Basically a layer 2 switch operates utilizing Mac addresses in it's caching
table to quickly pass information from port to port. A layer 3 switch utilizes
IP addresses to do the same. While the previous explanation is the "What", for folks in networking the following "How" is far more interesting. Essentially, A layer 2 switch is essentially a multiport transparent bridge. A layer 2 switch will learn about MAC addresses connected to each port and passes frames marked for those ports. It also knows that if a frame is sent out a port but is looking for the MAC address of the port it is connected to and drop that frame. Whereas a single CPU Bridge runs in serial, todays hardware based switches run in hybrid, as one can imagine, of a router and a switch. There are different types of layer 3 switching, route caching andtopology-
The RP must listen to the first packet to determine the destination. At that point the Switch Engine makes a shortcut entry in the caching table for the rest of the Switch Engine makes a shortcut entry in the caching table for the rest of the packets to follow. Due to advancement in processing power and drastic reductions in the cost of memory, today's higher end layer 3 switches implement a topology-based switching which builds a lookup table and and poputlates it with the entire network's topology. The database is held in hardware and is referenced there to maintain high throughput. It utilizes the longest address match as the layer 3 destination. Now when and why would one use a l2 vs l3 vs a router? Simply put, a router will generally sit at the gateway between a private and a public network. A router can perform NAT whereas an l3 switch cannot (imagine a switch that had the topology entries for the ENTIRE Internet!!).
In a small very flat network (meaning only one private network range for the whole site) a L2 switch to connect all the servers and clients to the internet is probably going to suffice. Larger networks, or those with the need to contain broadcast traffic or those utilizing VOIP, a multi network approach utilizing VLANs is appropriate, and when one is utilizing VLANs, L3 switches are a natural fit. While a router on a stick scenario can work, it can quickly overtax a router if there is any significant intervlan traffic since the router must make complicated routing decisions for every packet that it recieves.
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