Your IP address bitwise ANDed with the so called netmask yields your network address. The network address bitwise ORed with the negated netmask yields your so called broadcast address. The IP address of the router through which you connect to the Internet is referred to as the gateway.

A simple example is:

IP: 192.168.0.34 (0xc0a80022) Mask: 255.255.255.240 (0xfffffff0) Network: 192.168.0.32 (0xc0a80020 = 0xc0a80022 & 0xfffffff0) Broadcast: 192.168.0.47 (0xc0a8002f = 0xc0a80020 | ~0x0f)