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

IT PMP project managemnet., Identify at least eight milestones for this pro...

Identify at least eight milestones for this project. Write a one-page paper describing each milestone using the SMART criteria?

Explain user datagram protocol, Explain User Datagram Protocol. UDP(Use...

Explain User Datagram Protocol. UDP(User Datagram Protocol) : User Datagram Protocol uses a connectionless communication paradigm. It is an application using UDP does not re

What is associative search, What is associative search? The cost of an ...

What is associative search? The cost of an associative cache is higher that the cost of a direct mapped cache due to the need to search all 128 bit tag patterns to verify wheth

Name the switching schemes used in a digital exchange, Name the switching s...

Name the switching schemes used in a digital exchange? The several switching systems used are:  1. Strowger Switching System 2. Cross bar Switching. 3. Electronic Swit

Which objects are independent transport objects, Which objects are independ...

Which objects are independent transport objects? Domains, Data elements, Tables, Technical settings for tables, Secondary indexes for transparent tables, Structures, Views, Ma

Show the steps of execution of instructions, Q. Show the steps of execution...

Q. Show the steps of execution of instructions? Fetch First Instruction into CPU: Step 1: Find/calculate the address of first instruction in memory. In this machine illust

Highly encoded micro-instructions, Highly Encoded micro-instructions ...

Highly Encoded micro-instructions Encoded bits required in micro-instructions are small. It provided an aggregated view that is a higher view of CPU as just an encoded

Gralands robots, You have been contacted by Jean-Luc Picard commanding offi...

You have been contacted by Jean-Luc Picard commanding officer of Star Trek: The Next Generation. The Commander needs your support to develop a software routine to simulate the Robo

Minimum power dissipation of digital logic family, Which digital logic fami...

Which digital logic family has minimum power dissipation ? Ans. The minimum power dissipation of digital logic family is CMOS. CMOS being an unipolar logic family, occupy a to

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