GATE CSE 2019 | Question: 49

Question

Consider that $15$ machines need to be connected in a LAN using $8$-port Ethernet switches. Assume that these switches do not have any separate uplink ports. The minimum number of switches needed is ______

Comments

"these switches do not have any separate uplink ports." This means if you want to connect two switches together, you have to sacrifice one of the standard 8 ports on both switches to plug in the connecting cable.

• 1 Switch:

  • Capacity: 8 machines. (Not enough for 15).

• 2 Switches:

  • We connect Switch A to Switch B.

  • Switch A uses 1 port for the connection (7 left for machines).

  • Switch B uses 1 port for the connection (7 left for machines).

  • Total Capacity: $7 + 7 = \mathbf{14 \text{ machines}}$.

  • Result: Still not enough for 15.

• 3 Switches:

  • We connect Switch A $\rightarrow$ Switch B $\rightarrow$ Switch C.

  • Switch A: Uses 1 port to connect to B. (7 free for machines).

  • Switch B: Uses 2 ports (one to A, one to C). (6 free for machines).

  • Switch C: Uses 1 port to connect to B. (7 free for machines).

  • Total Capacity: $7 + 6 + 7 = \mathbf{20 \text{ machines}}$.

  • Result: Enough!

So, the minimum number of switches needed is 3.

Also ,
An Uplink Port is a special port on a switch designed specifically to connect to another network device (like another switch or a router) rather than a computer.

In modern switch , "Separate Uplink Port" implies an extra port that does not count against the standard port count.

• Example: A "24-port switch with 2 uplink ports" actually has 26 physical holes to plug cables into.

How would it affect the answer?

If the question said the switches DO have a separate uplink port, the math changes completely because you don't lose your "machine ports" to connect the switches.

Scenario with Separate Uplink Ports:

• Switch A: Has 8 ports for machines + 1 dedicated port to connect to Switch B.

• Switch B: Has 8 ports for machines + 1 dedicated port to connect to Switch A.

• Switch A connects 8 machines.

• Switch B connects 8 machines.

• The switches talk to each other via the separate uplink ports.

• Total Capacity: $8 + 8 = \mathbf{16 \text{ machines}}$.

Verdict: If separate uplink ports existed, you would only need 2 switches to connect 15 machines.

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is LAN technologies in syllabus of GATE 2026?

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@lord_vinayak yes, and for this question it's more of an aptitude.

take 2 switches, we have total of 16 ports.

now these 2 switches will connect by one port of switch A and switch B.

Available ports: 14

now for 15 machines, total 14 ports available.

therefore 1 more switch is needed.

hence a total of 3 switches.

Answer 1

Answer is $3.$ 

Using $3$ switches we can connect maximum $20$ machines together.

∴ We require at least $3$ switches to connect $15$ machines.

Comments

@Tuhin Dutta

I have read that part from the Furouzon and it has nothing to do with this topic according to me.

Why do you think the question is related to that in any way?

 

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We can further extend it,

With $n$ such switches, we can connect $6n+2$ machines.

In other words, for $m$ machines, we will need $\lceil\frac{m-2}{6}\rceil$ such switches.

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@jatinmittal199510 or we can do: for n switches: 14 + 6*(n-2) => ending switches have 7 devices at max and the intermediate ones have 6 devices each. 

But your M machine formula fails for M=2 or 1, we require 1 switch but formula gives 0 (though its obvious but formula is wrong)

Answer 2

There are 15 devices. And there are 8 ports in 1 Ethernet switch. So it's obvious that one switch is not sufficient. So one more switch is required. So in 1st switch only 7 ports are connected to 7 devices and 8th one is used for connecting to another switch. Now come to second switch. Only 7 ports are left as 1st port is used for connecting to 1st switch. Those 7 ports can be connected to 7 devices. But there are total 15 devices and so 1 would be left. So we need another switch. So now, in second switch we connect 6 devices to 6 ports and last port to third switch. And in the last switch 1st port is connected to 2nd switch and two ports to two left devices.So we require 3 switches in total.

Comments

Finally, I understood from this answer.

Thanks.

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Great explanation. Thank you.

Answer 3

Given :- A switch with $8$ ports and we require to connect $15$ machines together.

Using $1$ switch we can connect only $8$ machines together.

 

Using $2$ switches we can connect only $14$ machines together.

 

Using $3$ switches we can connect $20$ machines together.

 

$\therefore$ We require atleast $3$ switches to connect $15$ machines together.

Comments

@jeet even i have problem with this topic..

correct me if i am wrong here:

Here it is given in the question that 15 computers need to be connected.. we can connect all 15 computers as shown in fig.a.

But we need to connect as shown in the figure.b attaining the same functionality as shown in figure a.

It is given that switch has 8 ports and it is given that there are no uplink ports. So all 8 ports can be used for connecting other devices.

we can connect  8 devices to a single switch .In that way ,we can connect 15 computers with 2 switches. but these 2 switches need to be connected so that all the devices are connected.

So we have to dedicate 1 port to connect with other switch..

Now you can refer satbir's answer.

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Yeah I understood this basically, it is like this way:

M1

M2

M3

M4

M5

M6

M7

$\color{Red}{\mathbf{Ethernet-port1- out}}$

 

$\color{red}{\mathbf{Ethernet-port1- In}}$

M8

M9

M10

M11

M12

M13

$\color{red}{\mathbf{Ethernet-port2- out}}$

 

$\color{red}{\mathbf{Ethernet-port2- In}}$

M14

M15

M16

M17

M18

M19

M20

 

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@chirudeepnamini

Thanks.

Answer 4

$\frac{15}{7}=2.1$

So, Answer is $3$

Comments

is this question for 1 mark or 2 marks?

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2 marks

Answer 5

Out of 8 ports 1 port dedicated to the switch itself .hence 7 available ports for the clients.there are 15 clients s no of switches =3

Answer 6

In LAN all the machines are interconnected. If we use a switch for 8 machines, and another for 7 machines; the first 8 machines won't be connected to the latter 7. So using two switches won't be enough.

In the first switch A,

• First 7 ports — 7 machines.
• Last port — Connect to other switch B.

In the second switch B

• One port already connected to A
• 6 ports — 6 machines
• Last port — Connect to other switch C.

In the third switch C

• One port already connected to B
• 2 ports — 2 machines.

Done! We need 3 switches.

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Alternatively.

Machines to be connected = 15.

Ports available per switch = 7 (NOT 8)

So, 15/7 = 2.142 => 3 switches are required.

Comments

Hey!

Can you please explain this to me. I am not able to get the objective of this question.