Shaiq,
This is really only an exercise with numbers in binary.
If you take an octet and write it out in binary, you basically indicate the presence of a particular power of two in that octet, starting with 128 and going down through 64, 32, 16, 8, 4, 2, and ending with 1.
Now notice that in a binary number of the form xxxx-xx00, you are saying:
- There is no power of 2^0 = 1
- There is no power of 2^1 = 2
- There may or may not be the remaining powers:
- 2^2 = 4
- 2^3 = 8 = 2*4
- 2^4 = 16 = 4*4
- 2^5 = 32 = 8*4
- 2^6 = 64 = 16*4
- 2^7 = 128 = 32*4
So any number in the binary form of xxxx-xx00 consists of all possible combinations of 128, 64, 32, 16, 8, or 4 present in its binary representation - note that these powers of two as well as their arbitrary sums are always multiples of four. This is what I said when I indicated that the third octet of a matching address must be an integer multiple of four.
That is also what I said when I suggested that the IP address is of the form 192.168.<4xN>.<anything>. The third octet must be a multiple of four. Of course, no octet can be higher than 255, so the highest N you can have is 63, as 63x4 = 252. Any higher N would cause the third octet to be higher than 255 and that would no longer be a valid IP address.
You can also take it from another point of view if you are slightly fluent with binary arithmetics in computers (if not and all what follows is just gibberish to you, you can ignore it safely). Notice that the binary number in the form of xxxx-xx00 has six bits whose value can be arbitrary (the 'x' bits). If I had these six free bits isolated and wrote them down as a new binary number xx-xxxx, they would yield a value between 0 and 63, inclusive (6 bits give you 2^6=64 different combinations, ranging from 0 to 63). Now, you may know that a bit shift operation to the left is equivalent to multiplying the number by two. So if I bit-shifted the xxxxxx one time to the left, I would get a value of xxx-xxx0 (the former value in the range of 0-63 multiplied by 2), and if I bit-shifted the number to the left again, I would get a value of xxxx-xx00 (the former value in the range of 0-63 twice multiplied by two - that is, four). Hence the N, being nothing else than the xx-xxxx, in the range of 0-63, multiplied by 4 as I indicated in my IP address above.
Feel free to ask further!
Best regards,
Peter
