GATE CS 2019 Set 1 — Question 59
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Computer Networks → Medium Access & LANs → Switches & STP
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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 ________.
Correct answer
3 to 3
Solution
To connect switches in a network without dedicated uplink ports, standard ports must be used for interconnection. In a typical topology (like a chain or star), connecting switches requires links. Each link consumes 2 ports (one on each switch).Total ports available across switches = .
Ports used for interconnection = .
Ports available for connecting machines = .We need to connect 15 machines, so:
Since must be an integer, the minimum number of switches required is 3.Verification with :
Available ports = (Not enough for 15 machines).
Verification with :
Available ports = (Enough for 15 machines).
Ports used for interconnection = .
Ports available for connecting machines = .We need to connect 15 machines, so:
Since must be an integer, the minimum number of switches required is 3.Verification with :
Available ports = (Not enough for 15 machines).
Verification with :
Available ports = (Enough for 15 machines).
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