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Routers work at network layer 3 of the OSI model, and it deals with IP addresses. A router is specifically used to join networks together and routes traffic between them. When used at home, your router connect the internal local network to your ISP’s network. And it can be connected to your modem (provided by ISP) on one end and to a switch on the other end (local network). Usually, the Internet port on a router will connect to your modem and the rest of the ports are for switches. A modem has a single coaxial port for the cable connection from your ISP and a single Ethernet port to link the Internet port on your router. Modem is used to connect your ISP using phone line (for DSL), cable connection or fiber (ONT).

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A modem is provided by the Internet Service Provider (ISP) and provides a network access to the internet. Some ISPs, such as Verizon's FIOS service instead use an Optical Network Terminal (ONT) which provides many of the same capabilities. In order to use more than one device with a modem or ONT, a router is generally required in addition to the modem.

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Routers: these devices connect different networks, operating at Layer 3 (the network layer) of the OSI model. They maintain routing tables which map IP addresses (more correctly, IP prefixes) to an outgoing interface. Note that an interface may contain one or more ports (See below).

Switches: these maintain forwarding tables which map MAC addresses to physical ports, operating at Layer 2 (the data link layer) of the OSI model. This is not necessarily a one-to-one mapping; many MAC addresses can be bound to the same physical port. This is the case where you have multi-layer switched networks (think a Netgear or Belkin switch plugged into your office or university network), or a hub connected to a switch port.

Hubs: these are essentially multi-port signal repeaters, operating at Layer 1 (the phyiscal layer) of the OSI model. They can be either unpowered (simply providing a physical connection for the existing signal to propagate along), or powered, where they actually regenerate and/or amplify the signal they receive. The point to note here is that hubs are a single collision domain. A collision domain represents a set of devices all connected to the same physical transmission medium, such that only one of them can transmit at any given time (ignoring multiplexing technologies like wavelength division multiplexing, frequency-division multiplexing, time-division multiplexing, etc etc.).

In practice, hubs are found less and less in today's data networks, as they have poor performance (as only one user can transmit at a time) and poor security (anyone connected to the same hub can hear everything all other users transmit and receive).

Modems: MOdulator-DEModulator. Responsible for establishing a digital channel over an analogue medium, most commonly the telephone network. Modems again operate at Layer 2 (the data link layer), but use different protocols than Ethernet to communicate. They then offer protocols such as PPP to the network layer, to allow IP traffic to flow over their links.

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