Subnetting Related Math

In the IP address "10.0.0.0/16," the "/16" is a notation used to specify the subnet mask or prefix length of the IP address. It's also referred to as CIDR (Classless Inter-Domain Routing) notation. In CIDR notation, the number after the forward slash ("/") represents the number of bits that are used for the network portion of the IP address. In this case, "/16" indicates that the first 16 bits of the IP address are used for the network, and the remaining 32 - 16 = 16 bits are available for host addresses within that network. To break it down further: The IP address "10.0.0.0" is the network address. The "/16" means that the subnet mask is "255.255.0.0" in dotted-decimal notation. In binary, this is "11111111.11111111.00000000.00000000," which signifies that the first 16 bits are network bits, and the last 16 bits can be used for host addresses. So, with a "/16" subnet mask, you can have up to 2^16 (65,536) unique host addresses within the 10.0.0.0 network, ranging from 10.0.0.1 to 10.0.255.255. Problem 1: You have an IP address of 192.168.1.0 with a subnet mask of 255.255.255.0. Calculate the number of usable host addresses in this subnet. Solution 1: The subnet mask 255.255.255.0 corresponds to a /24 subnet. This means there are 32 - 24 = 8 bits available for host addresses. To calculate the number of usable host addresses, subtract 2 for the network and broadcast addresses: 2^8 - 2 = 256 - 2 = 254 usable host addresses. Problem 2: Given the IP address 10.0.0.0/16, how many subnets can you create, and how many hosts can each subnet have? Solution 2: The subnet mask 10.0.0.0/16 means there are 16 bits for the network and 16 bits for hosts. To calculate the number of subnets, use the formula 2^n, where n is the number of subnet bits: 2^16 = 65,536 subnets. To calculate the number of hosts per subnet, subtract 2 for the network and broadcast addresses: 2^16 - 2 = 65,536 - 2 = 65,534 hosts per subnet. Problem 3: You have been assigned the IP address 172.16.0.0/20. Calculate the subnet mask and the number of subnets and hosts per subnet. Solution 3: The subnet mask 172.16.0.0/20 means there are 20 bits for the network and 12 bits for hosts. To calculate the subnet mask: 255.255.240.0 To calculate the number of subnets, use the formula 2^n: 2^12 = 4,096 subnets. To calculate the number of hosts per subnet, subtract 2 for the network and broadcast addresses: 2^12 - 2 = 4,096 - 2 = 4,094 hosts per subnet. Problem 4: You have an IP address of 192.168.10.0 with a subnet mask of 255.255.255.248. Determine the network address, broadcast address, and the range of usable host addresses for this subnet. Solution 4: The subnet mask 255.255.255.248 corresponds to a /29 subnet, which means there are 3 bits for host addresses. To find the network address, subtract the host bits from 32: 32 - 29 = 3 bits for hosts. To calculate the network address, simply zero out the host bits: 192.168.10.0 is the network address. To find the broadcast address, set all the host bits to 1: 192.168.10.7 is the broadcast address. The range of usable host addresses is from the network address +1 to the broadcast address -1: Usable Range: 192.168.10.1 to 192.168.10.6 Problem 5: Given an IP address of 10.20.30.40/28, calculate the network address, broadcast address, and the number of usable host addresses. Solution 5: The subnet mask 10.20.30.40/28 corresponds to a /28 subnet, which means there are 4 bits for host addresses. To find the network address, subtract the host bits from 32: 32 - 28 = 4 bits for hosts. To calculate the network address, simply zero out the host bits: 10.20.30.32 is the network address. To find the broadcast address, set all the host bits to 1: 10.20.30.47 is the broadcast address. The range of usable host addresses is from the network address +1 to the broadcast address -1: Usable Range: 10.20.30.33 to 10.20.30.46