What is the smallest subnet mask that can support 719 hosts?

What is the smallest subnet mask that can support 719 hosts?
The answer is 255.255.252.0

can anyone here please explain to me how to get to this answer? I know that the number of host is= (2 to the power of the number of host bits-2) but I dont know how to reverse the operation.

Thank you,

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Comments

jeremylz

The max number of hosts for a common network 255.255.255.0 or /24 is 254 (256 -2 for the all zero and all 1 addresses, in this case x.x.x.11111111 and x.x.x.00000000 where the x's are 8 1's)

The max number of hosts for a /23 (255.255.254.0) network is 510 (512-2)

The max number of hosts for a /22 (255.255.252.0) network is 1022 (1024-2)

With this information, you need to just pick the smallest (highest / number) that has more hosts than is needed, which would be the /22 in this case

dlx509

Thank you sir!
I see what you did there lol.
so the max # of host for a /24 is 254
/23 is 510
/22 is 1022
/21 is 2046
and so on.......
but I was wondering is there a formula for it? or is this one more thing I need to memorize?

So the logic behind this is: to round the # of host to the next block ( ie 256,512, etc...) then use /24 as a starting point to move left or right depending on the number of host needed.

pamccabe

Try to memorize the powers of 2. In Jeremy's example, there are 24 network bits which leaves 8 host bits. 2 to the power of 8 is 256. However, you need to reserve two addresses. One for the subnet ID and the other is the broadcast address. So 256-2 is 254. If you had a /20 mask, that would leave 12 bits for hosts. 2 to the 12th power would be 4096, subtract two because we have a subnet ID and broadcast address that do not get assigned to hosts. That means 4094 hosts possible. memorizing the powers of two will make your subnetting go faster.

amclone

Check out the CBTNugget subnetting section on either the ICND1 or ICND2 videos. That is how I learned how to subnet. Jeremy breaks it down and makes it easy.

mella060

dlx509 wrote: »

but I was wondering is there a formula for it? or is this one more thing I need to memorize?

Yep there sure is. The hosts formula is 2^n-2 where n is the number of host bits or 0's.

So if you need 719 hosts on a subnet then you apply the formula to find the minimum number of host bits you require.

8 host bits 255.255.255.0... 2^8-2 = 256-2 = 254 not enough
9 host bits 255.255.254.0... 2^9-2 = 512-2 = 510 not enough
10 host bits 255.255.252.0... 2^10-2 = 1024-2 = 1022 hosts which is plenty

So basically you need to know your network (2^n) and host (2^n-2) formulas and your powers of 2.

Hatch1921

So the logic behind this is: to round the # of host to the next block ( ie 256,512, etc...) then use /24 as a starting point to move left or right depending on the number of host needed.

Yes... I use this method as well... my baseline numbers are /23 and /27 and when you have a particular starting point memorized, you can quickly determine which direction you need to work in. As soon as you asked for 700+ hosts.... I went to /23 for 512 host (510 usable) and just worked left of the scale and doubled it to a /22 or 1024 (1022) hosts.

Good info all around in this thread.

Hatch