Structure
Four bytes give about 4.3 billion possible addresses, which is why they have been running short. 192.168.1.1 is 11000000.10101000.00000001.00000001 in binary and 3,232,235,777 as one number; the IP Address Converter shows all the forms.
Public and private
Some ranges are reserved for private networks: 10.0.0.0/8, 172.16.0.0/12 and 192.168.0.0/16. Devices behind a router use these and share one public address. Find yours with the My IP Address tool.
IPv6
IPv6 uses 128-bit addresses to remove the shortage. The tools on this site handle IPv4 only.
Common misunderstanding
An IP address identifies a connection, not a person, and shows a rough location at best. See how to convert an IPv4 address and CIDR notation.