Previously network switches was using the 8 byte field Bridge Priority to identify a root on the network.When networks grows and becomes complex vlan creation comes into play the 2 bytes Bridge Priority was divided into two sub-fields 4 bit bridge priority and 12 bit for the system id extention to identify the VLAN. My question is how does the 4 bit bridge priority default value is 32,768? And why do we increments 4096 for the extended system id?

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The least-significant bits of the Bridge Priority are the ones repurposed for the extended system ID. Therefore, you can configure bridge priority to 32768, but you can't actually make it 32769! The precision is no longer increments of 1 but in fact the increments are 4096.

Here's an old post on this topic with some graphics that may help: Spanning tree Default Priority Values

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