Determining the Host Capacity of a n Network
To determine the host capacity of a network whose subnet mask is expressed in slash notation as /n, use the following formula: c = 2(32_n) - 2, where c represents the number of computers that can be accommodated by a given network, and n represents the number of bits in the network ID of that network.
For example, in a /20 network, n = 20. Therefore c= 2(32-20) - 2, or 212 - 2, or 4096 - 2, or 4094. So, a /20 network can accommodate 4094 computers.
Here is another example: In a /28 network, n = 28. Therefore, c=2(32-28) - 2, or 24 - 2, or 16 - 2, or 14. So, a /28 network can accommodate 14 computers.
This formula might look somewhat complicated, but if you have memorized your powers of 2, you should actually be able to perform the calculation in your head.
If you are not able to perform this calculation in your head, the problem might be that you are averse to mathematical formulas. In this case, use the following step-by-step instructions:
1. Take the value after the slash (n) and subtract it from 32. (This determines the value h or number of bits in the host ID. For example, in a /21 network, subtract 21 from 32 to obtain an h value of 11.)
2. Raise 2 to this power (h). (This yields a value p. You should have this value memorized. Following our example, you would raise 2 to the 11th power to obtain the value 2048.)
3. Subtract 2 (from p). (In our example, you would subtract 2 from 2048 to get 2046.)
That's it! In our example, we have determined that a /21 network can accommodate 2046 hosts.
Important Because the lowest and highest addresses in a subnet's address range cannot be assigned to computers, the host capacity of a subnet's address range is always two fewer than the actual number of addresses in that range.
Tip Because you know that a /24 network contains 256 addresses, you can easily determine in your head the host capacity for networks whose size is close to /24. The key to this method is the fact that every increment downwards of 1 in the slash notation doubles the size of a network, and every increment upwards halves it. For example, to determine the number of addresses in a /23 network, simply double the size of a /24 network (256) to obtain 512. To determine the number of addresses in a /22 network, double again to obtain 1024. To work the other way, a /25 network must have one-half of the 256 addresses in a /24 network (128), and a /26 network must have half of that (64). Don't forget that this doubling and halving only yields the number of addresses in a network. To then determine the host capacity of a given network, you must subtract 2.
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