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Difficulty: MediumIPv4 Addressing and Subnetting

A network engineer is configuring subnets within the 10.50.0.0/1610.50.0.0/16 address space for a new office building. Each subnet must support a minimum of 150150 usable host IP addresses. What is the maximum number of equal-sized subnets that can be created from this block while meeting the host requirement?

Answer: 256 subnets

Answer

The maximum number of equal-sized subnets that can be created is 256.
To support at least 150 host devices, 8 host bits are necessary (28−2=2542^8 - 2 = 254 usable hosts). Subtracting 8 host bits from 32 total address bits yields a /24 subnet mask. Borrowing 8 bits from the original /16 network prefix produces 28=2562^8 = 256 subnets.

Step-by-Step Solution

1
Determine the number of host bits (hh) required for each subnet to accommodate at least 150 usable host IP addresses.
8 host bits are required because 28−2=2542^8 - 2 = 254 usable host addresses (7 host bits only yield 27−2=1262^7 - 2 = 126 usable host addresses).
Two IP addresses per subnet are reserved for the network ID and broadcast address.
2
Calculate the prefix length required for the new subnets.
Prefix length /24/24 (32 total bits−8 host bits=2432 \text{ total bits} - 8 \text{ host bits} = 24).
IPv4 addresses consist of 32 bits divided between network/subnet and host portions.
3
Determine the number of subnet bits borrowed from the original /16 network mask.
8 bits borrowed (24−16=824 - 16 = 8).
Subtracting the original network prefix length from the new subnet prefix length gives the borrowed bits.
4
Calculate the total number of equal-sized subnets that can be created.
256 subnets (28=2562^8 = 256).
The number of subnets generated is 2n2^n, where nn is the number of borrowed subnet bits.

Key Concept

IPv4 Subnet Masking and Host Capacity Calculations
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Topics

IPv4 Addressing and Subnetting

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