To divide the IPv4 network address of 201.100.50.0/24 so that each subnet can support 40 hosts, we first need to determine the required subnet size.
Step 1: Determine the Number of Bits Required for Hosts
The formula to determine the number of host addresses that can be supported by a subnet is:
\[ 2^h - 2 \geq \text{{number of hosts needed}} \]
where \( h \) is the number of host bits. The "-2" accounts for the network and broadcast addresses.
For 40 hosts:
\[ 2^h - 2 \geq 40 \]
Calculating the powers of 2:
- \( 2^5 - 2 = 32 - 2 = 30 \) (not enough)
- \( 2^6 - 2 = 64 - 2 = 62 \) (sufficient)
Thus, we need at least 6 bits for the host addresses.
Step 2: Calculate the New Subnet Mask
The original subnet mask for 201.100.50.0/24 is 255.255.255.0. In CIDR notation, this is a /24 prefix, which means there are 32 - 24 = 8 bits available for hosts.
Since we need 6 bits for host addresses, we can use:
\[ 8 - 6 = 2 \text{ bits for subnetting} \]
This means the new subnet mask will use 24 + 2 = 26 bits for the network. Therefore, the new subnet mask in CIDR notation is \(/26\).
Step 3: Calculate the Number of Subnets
Using 2 bits for subnetting, the number of possible subnets is:
\[ 2^2 = 4 \text{ subnets} \]
Step 4: Determine the Address Range for the First Subnet
With a /26 subnet mask (255.255.255.192), we can calculate the subnets. Each subnet will have \(2^6 = 64\) addresses (including network and broadcast addresses):
- First subnet:
- Network Address: 201.100.50.0
- First usable address: 201.100.50.1
- Last usable address: 201.100.50.62
- Broadcast Address: 201.100.50.63
Summary
- Subnet Mask: 255.255.255.192 (or /26)
- Range of Addresses for the First Subnet:
- Network Address: 201.100.50.0
- First Usable Address: 201.100.50.1
- Last Usable Address: 201.100.50.62
- Broadcast Address: 201.100.50.63
This configuration allows for 4 subnets, each capable of supporting 40 hosts.