A network administrator needs to carve out a new subnetwork from the 172.16.64.0/22 enterp… — Cisco CCNA

A network administrator needs to carve out a new subnetwork from the $172.16.64.0/22$ enterprise address block for a remote branch office. The branch requires static IPv4 addresses for $26$ workstation PCs, $2$ IP phones, and $2$ network printers. Which IPv4 network address and prefix length combination provides the most efficient assignment to accommodate all required host addresses without wasting address space?

A
$172.16.64.0/28$
$172.16.64.0/27$ Answer
C
$172.16.64.0/26$
D
$172.32.64.0/27$

Answer

The most efficient subnet assignment is

172.16.64.0/27

because it provides exactly 30 usable IPv4 addresses within the valid RFC 1918 private block.

The required endpoint count is 30 hosts (

26 + 2 + 2 = 30

). To accommodate 30 usable hosts, 5 host bits are needed (

2^5 - 2 = 30

). Subtracting 5 host bits from 32 IPv4 total bits leaves a /27 prefix. Subnetwork

172.16.64.0/27

resides within the allocated

172.16.64.0/22

block and RFC 1918 private space, fulfilling all requirements with zero wasted IP addresses.

Step-by-Step Solution

Calculate the total host IP address requirement

Total endpoints =

26 \text{ PCs} + 2 \text{ phones} + 2 \text{ printers} = 30 \text{ usable IP addresses}

All active physical and virtual endpoints require individual host IPv4 addresses on the subnetwork.

Determine the host bit requirement (

h

)

Using

2^h - 2 \ge 30

, solving for

h

yields

h = 5

host bits (

2^5 - 2 = 30

Two IP addresses per subnet are unassignable to hosts: the network address (all host bits set to 0) and the subnet broadcast address (all host bits set to 1).

Calculate the subnet prefix length

Prefix length =

32 - 5 = /27

Subtracting the 5 host bits from the 32 total bits in an IPv4 address defines the 27 network prefix bits.

Verify address space validity and boundaries

Subnetwork

172.16.64.0/27

falls within the

172.16.64.0/22

parent block and belongs to the RFC 1918 private Class B range (

172.16.0.0 - 172.31.255.255

Internal enterprise subnets must utilize allocated private address space.

Key Concept

IPv4 Subnet Sizing and Usable Host Calculation

Question

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Key Concept

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