Final answer:
When you connect your wireless router to your cable modem, your ISP assigns your router one IP address dynamically. The PCs connected to the router are assigned private IP addresses by the router itself through Network Address Translation (NAT). These private IP addresses are unique and distinct from the public IP address assigned to the router.
Step-by-step explanation:
When you connect your wireless router to your cable modem, your Internet Service Provider (ISP) assigns your router one IP address dynamically. This IP address serves as the public address for all the devices connected to your router. When your PCs connect to the wireless router through 802.11, they are assigned a private IP address by the router itself. These private IP addresses are typically in the range of 192.168.x.x or 10.x.x.x.
Each PC connected to the router has a unique private IP address. The router uses Network Address Translation (NAT) to track the connections from each PC and manage the traffic between the private IP addresses and the public IP address assigned by the ISP.
For example, if your router is assigned the public IP address 203.0.113.1 and one of your PCs has the private IP address 192.168.0.10, when the PC sends a request to access the internet, the router replaces the source IP address of the packet with its public IP address before forwarding it to the internet. When the response comes back, the router uses the NAT table to deliver the response to the correct PC based on the private IP address.