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john July 31, 2018 42 Comments

## Half Adder and Full Adder Circuit

Half Adder and Full Adder circuits is explained with their truth tables in this article. Design of Full Adder using Half Adder circuit is also shown. Single-bit Full Adder circuit and Multi-bit addition using Full Adder is also shown.

TAKE A LOOK : BOOLEAN LOGIC

TAKE A LOOK : LOGIC GATES

TAKE A LOOK : FLIP FLOPS

### What is an Adder?

An adder is a kind of calculator that is used to add two binary numbers. When I say, calculator, I don’t mean one with buttons, this one is a circuit that can be integrated with many other circuits for a wide range of applications. There are two kinds of adders;

With the help of half adder, we can design circuits that are capable of performing simple addition with the help of logic gates.

Let us first take a look at the addition of single bits.

0+0 = 0

0+1 = 1

1+0 = 1

1+1 = 10

0+0 = 00

0+1 = 01

1+0 = 01

1+1 = 10

Here the output ‘1’of ‘10’ becomes the carry-out. The result is shown in a truth-table below. ‘SUM’ is the normal output and ‘CARRY’ is the carry-out.

INPUTS                 OUTPUTS

A             B             SUM      CARRY

0              0              0              0

0              1              1              0

1              1              0              1

From the equation, it is clear that this 1-bit adder can be easily implemented with the help of EXOR Gate for the output ‘SUM’ and an AND Gate for the carry. Take a look at the implementation below.

For complex addition, there may be cases when you have to add two 8-bit bytes together. This can be done only with the help of full-adder logic.

This type of adder is a little more difficult to implement than a half-adder. The main difference between a half-adder and a full-adder is that the full-adder has three inputs and two outputs. The first two inputs are A and B and the third input is an input carry designated as CIN. When a full adder logic is designed we will be able to string eight of them together to create a byte-wide adder and cascade the carry bit from one adder to the next.

INPUTS                 OUTPUTS

A             B             CIN         COUT    S

0              0              0              0              0

0              0              1              0              1

0              1              1              1              0

1              0              1              1              0

1              1              1              1              1

Thus, we can implement a full adder circuit with the help of two half adder circuits. The first will half adder will be used to add A and B to produce a partial Sum. The second half adder logic can be used to add CIN to the Sum produced by the first half adder to get the final S output. If any of the half adder logic produces a carry, there will be an output carry. Thus, COUT will be an OR function of the half-adder Carry outputs. Take a look at the implementation of the full adder circuit shown below.

Though the implementation of larger logic diagrams is possible with the above full adder logic a simpler symbol is mostly used to represent the operation. Given below is a simpler schematic representation of a one-bit full adder.

With this type of symbol, we can add two bits together taking a carry from the next lower order of magnitude, and sending a carry to the next higher order of magnitude. In a computer, for a multi-bit operation, each bit must be represented by a full adder and must be added simultaneously. Thus, to add two 8-bit numbers, you will need 8 full adders which can be formed by cascading two of the 4-bit blocks. The addition of two 4-bit numbers is shown below.

##### We recommend:
• zeinab
October 23, 2018

how make The output carry and the normal output as S in one output in full

• Abdullahzeese Ahuja
October 2, 2018

韦德体育投注网是什么,韦德体育appooohh, thanks sir, youve help me overcome my anxiety with this information. Now I can successfully deal with my wifes avrotion without having to use a coat hanger

• Syed Asad Shamsi
April 24, 2018

so nice explanation it can be understood easily….

• January 4, 2018

Nice information

• Aruna
December 2, 2017

Sir how to make a 4 bit full adder using half adder

• Yuval
November 17, 2017

This was a great explanation. Loved it thank you very much

• Dave Hinkins
February 23, 2017

Sir, wouldn’t it make more sense to use a half adder for the 0-bit, it would reduce the number of transistors by almost 1% in a 64 bit system and nearly 5% in a 32 bit system. or is there something I’m not seeing.

• abdelhalem
December 3, 2016

韦德体育投注网是什么,韦德体育appwhat the number of the new ic design full adder by 2 half adder ?

• February 17, 2016

韦德体育投注网是什么,韦德体育appthank u shaktiman

• October 7, 2015

韦德体育投注网是什么,韦德体育appcool notes here. simple and exact.

