4096...

the significance of 4096 is understood in relation to switching, especially spanning tree...

what is 2 to the 12th?

4096... 

from: http://www.cisco.com/en/US/docs/switches/lan/catalyst6500/ios/12.2SX/configuration/guide/spantree.html#wp1037363

A 12-bit extended system ID field is part of the bridge ID (see Table 28-1). Chassis that support only 64 MAC addresses always use the 12-bit extended system ID. On chassis that support 1024 MAC addresses, you can enable use of the extended system ID. STP uses the VLAN ID as the extended system ID.

When the extended system ID is enabled, the root bridge priority becomes a multiple of 4096 plus the VLAN ID. With the extended system ID enabled, a switch bridge ID (used by the spanning tree algorithm to determine the identity of the root bridge, the lowest being preferred) can only be specified as a multiple of 4096. Only the following values are possible: 0, 4096, 8192, 12288, 16384, 20480, 24576, 28672, 32768, 36864, 40960, 45056, 49152, 53248, 57344, and 61440. 


then given this:

 Bridge Priority (2 bytes)—The priority or weight of a switch in relation to all other switches. The Priority field can have a value of 0 to 65,535 and defaults to 32,768 (or 0x8000) on every Catalyst switch.

so interpreting hex here from right to left, the first zero is the one's place holder, the second zero is the 16's place holder, the third zero is the 256's place holder and the 8 is the 4096's place holder...

8 times 4096 is 32768

0x1000 equals 4096

0x0100 equals 256

0x0010 equals 16

0x0000 equals ?