Explain about hamming error correcting code, Computer Engineering

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.

Posted Date: 7/17/2013 6:58:56 AM | Location : United States







Related Discussions:- Explain about hamming error correcting code, Assignment Help, Ask Question on Explain about hamming error correcting code, Get Answer, Expert's Help, Explain about hamming error correcting code Discussions

Write discussion on Explain about hamming error correcting code
Your posts are moderated
Related Questions
When investing money, an important concept to know is compound interest. The equation FV = PV (1+rate)periods . This relates the following four quantities. The present value (PV)

Q. Show the properties of Text Box? The tag is used to specify where user input is expected. It has several attributes, of which TYPE attribute is used to specify th

Describe the advantage of using Booth algorithm? Ans:  a) It achieves efficiency in the number of additions needed when the multiplier has a few large blocks of 1's. b) It

Give your analysis for the following problem statement: You require to write a program that calculates the area and perimeter of a rectangle whose dimensions (Length &width) are gi

State the implementation of a security policy The implementation of a security policy should invariably cover all parameters of security such as physical access to the server,

Serial Execution Execution of a program consecutively, one statement at a time. In the easiest sense, this is what occurs on a one processor machine. However, even many of the

Q. Characteristics of Magnetic disk? Tracks and Sectors: Disk is divided in concentric rings known as tracks. Thus a track is one complete rotation of disk underneath read/wr

What are the techniques of Data Collection It can be either automatic or manual. Manual techniques can include: -  Keypads/Keyboards to type in data -  touch screens to s

Subtraction of 01100-00011 using 2's complement method Ans. Firstly 1's complement of 00011 is 11100 and 2's complement is 11100 + 1 = 11101. Thus If a last carry is

? Nodes: A node shows any hardware component. The configuration of hardware is shown by attributes of nodes. ? Components: A component shows software. Every component straight