Calculation of Network IP, Number of hosts, Range of IP addresses and Broadcast IP from a given Subnet.

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The sample IP and subnet for the above calculations is 193.16.20.35/29. The IP address is 193.16.20.35 and subnet is 29.

Calculating Network IP.

In the calulation of Network IP, the ip and subnet in binary form are necessary to get the Network IP. The binary form of the subnet is 29 up bits and 3 down bits which sums up 32 bits the allowed number of bits in an IP. The ups are designated 1 while downs 0.
```
     29 => 11111111.11111111.11111111.11111000
```
For the IP, each decimal value in the IP is converted to its binary form.
```
     193.16.20.35 => 11000001.00010000.00010100.00100011
```
The network address is the logical AND of the respective bits in the binary representation of the IP address and subnet(network mask)
```
     193.16.20.35 => 11000001.00010000.00010100.00100011
     29           => 11111111.11111111.11111111.11111000
                     --------- logical AND -------------
                     11000001.00010000.00010100.00100000
```
The logical AND value got is then converted to its decimal value to get its Network IP.
```
     11000001.00010000.00010100.00100000 => 193.16.20.32
```
Therefore the Network IP of 193.16.20.35/29 is 193.16.20.32
Number of hosts.

The number of hosts that can be assigned IPs on 193.16.20.35/29 is given by the formula
```
     Maximum Number of hosts = 2**(32 - netmask_length) - 2

     *where netmask_length = subnet value*
```
The minus 2 in the formula is to account for addresses reserved for the Network and Broadcast address.
```
     Maximum Number of hosts = 2**(32 - 29) - 2
     Maximum Number of hosts = 6
```
The number of hosts that can be asigned IP's on the network is 6.

Calculating Broadcast IP

To get the broadcast IP, the host bits of the subnet value are converted to ones, and network bits are converted to zeros.

     11111111.11111111.11111111.11111000 => 00000000.00000000.00000000.00000111

The broadcast IP is gotten by getting the logical OR operation of the IP address and the new subnet value.

     193.16.20.35     => 11000001.00010000.00010100.00100011
     New subnet value => 00000000.00000000.00000000.00000111
                         ----------- logical OR ------------
                         11000001.00010000.00010100.00100111

The logical OR value got is then converted to its decimal value to get its Network IP.

     11000001.00010000.00010100.00100111 => 193.16.20.39

Therefore the Broadcast IP of 193.16.20.35/29 is 193.16.20.39

Range of IP Addresses.

The range of IP addresses that can be assigned to hosts lie in between the value of the Network IP and the Broadcast IP i.e 193.16.20.32 - 193.16.20.39.
```
     193.16.20.33
     193.16.20.34
     193.16.20.35
     193.16.20.36
     193.16.20.37
     193.16.20.38
```
The above IPs are the acceptable IPs that can be assigned to hosts.