Redundancy - Formula to calculate Redundancy Bits

What is Redundancy?

Redundancy means provision of more than one resource to perform a task or a function. In the context of your lecture it means that you can ensure the security through redundancy. For example, if you are using multiple computers to accomplish a big task then in case of failure of any hardware and software, you will have the option of getting the piece of hardware or software from those computers which are working on those task.

What is the formula to calculate the number of redundancy bits required to correct a bit error in a given number of data bits?

Messages(frames) consist of m data (message) bits, yielding an n=(m+r)-bit codeword.

2^r>t+n
r = number of redundancy bits
t = number of errors
n = codeword length

Hamming code-Redundancy bit

Hamming code error correction example

Redundancy Bits (r)

r must be able to indicate at least m+r+1 states 

m+r+1 states must be discoverable by r bits 

Therefore, 2r ≥ m+r+1
If m=7, r=4 
as 24 ≥ 7+4+1