Can you identify how many hosts can fit on a subnet given the CIDR notation?

For example, can you answer this question that essentially asks “how many hosts?”

Bart is designing a network segment that only needs 24 IP addresses assigned. He needs to conserve the IP address space. What CIDR notation is the BEST choice for this network?

A. /25

B. /26

C. /27

D. /28

Answer below.

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## Looking at a Classful Range

Consider a classful IP range of 192.168.1.0/24. It supports 254 usable IP addresses in the range of 192.168.1.1 through 192.168.1.254.

Note that two IP addresses cannot be assigned to any host:

- 192.168.1.0 is the network ID.
- 192.168.1.255 is the broadcast address for the network.

## Using the Formula to Determine How Many Hosts

The formula for determining the number of hosts a network supports is 2^{n}-2, where n is the number of bits used for the host.

- 2
^{n}-2 is sometimes expressed as (2^n) – 2. Both indicate 2 raised to the power of n. - You subtract two to reserve one IP for the network ID and one for the broadcast address.

Consider the classful IP range of 192.168.1.0/24. The /24 is Classless Inter-Domain Routing (CIDR) notation indicating that 24 bits are used for the subnet mask. An IPv4 address includes a total of 32 bits. With 24 bits used for the subnet mask, that leaves 8 bits for the hosts (32-24).

If you plug 8 into the formula, it is (2^8) – 2. 2^8 is 256 and 256 – 2 is 254.

## Using a Calculator

Most calculators include a power formula, often listed as x^{y}. The following graphic shows the Windows 10 built-in calculator in Scientific mode.

To calculate (2^8) – 2, press the keys in the following sequence.

- 2
- x
^{y} - 8
- –
- 2

## Calculating Hosts in Subnets

The preceding sections focused on a classful range of IP addresses. However, you can use the same formula to determine how many hosts a subnet supports. For example, how many hosts can you fit on this network: 192.168.1.0/28?

Remember that the formula for determining the number of hosts a network supports is 2^{n}-2, where n is the number of bits used for the host. The /28 is CIDR notation indicating that 28 bits are used for the subnet mask. An IPv4 address includes a total of 32 bits. With 28 bits used for the subnet mask, that leaves 4 bits for the hosts (32-28).

If you plug 4 into the formula, it is 2^4 – 2. 2^4 is 16 and 16 – 2 is 14.

- 2
^{n}-2 is sometimes expressed as 2^n – 2. Both indicate 2 raised to the power of n. - You subtract two to reserve one IP for the network ID and one for the broadcast address.

You can use this method for any IP address with a CIDR notation of /25 or greater.

## Can You Use a Calculator to Determine How Many Hosts?

You cannot take a calculator into the exam room. However, some exams provide access to a simple calculator. Some don’t.

With this in mind, you should be able to recreate the following table from memory. This ensures you can identify the value of 2^{n}-2

CIDR | # of Bits for Hosts | Max Hosts 2 ^{n}-2 |
---|---|---|

/24 | 8 | 254 |

/25 | 7 | 126 |

/26 | 6 | 62 |

/27 | 5 | 30 |

/28 | 4 | 14 |

/29 | 3 | 6 |

/30 | 2 | 2 |

## How Many Hosts Answer

Bart is designing a network segment that only needs 24 IP addresses assigned. He needs to conserve the IP address space. What CIDR notation is the BEST choice for this network?

A. /25

B. /26

C. /27

D. /28

Answer: **C** is correct. The /27 Classless Inter-Domain Routing (CIDR) notation is the best choice. It indicates a subnet mask of 255.255.255.224, which supports 30 IP addresses and is the best choice to conserve IP address space.

The formula to determine how many hosts can operate on a network is 2^{n}-2, where n is the number of 0 bits in the subnet mask.

A subnet mask has 32 bits. If the CIDR notation is /27 it indicates that there are 5 bits left to create subnets. Using the 2^{n}-2 formula, or 2^{5} – 2, or 32 – 2, you see the answer is 30. This is how many hosts you can have on the network.

A is incorrect. A /25 CIDR notation indicates 7 bits are left for hosts (32 – 25 = 7). Using the 2^{n}-2 formula, or 2^{7} – 2, or 128 – 2, you see the answer is 126. In other words, /25 supports 126 hosts. This is much more than the 24 needed and wastes IP addresses.

B is incorrect. A /26 CIDR notation indicates 6 bits are left for hosts (32 – 26 = 6). Using the 2^{n}-2 formula, or 2^{6} – 2, or 64 – 2, you see the answer is 62. In other words, /26 supports 62 hosts. This is much more than the 24 needed and wastes IP addresses.

D is incorrect. A /28 CIDR notation indicates 4 bits are left for hosts (32 – 28 = 4). Using the 2^{n}-2 formula, or 2^{4} – 2, or 16 – 2, you see the answer is 14. In other words, /28 supports 14 hosts, which isn’t enough to meet the need of 24 addresses in the question.

Thanks a lot. But where did you get

[ Consider a classful IP range of 192.168.1.0/24. It supports 254 usable IP addresses in the range of 192.168.1.1 through 192.168.1.254. ]

from?

Can such a question that takes that long to answer appear on the exam?

Thanks

Those two sentences aren’t a question. Instead, they are part of the explanation of how to determine how many hosts are supported in a subnet when given the subnet mask (or CIDR notation).

Very good explanation.thanks.