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+25 votes

Host $X$ has IP address $$ and is connected through two routers $R1$ and $R2$ to an­other host $Y$ with IP address $$. Router $R1$ has IP addresses $$ and $$. $R2$ has IP addresses $$ and $$. The netmask used in the network is $$.

Given the information above, how many distinct subnets are guaranteed to already exist in the network?

  1. $1$
  2. $2$
  3. $3$
  4. $6$
asked in Computer Networks by Boss (19.1k points)
edited by | 2.5k views
Option C, Just perform bit wise AND of given IP addresses and subnet mask, we get 3 distinct subnet id
1) 011
2) 010
3) 100
routers also counted in subnets?
what the significance can someone explain?
Find first addresses i.e netaddress of all given IP's using subnetmask.You will find there are only three subnets.
Router's Interfaces have the same netId as the network they are part of. Here, three distinct netIDs are present, implying three sub-nets.
Actually, if there are 2 routers connected via a single interface, then that interface needs to be given a subnet ! And this the subnet id for the common interface between routers is -

Apart from this there are 2 more subnets in the network in which both the hosts are present distinctly - for 'X' and for 'Y'.

Also the interfaces of the routers connected to these hosts have IP addresses taken from the above 2 subnets respectively only !

i think (3) should be 000.
THIS SHOULD BE 2 ,becoz question is asking about distinct



@bikram sir

since we are calculating subnet-ids for each subnet by performing AND operation and finding no. of possible subnets as for each subnet a subnet id will exist.. dats fine...and giving answer which is asked in ques. but  why can't  we do like the normal method of calculating no. of subnets :

subnet mask :

no of subnets = (2^3) - 2 

4 Answers

+16 votes
Best answer

$  =  11111111.11111111.11111111.11100000$


We need to do bitwise AND with subnet mask.
the last $5$ bits are going to be 0 when ANDED.

No need to waste time in finding binary.
Only focus on $1$st $3$ bits of binary.  

(From left side, $1$st bit is $128$,next one is $64$,next one is $32$ goes like that you know.)

$\bf{97}$:    $0 + 64 + 32 +$ something  so $1$st $3$ bits will contain $011$
$\bf{80}$:    $0 + 64 + 0+$ something  so $010$
$\bf{135}$:  $128+0+0+$ something so $100$
$\bf{110}$:  $0+64+32+$ something so $011$
$\bf{67}$:    $0+64+0+$ something so $010$
$\bf{155}$:  $128+0+0+$ something so $100$

So we got $011, 010, 100$
$3$ subnets.... subnet id are...


answered by Boss (11.1k points)
edited by

Acc. to the topology given, there will be three networks :

N1: X and the interface of R1 connected to X

N2: Network containing the interfaces of R1 and R2 connected to each other

N3: Y and the interface of R2 connected to Y.

So why do we need to do ANDing?

Topology? Where?
Read the question. The topology will be like the diagram in my previous question
From this diagram how can you conclude there are 3 subnets? I did not get.
Okay, my mistake. From the diagram, it is evident that there are 3 networks. But to determine if they are subnets or not, we need to do ANDing. I missed the term distinct "subnets" in the question :|

in the question, they given that

how many distinct subnets are guaranteed

if it is class-less, questioner can't use the term subnet why because every subnet is a network in class-less. therefore it should be class-full IP address,

there are 3 networks, check each network network id's before subnetting.  ===> all 3 networks from same network before subnetting

∴ 3 subnets are guaranteed to already exist in the network.


@Shaik Masthan brother how a router can have two ip addresses? How's this possible?

router have so many interfaces, each interface is connected to one network ===> each interface assigned to a ip address which is from the pool of available ip address of the connected network.

In this question, each router has two interfaces, so each of router gets 2 ip address.
Makes sense thanks @Shaik.
+4 votes
Given all address are of class c Default mask for class c=24bit Given net mask = 11111111.11111111.11111111.11100000 Subnet id=3bit Simply BITWISE AND the bits of the first octet for each of the IP addresses we got 011, 010, 100 3 subnets. subnet id are
answered by Junior (785 points)
+2 votes
Simply BITWISE AND the bits of the first octet for each of the following IP addresses . You will get only
xx.xx.xx.96 ,xx.xx.xx.64 and xx.xx.xx.128  
Option C) 3 is the answer
answered by Active (3.7k points)
edited by
Not XOR,  bitwise AND.
Oh sorry.. !! :P
0 votes


answered by (11 points)

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