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IT Support Technician calculations with worked answers

Updated 15 September 2026 · 2 min read

Support technicians do not spend their days on arithmetic, but a few calculations come up often enough to be worth mastering. Estimating how long a file will take to copy tells a user what to expect. Knowing how much space a storage array provides prevents an awkward surprise. Each example below includes the full working, and every figure was verified by separate code before publication.

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. Converting an octet from decimal to binary

    Convert 24 to an 8-bit binary octet.

    Show the working
    1. Subtract the largest place value that fits, mark a 1, and repeat: 128 64 32 16 8 4 2 1.
    2. 24 = 16 + 8
    3. Mark those places with 1 and the rest with 0: 00011000

    Answer: 00011000

  2. How long a file takes to transfer

    How long does a 700 MB file take to copy over a 50 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. 700 MB × 8 = 5600 Mb
    3. Time = 5600 Mb ÷ 50 Mbps = 112 s ≈ 1.87 minutes
    4. Real transfers take longer: TCP/IP headers, retransmissions and disk speed all eat into the link rate.

    Answer: 1.87 minutes

  3. Usable space in RAID 10

    A server has 8 × 8 TB disks in RAID 10. How much usable capacity is there, and what failure can it survive?

    Show the working
    1. RAID 10 stripes across mirrored pairs, so half the disks count: (n ÷ 2) × size.
    2. Usable = 32 TB
    3. It survives one failure per mirrored pair.

    Answer: 32 TB; survives one failure per mirrored pair

  4. Subnet details for a /29 address

    A host is configured as 192.168.187.241/29. Find the subnet mask, network address, broadcast address, usable host range and number of usable hosts.

    Show the working
    1. /29 means 29 network bits, so the mask is 255.255.255.248.
    2. The interesting octet is the fourth, where the mask is 248. Block size = 256 − 248 = 8.
    3. The network address is the multiple of 8 at or below the address in that octet: 192.168.187.240.
    4. The broadcast is one below the next network: 192.168.187.247.
    5. Usable hosts run from 192.168.187.241 to 192.168.187.246: 2^3 − 2 = 6 addresses.

    Answer: Mask 255.255.255.248, network 192.168.187.240, broadcast 192.168.187.247, hosts 192.168.187.241–192.168.187.246 (6 usable)

  5. Converting an octet from decimal to binary

    Convert 2 to an 8-bit binary octet.

    Show the working
    1. Subtract the largest place value that fits, mark a 1, and repeat: 128 64 32 16 8 4 2 1.
    2. 2 = 2
    3. Mark those places with 1 and the rest with 0: 00000010

    Answer: 00000010

  6. 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

  7. Usable space in RAID 10

    A server has 8 × 2 TB disks in RAID 10. How much usable capacity is there, and what failure can it survive?

    Show the working
    1. RAID 10 stripes across mirrored pairs, so half the disks count: (n ÷ 2) × size.
    2. Usable = 8 TB
    3. It survives one failure per mirrored pair.

    Answer: 8 TB; survives one failure per mirrored pair

  8. Subnet details for a /25 address

    A host is configured as 172.20.223.49/25. Find the subnet mask, network address, broadcast address, usable host range and number of usable hosts.

    Show the working
    1. /25 means 25 network bits, so the mask is 255.255.255.128.
    2. The interesting octet is the fourth, where the mask is 128. Block size = 256 − 128 = 128.
    3. The network address is the multiple of 128 at or below the address in that octet: 172.20.223.0.
    4. The broadcast is one below the next network: 172.20.223.127.
    5. Usable hosts run from 172.20.223.1 to 172.20.223.126: 2^7 − 2 = 126 addresses.

    Answer: Mask 255.255.255.128, network 172.20.223.0, broadcast 172.20.223.127, hosts 172.20.223.1–172.20.223.126 (126 usable)

Calculations that come up in support work

Binary and decimal conversion underpins IP addresses and subnet masks, which technicians configure whenever automatic addressing is not available. Transfer time turns file sizes and connection speeds into a realistic wait, which helps when a user asks how long a backup or migration will take. RAID capacity matters when setting up a file server or network storage in a small office. Subnet details confirm whether a device's address, mask and gateway belong together.

Explaining the answer to a user

The number is only half the job. A user who hears that a transfer will take "about 20 minutes on the office cable connection, longer on Wi-Fi" can plan around it. Round sensibly, give a range when conditions vary, and avoid terms such as megabits unless the user asks for detail.

Common questions

Why does a file take longer to copy than the calculation says?

The calculation assumes the full link speed is available. Other traffic on the network, wireless interference, slow disks and protocol overhead all reduce the real speed.

How do I tell if two devices are on the same subnet?

Apply the subnet mask to both addresses. If the network portions match, the devices are on the same subnet and can reach each other without a router.

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