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 ______

GATE 2019 · Computer Networks · LAN Technologies · medium

Answer: The minimum number of 8-port Ethernet switches required is 3.

1. Derive available host ports formula: With k switches connected in a tree (minimum spanning), we need k-1 inter-switch links. Each link uses one port on each endpoint switch, so 2(k-1) ports are consumed. Host ports = 8k - 2(k-1) = 6k + 2.
2. Check k = 2: With 2 switches: 6(2)+2 = 14 host ports. We need 15 ports. 14 < 15, so 2 switches are insufficient.
3. Check k = 3: With 3 switches: 6(3)+2 = 20 host ports. 20 >= 15, so 3 switches are sufficient to connect all 15 machines.