# Hamming Distance, Bit message [closed]

My professor told us to try and remember the equation used for an upcoming exam, however I'm struggling to fit the equation into the question:

http://i.stack.imgur.com/RoPYG.png (need a high reputation to post image)

From the above information can anyone tell me how I'm supposed to slot in values in order to work out the following practise question:

Sixteen-bit messages are transmitted using a Hamming code. How many check bits are needed to ensure that receiver can detect and correct single-bit errors?

Answer given to us is "5 check bits for a total of 21 bits".

Can anyone help me out with this please, as I expect it will come up on the exam, bu with another bit message size.

• 1. Please use Latex to transcript mathematics, and don't forget to cite your sources. Questions should be self-contained; people shouldn't have to visit external sites to understand the question. 2. What have you tried? Where did you get stuck? We want to help you understand the materials, not just solve your exercise for you (which wouldn't help you or anyone else). – D.W. May 25 '15 at 4:54

## 1 Answer

The professor is asking you to find the lowest r such that the equation is true. At $r=1$, $2^1<17+1$,
$r=2$, $2^2=4<17+2=19$...
$r=4$, $2^4=16<17+4=21$
and finally $r=5$, $2^5=32\geq17+5=22$.