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Question on STP

Cisco says:
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 The exhange of BDPUs results in the following:
•      The election of a unique root switch for the stable spanning-tree network topology.
•      The election of a designated switch for every switched LAN segment.
•      The removal of loops in the switched network by placing redundant switch ports in a backup state.
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So as soon as a switch is powered on, it thinks it is the root bridge . An election process happens and the bridge (switch) with the lowest priority ID gets chosen as bridge root. Every port on the bridge root goes into forwarding mode. I think I understand that part

The part I dont understand is this:
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A BPDU exchange results in the following:
•      One switch is elected as the root switch.
•      The shortest distance to the root switch is calculated for each switch.
•      A designated switch is selected. This is the switch closest to the root switch through which frames will be forwarded to the root.
•      A port for each switch is selected. This is the port providing the best path from the switch to the root switch.
•      Ports included in the Spanning-Tree Protocol are selected.
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So if you have 5 switches in your LAN. One of them will become the root bridge obviously.  Then a "designated switch" is selected? And the 3 switches will forward STP info to this "Designated switch", which will in turn forward it to the root bridge?  Am  I understanding that correctly?
Thanks
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Don Johnston
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Thanks don.

Ok, to verify:

-SwA is the root bridge. Each interface on this switch is in forwarding mode (meaning it spews out BPDUs out all of it's interfaces)

-The top port of SwB becomes the designated root port. This is the interface SwB receives BPDUs from SwA on.  All other ports on SwB become designated ports (read: forwarding state).

-SwB uses it's designated ports and sends out BPDUs, that it received from SwA, out to Switches C and D.

-Cost and Bridge ID are the determinating factors when a switch decides which BPDU to discard

-A switch should never receive a BPDU on a Designated Port


So basically, each switch that is NOT the root bridge, will have one or more "designated ports" which it uses to send out BPDUs out.  
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"So basically, each switch that is NOT the root bridge, will have one or more "designated ports" which it uses to send out BPDUs out. " 

Correct. In my example I am only showing switch to switch connections. I left off end user connections for clarity. I should have specified that.

-Don
Thanks guys!