Example on hamming error correcting code, Computer Engineering

Assignment Help:

Q. Example on hamming error correcting code?

For illustration a 4-bit matching word can stand for 24=16 values that range from 0 to 15 as:

0000, 0001, 0010, 0011, 0100, 0101, 0110, 0111

1000, 1001, 1010, 1011, 1100, 1101, 1110, 1111

Value 0000 or 0 represent no error while other values that are 2i-1 (for 4 bits 24- 1=15 which is from 1 to 15) signify an error condition. Every one of these 2i - 1(or 15 for 4 bits) values can be used to signify an error of an individual bit. Because error can take place at the time of transmission of 'N' bit data and 'i' bit error correction code hence we need to have as a minimum 'N+i' error values to signify them. Thus number of error correction bits must be found from subsequent equation:

2i - 1     >= N+i

If we are presuming 8-bit word then we need to have

2i - 1     >= 8+i

Say at

i=3                     LHS = 23 -1 = 7; RHS = 8+3 = 11 

           i=4                      2i-1 = 24 - 1 = 15; RHS = 8+4 = 12  

Thus for an eight-bit word we need to have as a minimum four-bit error correction code for detecting and correcting errors in a single bit at the time of transmission.

In the same way for 16 bit word we require i = 5

25 -1 = 31 and 16+i = 16+5 = 21

For 16-bit word we require five error correcting bits.

Let's explain this with help of an illustration:

Let's presume 4 bit data as 1010

The logic is displayed in subsequent table:

Source:

This complete information that is (data and P1

1665_Example on hamming error correcting code.png

to P4) is transmitted.  

Presuming one bit error in data.

1140_Example on hamming error correcting code1.png

So  P1  - D1, P3 - D3, P4  -D4 pair are different so, as per Figure b1 is in error, so correct it by completing b1 to get correct data 1010.

Case 2:   Data Received as 1000  (Error in b2)

So   P1 - D1, P2 - D2,   P4 - D4 pair are different so as per figure bit b2 is in error.  So correct it by complementing it to get correct data 1010.

727_Example on hamming error correcting code2.png

Case 3:  

Now let's take a case when data received is correct however on receipt one of parity bit let's say P4 become 0.  Please note in this matter because data is 1010 destination parity bits would be D1=0, D2=1, D3=0, D4=1.  So P1- D1, P2 - D2, P3 - D3 would be same however P4 -D4 are different. This doesn't belong to any of combinations in Figure above. So we conclude P4 received is wrong.


Related Discussions:- Example on hamming error correcting code

Describe the fundamental characteristics of antennas, Question 1: (a) ...

Question 1: (a) Describe the two fundamental characteristics of antennas explaining in detail how it affects the security of wireless networks. (b) What is a wireless cli

Java, mine sweeper algorithm.

mine sweeper algorithm.

Explain the term - instruction execution, Explain the term - Instruction ex...

Explain the term - Instruction execution We  know  that  the  fundamental  function  performed  by  a  computer  is  the  execution  of  program. The program that is to be exec

.., 1mechanism of artificial satellite

1mechanism of artificial satellite

Seven segment decoder, A design for the seven segment decoder is required. ...

A design for the seven segment decoder is required. The decoder has four inputs which represent a number from 0 to 9 in binary and seven outputs which are connected to the seven

Biological motivation - two layer artificial neural networks, Biological Mo...

Biological Motivation : However remember there that in discussion first lecture is about how people have answered the question like: "How are we going to get an agent to proce

Explain organisations use in electronic data interchange, Explain about the...

Explain about the organisations use in EDI. Organisations, which are use Electronic Data Interchange. Extensive users of Electronic Data Interchange (EDI) include: BHS:

In 8085 which is called as high order / low order register, Flag is known a...

Flag is known as Low order register & Accumulator is known as High order Register.

Inter suffer buffer and execute an instruction, What are the basic steps ne...

What are the basic steps needed to execute an instruction by the processor? Ans: The basic steps needed to execute an instruction by the processor are: A)    First fetch th

Name some pure object oriented languages, Some pure object oriented languag...

Some pure object oriented languages are Smalltalk, Eiffel,  Java, Sather.

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