GATE | GATE IT 2006 | Question 70

A subnetted Class B network has the following broadcase address : 144.16.95.255. Its subnet mask
(A) is necessarily 255.255.224.0
(B) is necessarily 255.255.240.0
(C) is necessarily 255.255.248.0
(D) could be any one of 255.255.224.0, 255.255.240.0, 255.255.248.0


Answer: (D)

Explanation: Class B network has first 16 bits dedicated for network and last 16 for hosts.
In subnetting bits are borrowed from host part.144.16.95.255 In broadcast address the host bits are all made 1’s and the sub-network ID bits are kept as it is.
So ,144.16.95.255
10010000.00010000.01011111.11111111 Clearly, last 13 bits are 1 So, according to broadcast address definition last 13 bits can be host bits Now ,as the sub-network ID bits are kept as it is so these 13 bits can also be representing subnet. So,last 13 bits are representing subnet ID bits + host bits Subnet mask is represented by putting 1’s in place of all bits representing subnet ID and 0’s in place of all bits representing hosts.
a) 255.255.224.0

11111111.11111111.11100000.00000000

As last 13 bits can be host bits ,so this can be subnet mask but not necessarily as we have seen already that from last 13 bits can be subnet ID bits+ host bits.
So,not option a.
b) 255.255.240.0
11111111.11111111.11110000.00000000
As last 12 bits can be host bits ,so this can be subnet mask but not necessarily as we have seen already that last 13 bits can be host bits + subnet bits. So,not option b.
c) 255.255.248.0

11111111.11111111.11111000.00000000

As last 11 bits can be host bits ,so this can be subnet mask but not necessarily as we have seen already that last 13 bits can be host bits + subnet bits. So,not option c.



d) As shown in the above explanation 255.255.224.0, 255.255.240.0, 255.255.248.0 anyone can be subnet mask.

This solution is contributed by Shashank Shanker khare.
Another Explanation:

For broadcast address of a subnet, all the host bits are set to 1.
broadcast address for subnet is .95.255 => .0101 1111. 1111 1111
So possible host bits can be 13 to 0


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