Hello Pupils! I welcome you to

*I hope you are having a good day. Today, We’ll learn about another Digital Circuit. Before this, I explained Half Adder through XOR with AND Gate in Proteus. Let’s have a look at what we’ll learn today.*

**The Engineering Projects.**- What is Adder?
- What are Half Adder?
- How is the Truth Table of Half Adder
- Why is it called Half Adder?
- How can We make Half Adder Circuit through NAND Gate?
- How can We make Half Adder through just NOR Gate?

Hence without wasting time, Let’s find all the Answers.

## Adder

An Adder is a Circuit that may be Define as:

“AnAdderis a digital Circuit that takes theinputfrom the user and shows theadditionof the number. Where the number is in the form of bits.”

In computer system, Adders are used mainly for Arithmetic Logic Units where the Addition is an important Function. You will see more applications of Adders later in this essay.

There are two types of Adders in Computer system:

- Half Adder
- Full Adder

In this article, we’ll stress on the Half Adder only.

## Half Adder

Prior to start Implementation, it is always useful to study all basic Concepts a b out the topic. Hence we will define the Half Adder first as:

” AHalf Adderis a digital circuit that has two inputs,addsthe two bits and show us the resultantbitwithcarryat its two outputs.”

The user (may be a human or computer) give the bits in the form of binary number to the input and the Adder adds the bits and give the user an output through its output Terminal.

### DID YOU KNOW??????

The Half Adder is called **“Half”** because it has the capability to add two numbers and to show the carry but it can not store the carry bit in it so that use can use it in the next addition. Thus it can do only the Half Work and is considered as incomplete.

## Truth Table of Half Adder

The Truth Table of the Half Adder circuit is different from the basic Logic gate’s Truth Table as it has two output.

Hence in the Truth Table of Half Adder we observe two inputs and two output columns. Assume that the inputs are named as A and B the the sum is denoted by a Greek symbol **∑ ** and the carry is denoted by **C**_{0.}

Input | Output | ||

A | B | ∑ | C_{0} |

0 | 0 | 0 | 0 |

0 | 1 | 1 | 0 |

1 | 0 | 1 | 0 |

1 | 1 | 0 | 1 |

Truss when we work with half adder , we get the carry only, when both the inputs are **HIGH**.

## Half Adder through AND Gate

Prior to start, we’ll recall the basic concepts about the AND Gate. we define the AND Gate as:

“AND Gateis the two inputs Basic Logic gate that gives the outputLOWonly, when both its inputs areHIGHotherwise, givesHIGHoutput.”

The Truth Table of NAND Gate is given next:

A | B | (A.B)’ |

0 | 0 | 1 |

0 | 1 | 1 |

1 | 0 | 1 |

1 | 1 | 0 |

In the procedure of design the circuit, we’ll use more than one AND gate to get the required result.

Let’s rush towards the Proteus software to run our Half Adder.

### Simulation in Proteus ISIS

**Material Required **

- NAND Gate
- Logic Toggle
- LED
- Ground Terminal
- Connecting Wires

- Fire up Proteus software.
- Pick the required Material through the “P” Button.
- Arrange the AND Gate in the at the working Area.
- Choose total five AND gates and arrange them according to the image given below.
- Get Logic toggle from the Library and attach them with the inputs of AND 1 Gate.

The Circuit looks like this:

Swap the values of both Logic Toggles and record the input and output in the form of Truth Table. You will observe that we get the output as it was required for the Half Adder.

For best concepts, we will learn how will the output at each NAND Gate that successively makes the Half Adder. Let’s have a look.

Input | Output | |||||

A | B | 1 | 2 | 3 | 4(SUM) | 5(CARRY) |

0 | 0 | 1 | 1 | 1 | 0 | 0 |

0 | 1 | 1 | 1 | 0 | 1 | 0 |

1 | 0 | 1 | 0 | 1 | 1 | 0 |

1 | 1 | 0 | 1 | 1 | 0 | 1 |

## Half Adder through NOR Gate

Recall that a NOR Gate is the universal Gate and we may define the NOR Gate as:

” A

NORgateis a two input Logic Gate that gives the out putLOWonly when both of its inputs areHIGH.”

Hence we use the NOR Gate in such a manner that the output given to us give the addition of two bits with a carry.

When we observe the NOR Gate, the following Truth Table is obtained:

A | B | (A+B)’ |

0 | 0 | 0 |

0 | 1 | 0 |

1 | 0 | 0 |

1 | 1 | 1 |

To implement the Half Adder through NOR Gate you have to follow the simple steps given next.

**Material Required:**

- NOR Gate.
- Logic Toggle.
- LED.
- Ground Terminal.
- Connecting wires.

### Procedure

- Start your Proteus Software.
- Select first three components from Pick Library.
- Now, arrange the components at the working area according to the image given below.
- Attach Logic toggle at the inputs of switch labeled as 2.
- Connect LED with the output of switch 4 and 5.
- Ground the output terminals.

- Changing the values in Logic Toggle we get the result.

For the purpose of deep learning we’ll examine all the outputs at each NOR gate. Thus, we get the following Truth Table:

Input | Output | |||||

A | B | 1 | 2 | 3 | 4(SUM) | 5(CARRY) |

0 | 0 | 1 | 1 | 1 | 0 | 0 |

0 | 1 | 0 | 0 | 1 | 1 | 0 |

1 | 0 | 1 | 0 | 0 | 1 | 0 |

1 | 1 | 0 | 0 | 0 | 0 | 1 |

Hence, in the end, we get our required output.

**DID YOU KNOW?????????? **

NOR Gate and NAND Gate are considered as the Universal Gates. We can use them for the formation of other Gates as well. Truss, we just made the different gates through these universal Gates and implement them for our experimentation.

Consequently, at the Present Day, we learned many things about Half Adder. We saw what are the Half adders, how they work, How its Truth Table looks like and how can we use them just through a single gate. for this purpose, we used AND Gates and NOR Gate that is the universal Gates.