4.2.2. Full Adder

Now, when we talk about half adder necessarily that something will to come to your mind; that means, there may be some other adder also. Let’s see this is an adder circuit which can add a single bit number now just consider about sum 3 bit numbers then what will happen, we are going to add it so 1 and 1 is 0 and it is going to generate carry 1, then 1 and 1 we are going to add together then output is 0 and it is going to generate 1 carry.

The full adder is an extension of the half adder that incorporates an additional input for carry-in, allowing it to add three binary bits: A, B, and carry-in (C-in). When adding two bits together, if the sum exceeds the maximum number (1 in binary), a carry is generated. For example, when adding 1 and 1, the output sum is 0 but produces a carry of 1. This carry can then be added to the next pair of bits, thus enabling the addition of multiple bits.

Think of a full adder like a cashier at a store. If you purchase one item priced at $1 and pay with a$2 bill, you need to give back $1 in change (the sum). If instead, you buy two items (totaling$2) and pay with a $3 bill, the cashier would record$0 as the change (the sum) but has to keep track of an extra dollar carried over for upcoming transactions.

So in case of full adder, now you just see that we are having 3 input 𝐴, 𝐵 and carry in 𝐶 the 𝑖𝑛. 𝐶 is coming from the previous bit position. So, it is coming from here and we are going to get this 𝐶 and when we add them together it will generate a carry out 𝐶.

The full adder takes in three inputs: two bits (A and B) and a carry-in (C-in). The output consists of a sum output (S) and a carry-out (C-out). The full adder produces a sum that is based on the exclusive OR (XOR) output of A, B, and C-in, while the carry-out is produced using an AND gate that combines A and B. If A and B are both 1, a carry is sent to the next significant bit.

Imagine a birthday party, where each guest can bring snacks (A and B), and you might already have a few treats left over (C-in). The snacks everyone brings will produce a goodie bag (S) for everyone to take home. If too many snacks are brought (e.g., both guests brought fruit platters), you know you’ll need a bigger box (C-out) to hold all the goodies for the next guests!

The behaviour of this circuit can be represented with the help of this particular truth table. Now, since we are having 3 inputs over here. So, total input combination will be your 2^3 which is your 8.

A truth table for the full adder indicates all possible input combinations of A, B, and C-in, totaling eight combinations (from 000 to 111). For each combination, the corresponding sum (S) and carry-out (C-out) are determined, highlighting how the sum changes based on different binary inputs. This helps in understanding the functioning of the full adder logically by assessing its outputs for each input scenario.

A truth table can be compared to a recipe book where you can see all possible ways to mix ingredients (inputs) to create different dishes (outputs). Just as a recipe offers different outcomes based on the ingredients used, the truth table reveals the resulting sums and carries based on the binary input combinations.

Now, we have to see one more things. Now, said these are some logic gates or electronic component when you put signal 1 and 1 immediately we are not going to get the result over here because this electronic components are having some delays, it need some times and that time whatever time it is required we say this is the propagation delay of that particular block.

Propagation delay refers to the time it takes for an input change to affect the output of a digital circuit. In the case of full adders, there is a delay involved from the moment the inputs are applied until the correct sum and carry outputs are generated. This is critical for understanding how quickly a circuit can perform multiple operations especially in larger systems like processors where many adders might interact.

Think of propagation delay like passing a message through a chain of friends at a party. If you whisper a secret to one friend, it takes time for the message to travel from one person to the next until the final person hears it. Just as the message may take time to pass along, the output of a full adder also takes time to reflect the input changes due to its internal processes.

Now, if we are going to construct a 4 bit adder then how we are going to construct it; that means, we need to add 4 bits so that means we need 4 adder or here we can use the full adder even.

To create a 4-bit adder, multiple full adders are linked together in a series or cascade. Each full adder handles one bit of the input numbers and takes carry from the previous adder (if any). This allows for the addition of larger binary numbers beyond a single bit. For instance, when adding binary numbers 1101 and 1011, the least significant bit is processed by the first full adder, while any carry is passed on to the next full adder in line.

Think of multi-bit adders like a team of students working on a group project. Each student (or adder) completes a part of their work (a bit) and then passes any unfinished tasks (carries) onto the next student. This way, together, they can finish the entire project more efficiently.

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