Understanding Default IP Address for a Router with Assigned IP and Subnet Mask

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When assigning the IP address 00001010.11111110.00000001.00001001 with a subnet mask of 11111111.11111111.11111111.11111000, the default IP address for the router is identified as 00001010.11111110.00000001.00001110. This address is derived from the given subnet mask, which allows for a specific range of addresses within the subnet. It's important to note that a switch, being a Layer 2 device, typically does not have IP addresses assigned to its ports, except for management purposes. In contrast, Layer 3 switches do require IP addressing for their ports. Additionally, the subnet mask indicates a /29 subnet, which allows for a limited number of host addresses, raising the question of how many devices can be accommodated within that subnet. Further resources on subnet masks and their functionality are available for those seeking more detailed information.
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If we assign the IP address 00001010.11111110.00000001.00001001 and the subnet mask 11111111.11111111.11111111.11111000 to a switch, what is the default IP address for the router?

Answer: 00001010.11111110.00000001.00001110

Why? Why 00001010.11111110.00000001.00001110 and not something else?
 
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could you pls provide more context to the question? The IP address in your answer is correct, but it is not the only correct possibility.

First of all, switch is a L2 device, there are no IP addresses assigned to its ports (maybe just admin IP for remote management?) There exists L3 switches which operate at the network layer and needs IP addressing for their ports, but their usage is very specific. Is this your case?

Regardless the above, let me ask you question:
if you define a subnet with a mask 11111111.11111111.11111111.11111000 (/29), how many hosts (devices) you can actually address within that subnet?
 
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