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.
2r >= 16 + r + 1. The relation satisfies for r=5.
So we need 5 check bits.