Question

Suppose we want an error correcting code that will allow all single-bit errors to be corrected for data of length 11. How many check bits are necessary?

Answer 1

In order to correct all single-bit errors in data of length 11, we need 4 check bits.

Step-by-step explanation:

In order to correct all single-bit errors in data of length 11, we need to calculate the number of check bits required. The formula to determine the number of check bits is 2^r ≥ m + r + 1, where r is the number of check bits and m is the number of data bits. Here, m = 11 and we need to find the minimum value of r that satisfies the equation.

Let's substitute the values into the equation: 2^r ≥ 11 + r + 1.

By trial and error, we find that when r = 4, 2^4 = 16 ≥ 11 + 4 + 1. Thus, we need 4 check bits to be able to correct all single-bit errors in data of length 11.