a particularly annoying subnetting question

usgrant

I was grinding away on Subnettingquestions.com like a champ, and then i got this one:

Question: How many subnets and hosts per subnet can you get from the network 172.23.0.0/23?
Answer: 128 subnets and 510 hosts

I cant even begin to follow the math on this one. I would really appreciate anyone helping me on this one. I gound away at this one for an hour!

IRONMONKUS

So, you are given an IP and a subnet mask of 172.23.0.0/23

The easiest way that I do it is I break it down like this.

1. To find how many subnets, you need to know the difference between classful and classless. The classful ranges are A = 1-126 with a subnet mask of /8 (127 is in here, but it's loopback), B = 128-191 with a subnet mask of /16, and a C = 192-223 with a subnet mask of /24. They have given you a classless, so find the difference. Well, 172 is in a Class B range, so the difference of /23 and /16 is 7.

- So, I set up my decimal to binary chart of 128 64 32 16 8 4 2 1, I guess it's a per bit representation of an octet. Don't qoute me... Anyway count over from right to left starting at 2 (because binary is multiples of 2) 7 times and you get 128. So you have 128 subnets. If you're good at math, you can do the 2 to the nth, nth being 7. I just like the graph.

2. For how many hosts, you use the leftover bits. You know there is 32 bits. So, the difference of /32 and the given /23 is 9.

- This time, your chart needs to be bigger. Binary is multiples of 2, so just go out two more times
512 256 128 64 32 16 8 4 2 1. Count over 9 times from right to left, starting at 2 and you get 512. Remember that for hosts, the math is 2 to the nth - 2. nth being 9. Minus 2, because you have a network IP and a broadcast IP. So 512 - 2 = 510.

I hope this helped and actually didn't confuse you even further...