Subnetting question - similar to my last one

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Had this Q in an exam sim;

You are planning the IP address configuration for your network. You plan to use addresses from the private IP address block 172.16.0.0/12.

You want to define a single subnet mask to be used throughout the network. You need to plan for the future growth of the network of up to 500 subnets with at most 2,000 hosts on each subnet.

What subnet mask should you use?

255.255.252.0

255.255.224.0

255.255.248.0

255.255.240.0

I really am having a bit of a mental block with this, could anyone (harry?) offer an alternative explanation??

The answer was given as follows;

You should use the subnet mask 255.255.248.0. This reserves nine bits for the subnet identifier and eleven bits for the host identifier. Nine bits will allow you to define up to 510 subnets. Eleven host bits will allow you to define up to 2046 hosts on each subnet.

 

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Thats pretty much how I did it. I am not very experienced in this sort of question, and there are variable rules about the use of subnets with all 0s and all 1s depending on the exam board.

My first thought was "next highest power of 2 over 2000 is 2048", which implies 11 bits. Then next highest over 500 is 512, which is 9 bits. And 12 (the original mask) + 9 + 11 = 32 - so it fits.

So universal mask is 12 + 9 = 21 bits. Hence 248 in the third byte.

I note in the answer they have the old rule that subnets of all 0s and all 1s can't be used - but fortunately it still works!

Harry.

 

i will also give it a shot.

you have: 172.16.0.0/12
you need: 500 subnets, 2000 hosts

first lets see how many bits we will need for the host portion of the mask.

0 - 2
0 - 4
0 - 8
0 - 16
0 - 32
0 - 64
0 - 128
0 - 256
.
0 - 512
0 - 1024
0 - 2048
--------
2048 - 2 (we minus 2 for the all 1's and all 0's combinations)
= 2046 which will accomodate all the required hosts.

bits used = 11 (that's base ten :P )

so lets look at our subnet mask now.

(h = the bits necessary to support 2000 hosts)
11111111.11110000.00000hhh.hhhhhhhh (/12)

so now we want to create 500 subnets. and we have 9 left-over bits from the host portion. well let's see what we can do with that.

2 to the power of 9 = 512 - 2 = 510 subnets.

so now that we gave the network portion an extra 9 bits, the mask is /21, or 255.255.248.0

so, if i didn't go totally off, you are left with 510 subnets each containing 2046 hosts and a subnet mask of 255.255.248.0

 

Thanks guys.

Thats a good explanation Omni. Thank you.