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Difficulty: EasyIPv4 Addressing and Subnetting

A network administrator assigns the IPv4 subnet mask 255.255.255.224255.255.255.224 to a VLAN interface on a Cisco switch. What is the maximum number of usable host IPv4 addresses that can be assigned to end devices in this subnet?

Answer: 30 addresses

Answer

The maximum number of usable host IPv4 addresses is 30.
A subnet mask of 255.255.255.224255.255.255.224 corresponds to a CIDR prefix of /27, leaving 5 bits for host addressing. Using the formula 2n−22^n - 2 (where n=5n = 5), the calculation yields 25−2=32−2=302^5 - 2 = 32 - 2 = 30 usable host IP addresses.

Step-by-Step Solution

1
Determine the number of host bits (nn) available in the 255.255.255.224255.255.255.224 subnet mask.
The mask has 27 network bits and 5 host bits (32−27=532 - 27 = 5).
The last octet value 224224 in binary is 11100000211100000_2, meaning 3 bits belong to the network/subnet portion and 5 bits belong to the host portion.
2
Calculate the number of usable host IP addresses using the formula 2n−22^n - 2.
25−2=32−2=302^5 - 2 = 32 - 2 = 30 usable host addresses.
The formula 2n−22^n - 2 accounts for the total IP addresses (2n2^n) minus the reserved network identifier (all host bits set to 0) and the broadcast address (all host bits set to 1).

Key Concept

Usable Host Address Calculation
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Topics

IPv4 Addressing and Subnetting

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