We have to transfer m message bits, and employ error correction. For that purpose let no of parity bits added be p. Now error can occur in m message bits or p parity bits or no error therefore total
m+p+1 possibilities , one bit error at any m+p places because parity bit can also get corrupted and + 1 if there is no error. so
2^p >=m+p+1
coz after receiving parity bits using those p bits we must be able to identify all these possibilities.
eg
0 0 0 ( no change in p4,p2,p1 after calculating at receiver end) it means no error in data and parity
If its
1 0 1 means error in pos 5 ( p1 covering 1,3,5,7 and p4 covering 4,5,6,7
Both doesnt match means error at pos 5)
Thus with 3 bits u can cover 8 possibilities