Serial Interface default broadcast address
A serial interface is considered a point-to-point network. It is not a multi-access network like Ethernet where you can have more than two hosts on a single network segment. There is only a single destination on the other end of the link.
Now serial links can be assigned IP addresses, but they can also function without IP addresses. These would be called unnumbered IP interfaces. This is because any packets exiting a serial interface will necessarily enter the interface of the device on the other end. The routing table in a router can have an exit interface as the "next hop" without the need for an IP address.
Now having said that, if you want to access a particular router using the serial interface, then you do require an IP address there. Because of the nature of serial links, they will by default automatically use the broadcast address of 255.255.255.255 simply because it has the same result as using the network broadcast address. There is only a single other device on the network so there is no need to be more specific.
However, you can change this if you like by using the
ip broadcast-address command under the serial interface configuration.
The configured subnet mask has no effect on what the default broadcast address will be.