How are the default IP addresses of my computer chosen when I don't assign one?

The Dynamic Host Configuration Protocol (DHCP) is a standardized networking protocol used on Internet Protocol (IP) networks for dynamically distributing network configuration parameters, such as IP addresses for interfaces and services. With DHCP computers request IP addresses and networking parameters automatically from a DHCP server, reducing the need for a network administrator or a user from having to configure these settings manually

its sorta like your devices (phones, tivos, computers, wii, xbox, etc) asking for its own phone number. it is handed out automatically to each device in your home that needs the internet.