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

Fetching a word from memory - computer architecture, Fetching a word from m...

Fetching a word from memory: CPU transfers the address of the needed information word to the memory address register (MAR). Address of the needed word is transferred to the pr

Embedded system design using c, W To date we have discussed elementary high...

W To date we have discussed elementary high level language programming and low level assembler programming, one of the benefits of C is the integration of both , this requires a re

What are the general security issues, What are the General Security Issues ...

What are the General Security Issues Many issues exist when linking a computer system to the Internet or indeed to an external link via a network set up. There are numerous way

Compare hypertext versus hypermedia, Compare hypertext versus hypermedia.  ...

Compare hypertext versus hypermedia.  Hypertext is basically similar as regular text - it can be stored, read, searched, or edited - with a significant except ion: hyper text h

Difference between latches and flip-flops based designs, What is the differ...

What is the difference between latches and flip-flops based designs Latches are level sensitive whether flip-flops are edge sensitive. So, latch based design and flop based des

Short notes on displacement only addressing mode, (a) Write short notes on...

(a) Write short notes on displacement only addressing mode. (b) Explain the formats of a 80-bit floating point number. (c) Given the following assembly program. Instructi

Different types of layers in tcp/ip protocol stack, What are the different ...

What are the different types of layers in TCP/IP protocol stack? Layers into the TCP/IP protocol architecture are as given below: • Application Layer, • Host-to-Host Tra

What is an xml entity, Problem : (a) Show whether or not a standard for...

Problem : (a) Show whether or not a standard format for representing data, such as XML, is needed. (b) Using an appropriate example, describe how data is organized in a dat

Find 9''s complement for decimal number, Q. Find 9's complement for decimal...

Q. Find 9's complement for decimal number? The 9's complement is achieved by subtracting every digit of number from 9 (the highest digit value). Let's assume that we want to si

Meaning of every field in mips instruction, Q. Meaning of every field in MI...

Q. Meaning of every field in MIPS instruction? The meaning of every field in MIPS instruction is given below: op: operation code or opcode rs: First register source

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