What should be the network of ranges for 500, 250, 130, 90, and 10 hosts? Solve it step by step with explanation.
Understand the Problem
The question is asking to determine the network ranges for different host counts: 500, 250, 130, 90, and 10. It requires knowledge of subnetting in networking, including calculating the required subnet mask for each host count and then deriving the range of IP addresses for each subnet. The approach will involve determining the number of bits required for the hosts and using that to find the subnet size.
Answer
- 500 hosts: 0.0.0.0 to 0.0.1.255 - 250 hosts: 0.0.2.0 to 0.0.2.255 - 130 hosts: 0.0.3.0 to 0.0.3.127 - 90 hosts: 0.0.3.128 to 0.0.3.255 - 10 hosts: 0.0.4.0 to 0.0.4.15
Answer for screen readers
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For 500 hosts:
- Required bits: 9
- Subnet Mask: /23
- Total IPs: 512
- Range: 0.0.0.0 to 0.0.1.255
-
For 250 hosts:
- Required bits: 8
- Subnet Mask: /24
- Total IPs: 256
- Range: 0.0.2.0 to 0.0.2.255
-
For 130 hosts:
- Required bits: 8
- Subnet Mask: /25
- Total IPs: 128
- Range: 0.0.3.0 to 0.0.3.127
-
For 90 hosts:
- Required bits: 7
- Subnet Mask: /25
- Total IPs: 128
- Range: 0.0.3.128 to 0.0.3.255
-
For 10 hosts:
- Required bits: 4
- Subnet Mask: /28
- Total IPs: 16
- Range: 0.0.4.0 to 0.0.4.15
Steps to Solve
-
Identify the number of hosts required
List the different host counts: 500, 250, 130, 90, and 10. -
Calculate the required bits for hosts
Use the formula to determine the number of bits needed for each host count. The formula is:
$$ n \geq \log_2(H + 2) $$
where ( H ) is the number of hosts. The "+2" accounts for the network and broadcast addresses. -
Calculate required subnet mask
Convert the number of bits needed for hosts into a subnet mask. The subnet mask is given by:
$$ \text{Subnet Mask} = 32 - n $$
where ( n ) is the number of bits calculated. -
Determine the number of IP addresses per subnet
Calculate the total IP addresses available with the subnet mask:
$$ \text{Total IPs} = 2^{(32 - \text{subnet mask})} $$ -
Calculate the IP address ranges
Identify the range of IP addresses for each subnet by the subnet mask. The first IP address in the range is typically the network address, and the last IP address is the broadcast address. -
List the ranges for each host count
For each calculated subnet, present the total IPs and the respective ranges.
-
For 500 hosts:
- Required bits: 9
- Subnet Mask: /23
- Total IPs: 512
- Range: 0.0.0.0 to 0.0.1.255
-
For 250 hosts:
- Required bits: 8
- Subnet Mask: /24
- Total IPs: 256
- Range: 0.0.2.0 to 0.0.2.255
-
For 130 hosts:
- Required bits: 8
- Subnet Mask: /25
- Total IPs: 128
- Range: 0.0.3.0 to 0.0.3.127
-
For 90 hosts:
- Required bits: 7
- Subnet Mask: /25
- Total IPs: 128
- Range: 0.0.3.128 to 0.0.3.255
-
For 10 hosts:
- Required bits: 4
- Subnet Mask: /28
- Total IPs: 16
- Range: 0.0.4.0 to 0.0.4.15
More Information
The calculations use binary logarithms to determine how many bits are needed to represent the number of required hosts. Additionally, the understanding of subnet masks is essential, as each mask represents a different number of available addresses. This process is crucial in efficient IP allocation.
Tips
- Failing to account for the network and broadcast addresses can lead to underestimating the required number of addresses.
- Not converting correctly between bit counts and subnet masks can lead to incorrect ranges.
- Misunderstanding how to calculate the total addresses available can result in incorrect subnetting.
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