When you plug the power supply into the power jack of the device and the other end into the power outlet of the wall, the Barix devices, when using their default configuraton, will search for a DHCP server to get an IP address. If no DHCP Server is found, the device will try to sniff the network to find a "free" IP address. This function is called IP-Zator. When the network addressed is detected then it will always try the x.x.x168 address first.
If that does not work either (because there are no other devices generating traffic), the device will pick an IP address of 169.254.x.x, according to the "Auto-IP" standard. In any case, after max. 5 minutes the device will have an IP Address and announce it via the audio interface (headphone interface on encoding products).
You can also use the Barix Discovery tool (Java based software), this software will find all Barix devices in the local network (if their firmware is newer than 2012).
Read more in this AutoIP Howto