Consider that 15 machines need to be connected in a LAN using 8-port Ethernet…

Concept Understanding

• Each switch has 8 ports, but some ports are used for inter-switch connections

• Since there are no dedicated uplink ports, these connections consume normal ports

• Objective: Connect all machines using minimum switches

Key Observation

• To connect n switches, we need at least n−1 links

• Each link consumes 2 ports (one on each switch)

Total Ports Available

• If number of switches = n

• Total ports = 8n

Ports Used for Interconnection

• Number of links = n−1

• Ports used = 2(n−1)

Ports Available for Machines

• Usable ports = Total ports − Interconnection ports

• = 8n−2(n−1)

• = 6n+2

Condition for 15 Machines

• 6n+2≥15

• 6n ≥ 13

• n ≥ 2.17

Final Calculation

• Minimum integer value of n=3

Final Answer

Minimum number of switches required = 3