 ## Understanding the PCB Design for Half Adder

Posted On 16 August 2022 BY

Multiple circuits’ combination involves various logic gates to create a multiplexer, encoder, de-multiplexer, and decoder. Such circuits have certain qualities, such as the circuit’s output more depends on the levels which are present at the input terminal.
Such a circuit lacks memory, and the previous input can’t influence the current input. The combined circuits consist of inputs and outputs.
A half adder is an electronic circuit that adds two binary numbers. So, two single binary numbers act as adders in this case. It can return the carry and the output, and the representation in practice involves the XOR and AND logic gates. There are two inputs in a half adder circuit, including A and B, generating the Sum and Carry. So, the number of outputs is also two in this case, like S and C.

## Types of Combinational Circuits

• Encoder
• Subtractor
• Decoder
• Multiplexer
• De-multiplexer

Half adder is a digital circuit in PCB that provides an addition to binary numbers. In a half adder, a number’s weight is based on the binary digits’ position. The binary numbers are only from 0 to 1 of which 1 acts as the largest number and 0 as a smaller digit.
The two inputs of the half adder generate two outputs, so it is the simplest electronic circuit in the PCB. The inputs A and B are the bits where addition is required, whereas the Sum and Carry are the outputs abbreviated as S and C.

The half adder circuit has two gates, including XOR and AND, and both have the same inputs. However, each gate generates the output, like XOR generates the Sum and AND generates Carry.

According to engineers’ calculations if both ‘A and B’ inputs are 0, then both outputs like S and C would be 0.
However, if any of the input is 1, then the S or sum will be 1, but the C or carry will be 0.
However, if both A and B inputs are 1, then the S or sum will be 0, and the C or carry will be 1.
The half adder in a PCB performs additions according to the inputs applied.

You can have the following combinations, such as

0+0=0

0+1=1

1+0=1

1+1=10

In this equation, 1+1=10, but it should be 2-bit output if rewritten, such as

0+0=00

0+1=01

1+0=01

1+1=10

In this case, the normal output is the Sum, whereas you should consider Carry as a carry-out. It is easy to implement a 1-bit adder through an XOR gate.
If you want to add two 8-bit, you can do it through the full adder because the half adder is suitable for the addition of one binary digit.
For two-binary digits, you will have to reduce the truth table. But, for a three-binary digit adder, the process of addition through a half adder should be done twice. Likewise, a four-digit adder involves another repetition of the half adder addition.
The entire process shows that it is easy to implement, but it takes lots of time.

You can implement the half adder by using the high-speed CMOS digital and logic-based Printed Circuit Board.

## Understanding Equation

It is easy to identify the equation of the half adder PCBs through two concepts, such as the Sum of Products, SOP, and the Products of sum, POS. The Boolean system of such PCBs helps find the relations between the inputs applied and the generated outputs.
Designers draw the K maps to find the equation and the maps are based on the facts. The k map has two equations, as it has two logic gates.

The K map for the Carry brings the below facts.
C=A.B
Whereas the K map for the Sum or XOR brings
S= A⊕ B

## Applications of A Half-Adder PCB

The basic half adder has several applications, such:

• It offers additions on the binary bits, and the logic unit and arithmetic lying in the computer need a half-adder circuit.
• Such logic of half-adder circuits helps in designing calculators. So, the PCB in a calculator prefers a half-adder circuit.
• Other than additions, the half-adder circuits can also handle different digital circuits’ applications. So, you can consider it a vital part of digital electronics.

Implementing The Half Adder Through An NOR Gate: NOR is a universal gate that helps implement a half adder.

## Implementing The Half Adder Through NAND Gate

The NAND is also a universal gate that shows that you can design any type of PC Board through NAND gates. In this type, the carry output is produced through one NAND gate’s output being applied to the input which is another NAND gate. The second NAND gate is AND-gate generated output.

The Sum’s output equation can be produced through the output of the initial NAND, but with A and B inputs. In the end, the outputs generated by the NAND gates are again tried on the gate, producing the Sum’s output.
Hence, the standard adder in a digital PCB is easy to design through different logic gates. However, the addition of multiple bits is hard and it becomes a half-adder’s limitation.

