A network administrator is designing a dedicated VLAN for a warehouse automation system th… — CompTIA Network+

A network administrator is designing a dedicated VLAN for a warehouse automation system that requires static IPv4 addresses for $15$ smart sensor nodes. To conserve network address space, the administrator must select the smallest possible CIDR subnet prefix that accommodates all required host nodes. Which prefix length should be configured for this subnet?

/27Answer
B
/28
C
/26
D
/29

Answer

The prefix /27 is the correct choice because it provides 30 usable host IP addresses, satisfying the 15-node requirement while minimizing wasted address space.

To calculate usable IPv4 addresses, the formula

2^n - 2

must be used, where

n

is the number of host bits. For

15

devices, a /28 mask provides

2^4 = 16

total addresses, but only

16 - 2 = 14

usable host addresses, which is insufficient. Moving to a /27 mask provides

n = 5

host bits, yielding

2^5 - 2 = 30

usable host addresses. This is the smallest prefix length that satisfies the requirement of 15 hosts.

Step-by-Step Solution

Determine host bits required using the formula

2^n - 2 \ge \text{required hosts}

For 15 hosts:

2^n - 2 \ge 15 \implies 2^n \ge 17

. The smallest integer

n

satisfying this is

n = 5

host bits (

2^5 = 32

Two IP addresses in every standard IPv4 subnet are reserved for the Network ID (all host bits 0) and Broadcast address (all host bits 1).

Calculate the CIDR prefix length from the host bits

Prefix length

= 32 - 5 = 27

(written as /27).

An IPv4 address consists of 32 bits total. Subtracting host bits yields network prefix bits.

Verify usable host count for /27

2^5 - 2 = 30

usable addresses. Since

30 \ge 15

, /27 is the smallest valid subnet mask.

A /28 prefix only yields

2^4 - 2 = 14

usable host addresses, failing to support 15 nodes.

Key Concept

Subnet Usable Host Calculation

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