Reverse Engineering the Subneting Problem

Scenario #1

In this scenario, a computer is connected to the Ethernet switch and has an IP address of 192.168.1.125 and subnet mask 255.255.255.224. Now, we want to find on which subnet the computer belongs to and the IP is usable IP address or not.
Now,
i) We take the lowest subnet mask i.e. in our case, 224 and convert it in binary.
    255.255.255.224 = 255.255.255.11100000
ii) From the binary we know that our incremental = 32 (crossed one from binary).
iii) So, from the incremental, our subnets will be:
     0 - 31
    32 - 63
    64 - 95
    96 - 127
    128 - 179
iv) So, the IP address falls in Network add of 96 and Broadcast address of 127. And yes, it is a valid IP address.

Scenario #2

In this scenario, a computer is connected to the Ethernet switch and router and has an IP address of 127.16.68.65 and subnet mask 255.255.255.240. Now, we want to find on which subnet the computer and the router belongs to and the IP addresses are usable or not. And, is there any network problem ??
Now,
i) We take the lowest subnet mask i.e. in our case, 240 and convert it in binary.
    255.255.255.240 = 255.255.255.11110000
ii) From the binary we know that our incremental = 16 (crossed one from binary).
iii) So, from the incremental, our subnets will be:
     0 - 15
    16 - 31
    32 - 47
    48 - 63
    64 - 79 
    
iv) So, from the above the router falls in subnet of 48 and PC subnet of 64. Both the IP addresses        assigned to router and PC are valid but, there is a network problem, because gateway IP and IP of the PC are different.
v) To solve this problem, we have to either assign the IP address subnet of 48 or 64 on both PC and Router.