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Network Administrator calculations with worked answers

Updated 15 September 2026 · 2 min read

Network administration involves less arithmetic than electrical work, but the arithmetic it does need comes up constantly, and it has to be right. A wrong mask can take a whole office offline. Each example below shows the full working, and every figure was recalculated independently before it was published.

How this guide was made

Written for this site with AI assistance, then checked automatically before publishing. The topic table, sample questions, worked examples and study plan are generated from this site’s question bank: each worked example is recalculated by separate code, and each sample answer says where it came from.

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Worked examples

Try each one on paper first. Every figure is generated and then recalculated by separate code before it is published.

  1. Subnet details for a /27 address

    A host is configured as 10.200.34.172/27. Find the subnet mask, network address, broadcast address, usable host range and number of usable hosts.

    Show the working
    1. /27 means 27 network bits, so the mask is 255.255.255.224.
    2. The interesting octet is the fourth, where the mask is 224. Block size = 256 − 224 = 32.
    3. The network address is the multiple of 32 at or below the address in that octet: 10.200.34.160.
    4. The broadcast is one below the next network: 10.200.34.191.
    5. Usable hosts run from 10.200.34.161 to 10.200.34.190: 2^5 − 2 = 30 addresses.

    Answer: Mask 255.255.255.224, network 10.200.34.160, broadcast 10.200.34.191, hosts 10.200.34.161–10.200.34.190 (30 usable)

  2. Choosing the smallest subnet that fits

    A department needs 60 usable IPv4 host addresses on one subnet. What is the longest prefix (smallest subnet) that fits, and how many usable addresses does it give?

    Show the working
    1. Usable hosts = 2^(host bits) − 2, because the network and broadcast addresses cannot be assigned.
    2. Find the fewest host bits h where 2^h − 2 ≥ 60: h = 6 gives 62, while h = 5 gives only 30.
    3. Prefix = 32 − 6 = /26.

    Answer: /26, giving 62 usable addresses

  3. Converting an octet from binary to decimal

    Convert the binary octet 10110110 to decimal.

    Show the working
    1. Write the place values under each bit: 128 64 32 16 8 4 2 1.
    2. Add the place values where the bit is 1: 128 + 32 + 16 + 4 + 2
    3. = 182

    Answer: 182

  4. How long a file takes to transfer

    How long does a 1.5 GB file take to copy over a 100 Mbps link? Use decimal units (1 GB = 1,000 MB) and ignore protocol overhead.

    Show the working
    1. Storage is sized in bytes, link speed in bits. Multiply megabytes by 8 to get megabits.
    2. 1500 MB × 8 = 12000 Mb
    3. Time = 12000 Mb ÷ 100 Mbps = 120 s ≈ 2 minutes
    4. Real transfers take longer: TCP/IP headers, retransmissions and disk speed all eat into the link rate.

    Answer: 2 minutes

  5. Subnet details for a /30 address

    A host is configured as 10.102.92.27/30. Find the subnet mask, network address, broadcast address, usable host range and number of usable hosts.

    Show the working
    1. /30 means 30 network bits, so the mask is 255.255.255.252.
    2. The interesting octet is the fourth, where the mask is 252. Block size = 256 − 252 = 4.
    3. The network address is the multiple of 4 at or below the address in that octet: 10.102.92.24.
    4. The broadcast is one below the next network: 10.102.92.27.
    5. Usable hosts run from 10.102.92.25 to 10.102.92.26: 2^2 − 2 = 2 addresses.

    Answer: Mask 255.255.255.252, network 10.102.92.24, broadcast 10.102.92.27, hosts 10.102.92.25–10.102.92.26 (2 usable)

  6. Choosing the smallest subnet that fits

    A department needs 250 usable IPv4 host addresses on one subnet. What is the longest prefix (smallest subnet) that fits, and how many usable addresses does it give?

    Show the working
    1. Usable hosts = 2^(host bits) − 2, because the network and broadcast addresses cannot be assigned.
    2. Find the fewest host bits h where 2^h − 2 ≥ 250: h = 8 gives 254, while h = 7 gives only 126.
    3. Prefix = 32 − 8 = /24.

    Answer: /24, giving 254 usable addresses

  7. Converting an octet from binary to decimal

    Convert the binary octet 01000001 to decimal.

    Show the working
    1. Write the place values under each bit: 128 64 32 16 8 4 2 1.
    2. Add the place values where the bit is 1: 64 + 1
    3. = 65

    Answer: 65

  8. How long a file takes to transfer

    How long does a 4.7 GB file take to copy over a 10 Mbps link? Use decimal units (1 GB = 1,000 MB) and ignore protocol overhead.

    Show the working
    1. Storage is sized in bytes, link speed in bits. Multiply megabytes by 8 to get megabits.
    2. 4700 MB × 8 = 37600 Mb
    3. Time = 37600 Mb ÷ 10 Mbps = 3760 s ≈ 1.04 hours
    4. Real transfers take longer: TCP/IP headers, retransmissions and disk speed all eat into the link rate.

    Answer: 1.04 hours

The calculations that matter in this job

Subnetting is the big one: finding the mask for a prefix, the network and broadcast addresses, the usable range, and the smallest subnet that fits a given number of hosts. Binary-to-decimal conversion sits underneath all of it. Transfer-time estimates come up whenever someone asks how long a backup or a software rollout will take over a particular link.

Checking an answer in seconds

A few quick tests catch most slips before they cost marks. A network address is always a multiple of the block size in the interesting octet. A broadcast address is always one less than the next network. Usable host counts are always even, because they come from a power of two minus two. And when a transfer time looks eight times too fast, you have probably forgotten that link speeds are in bits while file sizes are in bytes.

Common questions

Do I need a calculator for subnetting questions?

No, and you should not count on being allowed one. The block-size method needs only subtraction and counting in steps, which is exactly why it is worth practising until it is quick.

Why do usable hosts subtract two?

In each IPv4 subnet the first address identifies the network and the last is the broadcast address. Neither can be assigned to a host. Point-to-point /31 links are a special case defined separately.

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