• thembisile sukwana
May 25, 2015

韦德体育投注网是什么,韦德体育apphonestly I had a problem with these adders so you played a prominent role in my life….thank you may God bless you

• Remo mantesh
May 21, 2015

its Realy Nice Sir

• May 14, 2015

韦德体育投注网是什么,韦德体育appThnx a lot 🙂

• Ahmed
April 10, 2015

sir is there a way to establish a full adder with only 3 gates not 5 ?

• M.Zeeshan Tahir
February 2, 2015

韦德体育投注网是什么,韦德体育appsir i want a 2-bit half adder and full adder table….

• Engr Shahkaz Khalid Butt
January 30, 2015

you did not clearly explain the difference between half and full adder.its not sufficient method for bignners or students to understand it.

• October 28, 2014

please give the logic diagram of full adder using NAND,NOR GATES

• October 21, 2014

韦德体育投注网是什么,韦德体育appThe demonstration is Crystal clear!

• vishal
September 8, 2014

韦德体育投注网是什么,韦德体育appHow to make full adder circuit using two half adder circuit

• GOURAB
August 30, 2014

韦德体育投注网是什么,韦德体育appvery useful for physics hons. student…..too simple too understand.:-)

• Waseem
May 24, 2014

Nice Sir,very simple and clear explanation

• PRACHI SINGH
May 17, 2014

NOT FULFILLED WITH THE RESULT

• Engr_underconstruction
February 16, 2014

Awesome n easy explanation. thanks sir for such a great work

• February 8, 2014

韦德体育投注网是什么,韦德体育appFantastic ideas…

• Gopi aravind sastry
January 21, 2014

Thanks sir for simple and clear explanation

• December 19, 2013

sir,i have to know the brief explanation of truth table of full adder

• December 19, 2013

韦德体育投注网是什么,韦德体育appsir please specify the important question list from ‘combination&sequential logic circuits’

• KIRAN
September 1, 2013

韦德体育投注网是什么,韦德体育appsir i need your help. and be-3 sem ADE sub in MOST IMP quns. for GTU.

August 26, 2013

韦德体育投注网是什么,韦德体育appsir,please specify the applications of full and half adders in brief manner.

• seetharaman
August 27, 2013

韦德体育投注网是什么,韦德体育appHi Mounika say you have four full adders you can make a 4 digit display that is from 0 to 9999. if you take the first overflow and set as 1 before 9999 it will become 19999, the measuring range is doubled with simple one overflow counter from 9999 to 19999. with second overfow it will indicate over range. Due to this half adder additon say to a 3 digit meter with a measuring range of 0-999 is increased 0 to 1999. That is why the 999 meter is called a 3 digit meter and 1999 is called 3 1/2 digit multimeter (as the half adder is added to double the measuring range).

• Aminu
April 25, 2013

Thank u very much the article is a very 9c 1

• aman gupta
January 12, 2013

sir,i need ur help i want to know about on application of full and half adder and its working. Thank you

• ashok
November 3, 2012

its awesome article…. its very useful… but it may have little simplification

• Akram
September 12, 2012

its very useful for me…

July 18, 2012

hi!i wnt to know hw to design a circuit?

• jojo
July 18, 2012

@priya – What kind of circuit ? Please specify!

• July 17, 2011

sir i need your help. i want the information about half adder and full adder using operational amplifier.
thanks

• a.j.azimathul marliya
July 16, 2012

韦德体育投注网是什么,韦德体育appsir,i need ur help,i want to know about on applications of full and half adder using logic gates,please response as soon as possible, thank you

• PseuffHut
October 3, 2010

Hi newbie in http://xpatre.com boards.
great to become member of this neighborhood

PS Mod: Please take away this thread if it isn’t the appropriate place this category:

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• deep
April 17, 2010

respected sir ,
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i wants to know about IR led and how does they work and why do we use IR led in remote operation and etc.

sir please show your response immediatly as soon as possible , i will very thankful your for this.

pls email me with this topic

“HAVE A NICE DAY”

• faisal saidy
September 5, 2014

韦德体育投注网是什么,韦德体育appThanks a lot sir for your helpful information

• September 10, 2014

Very clear and understandable