routers use routing protocols to exchange routing information.
check out the link below for lots of information on routing protocols.
Wireless routers are required to have a wireless network connection. The stronger the wireless signal the further the signal will reach. Although the network can be seen by others within it's signal range, for security reasons your network cannot be accessed without a network key. Specifically a N rated wireless router has a powerful signal. G routers are much less powerful. For any router to work you need to connect a wireless receiver to the computer you want on the network.
The Cisco Wireless Network works by making all of the computers connect to the internet through the same router. Most Cisco routers have the wireless connect by using a password so others can not steal the bandwidth.
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Some are for the effective transmission of data from one point to another (routers, hubs, etc) some are for physical protection of the network like a firewall, others like servers and mainframes are for data storage.
To make a website available to others, you need to host it. This is made possible by use of a web server. The web server is linked to the internet by an internet service provider.
You will have to use a router. Routers act as a 'single' device and make any others, such as your computers, 'invisible' to the modem. Cable internet does not allow more than one device to be connected, but routers are usually allowed as a work-around. You may also see Switches and Hubs. These DO NOT mask your computers and will not function. Make sure it's a router! Routers may also have wireless capabilities- These are not required, and it may be cheaper to get a non-wireless router.
To make it secure you have to use encryption which is available in almost all routers.
Yes apple routers will repeat each others signal as long as you set them up to do so, which is very easy with apples airport utility app
To make a website available to others, you need to host it. This is made possible by use of a web server. The web server is linked to the internet by an internet service provider.
Many online sites have wireless router charts to compare models. One such site is the Best Buy website. They have many different routers and you can compare them with others.