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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 ______
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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
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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.



 

Alternatively.

Machines to be connected = 15.

Ports available per switch = 7 (NOT 8)

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

Answer:

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