Explain about hamming error correcting code, Computer Engineering

Assignment Help:

Q. Explain about Hamming error correcting code?

Richard Hamming at Bell Laboratories worked out this code. We will only introduce this code with help of an illustration for 4 bit data. Let's presume a 4 bit number b4, b3, b2, b1.  In order to create a simple error detection code which detects error in one bit only we can just add an odd parity bit.  Though if we want to find which bit is in error then we may have to employ parity bits for different combinations of these 4 bits in such a way that a bit error can be recognized uniquely.  For illustration we can create four parity sets as below

Source Parity                            Destination Parity

b1, b2, b3                                                        P1                                            D1

b2, b3, b4                                                        P2                                            D2

b3, b4, b1                                                        P3                                            D3

b1, b2, b3, b4                                                  P4                                            D4

Now very interesting phenomenon can be noticed in above displayed parity pairs.  Assume data bit b1 is in error on transmission then it will cause alteration in destination parity D1, D3, D4.

ERROR IN                                                     Cause change in Destination Parity 

(One bit only)

b1                                                                                             D1, D3, D4

b2                                                                                             D1, D2, D4

b3                                                                                             D1, D2, D3, D4

b4                                                                                             D2, D3, D4

Figure: The error detection parity code mismatch

So by simply comparing parity bits of source and destination we can recognize that which of four bits is in error. This bit then can be complemented to eliminate error. Please note that even source parity bit can be in error on transmission but under assumption that just one bit (irrespective of data or parity) is in error it would be detected as just one destination parity would be different. What should be length of error detection code that detects error in one bit? Before responding this question we have to look in comparison logic of error detection. Error detection is done by comparing two ‘i’ bit error detection and correction codes fed to comparison logic bit by bit (see figure below). Let’s have comparison logic that produces a zero if compared bits are same or else it generates a one. Consequently if similar Position bits are similar then we obtained zero at that bit Position however if they are dissimilar that is this bit position may point to an error then this Particular bit position would be marked as one. This way a matching word is built. This matching word is ‘i’ bit long so can signify 2i values or combinations.


Related Discussions:- Explain about hamming error correcting code

Cn, What is the basic requirement for establishing VLANs?

What is the basic requirement for establishing VLANs?

How address resolution is performed with table lookup, How address resoluti...

How address resolution is performed with table lookup? Explain with the help of a suitable example. The approach of table lookup to address resolution needs a data structure wh

Interaction design and human–computer interaction, You should now have a re...

You should now have a reasonably clear understanding of what is meant by interaction design. However, there are several other terms which are often used to refer to particular aspe

State the importance of CRT monitor, State the importance of CRT monitor ...

State the importance of CRT monitor CRT is considered to be one of the most important component because the quality of displayed image influences the perception of generated de

Bidirectional search, Bidirectional Search: We've concentrated so far ...

Bidirectional Search: We've concentrated so far on the searches where the point of view for the search is to find a solution, but not the path to the solution. Like any other

Draw layout cells in a table, Now add layout cells into which you will add ...

Now add layout cells into which you will add text about travel locations. 1.  In Objects panel, click the Draw Layout Cell icon and move the pointer to layout table you just dre

General concepts of links and association, General Concepts of links and as...

General Concepts of links and association A link is a conceptual or physical connection among objects for instance. Mathematically, you can define a link as a tuple which is a

Testmanagers wizard, TestManager has a wizard that you can use to copy or i...

TestManager has a wizard that you can use to copy or import test scripts and other test assets (Datapools) from one to another.

Nand gate, The NAND gate. The NAND gate is equivalent to an AND gate fo...

The NAND gate. The NAND gate is equivalent to an AND gate followed by a NOT gate so that the output is 0 when all of the inputs are high, otherwise the output is 1. There may

Including the titles, Your company is planning a party for employees, and y...

Your company is planning a party for employees, and you have been asked to set up a spreadsheet to track the attendees and to measure the associated cost. Every employee is permitt

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd