/13 Subnet Mask (255.248.0.0): Hosts, Range and Example

How many /13 networks fit

Eight /16s per /13 means one /13 can hold eight full-size AWS VPCs (the largest VPC CIDR AWS allows is /16).

Your EMEA region was given a /13 out of 10.0.0.0/8. A server at 10.21.130.9 fails to route. Which /13 is it in?

The mask is 255.248.0.0. The second octet (248) is the "interesting" one — the first that is not 255.
Block size = 256 − 248 = 8. Networks start at multiples of 8 in the second octet: 0, 8, 16, …
The second octet of 10.21.130.9 is 21. 21 ÷ 8 = 2 remainder 5, so the block starts at 2 × 8 = 16.
Network = 10.16.0.0 (octets after the second become 0). Broadcast = 16 + 8 − 1 = 23, giving 10.23.255.255 (octets after it become 255).
Usable hosts: 10.16.0.1 to 10.23.255.254, which is 2¹⁹ − 2 = 524,286 addresses.

Same thing in binary (network bits | host bits):

Address  00001010.00010|101.10000010.00001001
Mask     11111111.11111|000.00000000.00000000
Network  00001010.00010|000.00000000.00000000

One region, eight VPCs

Give each cloud region a /13 and each VPC in it a /16. The region is then a single summary route on your transit gateway or SD-WAN.
Summarising eight sites

If sites use 10.8.0.0/16 to 10.15.0.0/16, a hub can advertise 10.8.0.0/13 as one route. This only works because 8 is a multiple of 8; sites 10.5 to 10.12 could not be summarised as one /13.

Picking region blocks that do not start on a multiple of 8, like 10.4.0.0 to 10.11.0.0. That range cannot be one /13; it needs two (a /14 and a /14 at different boundaries), which breaks clean summarisation.
Converting 255.248.0.0 to a wildcard as 0.8.255.255. The right answer is 0.7.255.255.

How many /16 networks are in a /13?

Eight. Going from /13 to /16 adds 3 bits, and 2^3 = 8.

How many usable hosts are in a /13?

524,286: 2^19 = 524,288 addresses minus network and broadcast.

What are valid /13 starting points?

Any address whose second octet is a multiple of 8 and whose last two octets are 0, for example 10.0.0.0, 10.8.0.0, 10.16.0.0 or 10.248.0.0.