4.2.1. Half Adder

Now, we are going to see... here we can use the full adder even.

A half adder is a basic digital circuit used for adding two single binary numbers. It produces two outputs: the sum and the carry. When adding two bits, the result can be 0, 1, or a carry needs to be generated when both bits are 1. The half adder does not take any carry input from previous additions as it can only add two bits.

Consider a situation where you are collecting apples from two baskets. If the first basket has 0 apples and the second has 0 apples, you have 0 apples in total. If the first basket has 1 apple and the second has 0 apples, you have 1 apple. If both baskets have 1 apple, you have 0 apples in your hands, but you need to borrow an apple from the next basket. This borrowing represents the carry in binary addition.

this behaviour of half adder can be represented with the help of this particular truth table...

The behavior of a half adder can be illustrated using a truth table. In this table, we display all possible combinations of inputs and their corresponding outputs. For two inputs A and B, the table would look like this:

This table indicates that the sum is 1 whenever either A or B is 1, but when both are 1, the sum is 0 and we have a carry of 1.

Imagine you have two light switches representing inputs A and B. If both switches are off (0), the light (sum) is off. If one switch is on (1), the light is on. But if both switches are on, the original light might not be useful; instead, you activate another light (carry) to symbolize that both were on.

Just look into the behaviour of S, here we are going to say that this is nothing but the exclusive OR...

The output functions for the sum and carry of a half adder are derived from logical expressions. The sum (S) output is produced using an Exclusive OR (XOR) gate, which gives a high output when either input A or B is high, but not both. The carry (C) output is produced using an AND gate, which only outputs a high signal when both A and B are high. Thus, the equations representing a half adder are:

• Sum (S) = A XOR B
• Carry (C) = A AND B

Think about a party where you can invite two friends, A and B, to join. If you ask A or B to come, one of them shows up, so everyone is happy (this is the sum). However, if both bring snacks, you have to figure out how to manage them (this is the carry). Hence, the XOR symbolizes the happy attendance of either friend, while the AND symbolizes the situation when both friends contribute.

Now, we have seen the behaviour of half adder... necessary that something will to come to your mind...

Having understood the half adder, it's essential to note that it cannot handle multiple bits effectively, such as in larger binary additions like 3-bit numbers. Therefore, we introduce the full adder. A full adder includes an additional input for carry and can add three bits together (two bits and a carry-in). The design of a full adder evolves from that of a half adder by incorporating an extra input and the capability to process carries from previous operations.

If you have a single bowl (half adder) to mix two types of fruits, it works fine. But if you want to mix two types with an extra fruit from the previous mix, you need a bigger bowl (full adder) to include all items properly. The transition from mixing in pairs to handling a mix that includes a previous leftover demonstrates the need for more complex additions in digital electronics.

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