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I know that to discover the unknown details (IP/MAC) in a network the broadcast address is used. For example: DHCP client broadcasts request to get network detail from DHCP server, one host gets MAC-address of destination host using an ARP broadcast in Ethernet medium.
However, what I don't know is when the broadcast MAC address, broadcast IP address, or both are used?
Is the broadcast MAC address used only with ARP broadcast in Ethernet?
Most questions like this can be answered by having a proper understanding of the OSI Network Model. When you know what layer a protocol or service operates at, then you know how it communicates. You then realize that the comment:
"I found that broadcast MAC address is used with ARP broadcast in Ethernet, as data are transferred in the data link layer in Ethernet. However, this still made me confused, How does data get transferred in Wi-Fi local network?"
can be easily answered by the fact that the Data Link layer is Layer 2, which is above Layer 1 where Wi-Fi / Ethernet operate.
In other words, ARP doesn't care how the physical data (on Layer 1) gets from one place to another (wireless or wired). It only cares about what is happening at Layer 2.
So, to answer your question on what type of broadcast is used, it totally depends on what layer the protocol operates on. If it operates on Layer 2 (Like ARP) then it will use MAC broadcasts. If it operates on Layer 3 or above (Like DHCP) it will use IP broadcasts.
But, here's the thing, it really doesn't matter. Network cards, including wifi adapters, do NOT respond to IP addresses (that is a function of the IP stack in the OS). They respond to MAC addresses on Layer 2. So, even if a protocol operates at Layer 3 or above and sends out an IP broadcast, it gets converted to a MAC broadcast at Layer 2 before it is sent out "on the wire" at Layer 1 for all others to see.
