# Solving equations via substitution

1. Apr 13, 2012

### jackscholar

I am trying to solve an equation that involves substitution.

I was given k= 7 in the equation n=k+c
i was also given n=2^c-1
I figured that 7+c could be substituted into the equation as n, so I got
7+c=2^c-1 and therefore c=2^c-8.
The problem is that the answer I want is c=4...but substituting 4 as C does not give me a correct answer. Any help would be greatly appreciated.
Thank you

2. Apr 13, 2012

### Stephen Tashi

Maybe the probem should say n = k + 2c

3. Apr 13, 2012

### jackscholar

This pertains to hamming codes, so n is the total number of bits, k is the amount of information digits and c is the amount of check digits. I was given another example aswell. This example says: Suppose there are four information digits.
Then n=4+c
and n=2^c-1
then 4+c=2^c-1
hence c=2^c-5

4. Apr 14, 2012

### Stephen Tashi

The inequation I see on the web for hamming codes is $n \le 2^c -1$