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5 Answers

Best answer
10 votes
10 votes
I dont know the reason behind this, but I have read from the PDF downloaded from NPTEL Website that for detecting d bit error, we need d+1 bits and for correcting d bit error we need 2d+1 bits

In our example, we have to detect 2 bit errors. So for this 2+1 = 3 bits are required

For correcting 1 bit error 2*1+1=3 bits are required..

So in total 6 bits are required to correct 1 bit error and detect 2 bit error..

 

I will be grateful if anyone can provide explanation behind the formulas 2d+1 and d+1

 

Source : nptel.ac.in/courses/106105080/pdf/M3L2.pdf
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8 votes
8 votes

Answer is a) 5

To calculate the numbers of redundant (check) bits (r) required to correct d data bits.

We have (d+r) as the total number of bits, which are to be transmitted; then r must be able to indicate at least d+r+1 different values. Of these, one value means no error, and remaining d+r values indicate error location of error in each of d+r locations.

So, d+r+1 states must be distinguishable by r bits, and r bits can indicates 2r states. Hence, 2r must be greater than d+r+1. 2r >= d+r+1

The value of r must be determined by putting in the value of d in the relation. 

In the problem it is given that check bits are required for 16 bit data word. So d = 16.

2>= 16 + r + 1. The relation satisfies for r=5.

So we need 5 check bits.

1 votes
1 votes
Option a is answer .

you would have parity bits at the position 1,2,4,8,16  ( assuming my rep start from 0)
1 votes
1 votes

As per the Key Provided by ISRO -2013

Answer is B

There will be parity bits at 1,2,4,8,16 = 5 bits

One bit for error correction 5+1 =6

Correct me if i am wrong.

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