Software-Engineering
December 12, 2023Question 13197 – Probability-and-statistics
December 12, 2023Question 2073 – Nielit Scientific Assistance CS 15-10-2017
If the original size of data is 40 then after adding error detection redundancy bit the size of data length is
Correct Answer: C
Question 17 Explanation:
→ Imagine that we want to design a code with m message bits and r check bits that will allow all single errors to be corrected.
→ Each of the 2 m legal messages has n illegal codewords at a distance of 11 from it.
→ These are formed by systematically inverting each of the n bits in the n-bit codeword formed from it. Thus, each of the 2 m legal messages requires n+1 bit patterns dedicated to it.
→ Since the total number of bit patterns is 2 n , We must have (n+1)2 m ≤ 2 n .
→ Using n=m+r, this requirement becomes
= (m+r+1) ≤ 2 r
= 40+6+1 ≤ 26
= 47 ≤ 2
r=6
Message size will be 6+40=46
→ Each of the 2 m legal messages has n illegal codewords at a distance of 11 from it.
→ These are formed by systematically inverting each of the n bits in the n-bit codeword formed from it. Thus, each of the 2 m legal messages requires n+1 bit patterns dedicated to it.
→ Since the total number of bit patterns is 2 n , We must have (n+1)2 m ≤ 2 n .
→ Using n=m+r, this requirement becomes
= (m+r+1) ≤ 2 r
= 40+6+1 ≤ 26
= 47 ≤ 2
r=6
Message size will be 6+40=46
26
36
46
56