## Understanding A Full Adder PCB

The full-adder circuit includes three inputs, such as A, B, and C which add three numbers for input, generating the Carry and Sum. Whereas the number of the outputs is two. The main reason for half and full adders is the addition.
If Carry is produced through a previous addition, you can add it to another, unlike a half adder.

## Difference Between A Half And Full Adder

A full adder involves two AND gates, two OR, and two EX-OR gates. Full adder is applicable in digital processors, and additions of several bits.
You have to combine two logic gates for PCB design with a half adder. But, a full adder consists of three gates.
Half adder is required in the electronic devices to calculate additions. But, the full adder is applied to the digital processors to add a long bit.
You can have a high output in full adders. Moreover, they involve a high speed and are very powerful in supplying voltage.
Full adder is also suitable for GPU, or Graphics Processing Unit.
Half adder and full adder have one thing in common and that is the addition, as both are combinational circuits and don’t need a memory, like sequential circuits.

## FAQs

#### What Is An Adder In PCB?

The digital circuits have different benefits, and if their main focus is to provide an additional, it is called Adder. It has two types, including the half adder and the full adder, depending on its inputs and output. However, the output is called Sum and Carry.
Adder is used in different kinds of processors other than just computers. They are constructed for several numerical elements, such as binary code decimal or excess-3.

#### Is There Any Limitation Of A Half Adder?

Yes, the half adder has some limitations. Like, it cannot add the carry bit produced from the previous or old bit. So, the half adders can’t perform additions in the case of multiple bits.

#### What Is A Full Adder In PCB?

A full adder includes three inputs, such as A, B, and C which add three numbers for input, generating the Carry and Sum. Whereas the number of the outputs is two.

#### Where To Use A Half-Adder Circuit?

PCB with a half adder is used in calculators and digital devices. It has a simple design and you can convert it to a half subtractor.

#### How Many Types Of Combinational Circuits Are There?

The types of combinational circuits include the half adder, full adder, encoder, subtractor, decoder, multiplexer, and de-multiplexer.

#### What Are The Uses Of A Half Adder?

A half adder offers additions on the binary bits, and the logic unit and arithmetic lying in the computer need a half-adder circuit. Moreover, half-adder circuits when combined can produce full-adder circuits. The logic in designing calculators. So, the PCB in a calculator prefers a half-adder circuit. The half-adder circuits can also handle different digital circuits’ applications.

## Wrap Up

A half adder is an electronic circuit that adds two binary numbers. So, two single binary numbers act as adders in this case. It can return the carry and the output, and the representation in practice involves the XOR and AND logic gates. There are two inputs in a half adder circuit, including A and B, generating the Sum and Carry. So, the number of outputs is also two in this case, like S and C.
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#### Written by Sam Sangani Sam Sangani is the President & CEO of PNC Inc., a Nutley, NJ based Printed Circuit Board manufacturer. Sam graduated from L. D. Engineering College with a BS Degree in Mechanical Engineering. He also continued his education and graduated from Steven’s Institute of Technology where he acquired a Master’s degree in Computer Science.

After completion of his BS, Sam worked as a QC Manager, for Xerox, Romania and London. He was responsible for the Quality Control of Cable and Wire Harness imports from Romania. After completing his Master’s Degree, he worked as a Senior Programmer with IBM, Tucson, Arizona. Sam was responsible for leading the Mainframe System Programming Team.

In 1997, Sam acquired PNC INC., a Nutley, NJ based PC Board fabrication Shop. From 1997-2013, Sam has made tremendous improvements and changes within PNC INC., as he added many new Products and Technologies in PNC’s portfolio. With his proven track record and leadership, PNC has never had an unprofitable year and has continued its growth yearly since 1997.

His current responsibilities are Strategic Planning, Corporate Management, New Business Ventures, Sales & Marketing, Trade Shows, Professional Services and leading productive teams to achieve peak potential. He has also utilized Lean Management techniques which have built a foundation for PNC’s high-paced growth. Sam also enjoys real-estate investing, web design & SEO, trading stocks, options, futures and Forex markets.

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