DHCP IP allocations are based off MAC addresses of a particular network adapter trying to access the network. The cable modem has a MAC address just as your network card has. Your reinstall wouldn't have changed the MAC address - as it's hardcoded into a ROM chip. Basically the DHCP server at the Optus end had previously registered your MAC address from the cable modem and when the same MAC address asked the server for an IP address, since the lease was still valid for the server, then the server just tells the modem the same IP as it previously had before and off it goes. For the server, all that happened was the cable modem was off the network for a few hours, nothing more.