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

A minimum of 4 check bits is required for an error correcting code to correct all single-bit errors in an 11-bit long data sequence.

Step-by-step explanation:

To determine the number of check bits necessary for an error correcting code that corrects all single-bit errors for data of length 11, we can use the Hamming Code formula:

2r ≥ m + r + 1

Here, m represents the number of data bits, and r represents the number of check bits required. For data of length 11 (m=11), we find the smallest value of r that satisfies the inequality.

Let's check for r=4:

24 = 16 ≥ 11 + 4 + 1 = 16 (True)

Therefore, for m = 11, we need at least 4 check bits to correct all single-bit errors.