the FullAdder::FA function behavior, we design a test harness (HarnessFA) in a test module (TestNbitAdder):

   
   
   

2. Simulation Trace

   The simulation is launched with 8 steps.

   The simulation trace shows that our truth table is verified; we can check by reading the signals in each step:

   

In the next part, application examples of the full adder are presented.