A network technician is configuring a new subnet to accommodate a cluster of 40 usable hos… — CompTIA Network+

A network technician is configuring a new subnet to accommodate a cluster of $40$ usable host interfaces. What is the minimum IPv4 prefix length (in CIDR notation, e.g., $24$ for $/24$ ) required to support this number of hosts?

Answer: 26

Answer

The minimum IPv4 prefix length required is 26.

To support

40

usable hosts, a subnet requires

6

host bits because

2^6 - 2 = 62

usable IP addresses (

2^5 - 2 = 30

is too small). Subtracting

6

host bits from

32

total IPv4 bits results in a prefix length of

26

(or

/26

Step-by-Step Solution

Determine host capacity requirement

Need a subnet that provides at least

40

usable host IP addresses.

Each subnet reserves two IP addresses: one for the network ID and one for the broadcast address.

Find host bits needed

6

host bits are required (

2^6 - 2 = 62

usable hosts).

5

host bits only yield

30

usable addresses, which fails the requirement of

40

hosts.

Compute CIDR prefix length

32 - 6 = 26

An IPv4 address consists of

32

total bits; subtracting the host bits gives the network prefix bits.

Key Concept

Host capacity formula and CIDR prefix length calculation

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