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Network Address Translation (enables you to hide a group of computers (such as a network) behind one IP address. In the good old days of computing, which weren’t that good and certainly weren’t that long ago, this was known as IP masquerading. Basically, your network sits behind the NAT server, meaning that you need only one “legal,” or public, IP address for the server running the NAT software. The IP addressing scheme that you use on the computer network behind the NAT server is really up to you (although ranges of IP addresses are reserved for this purpose).
When the Internet Assigned Numbers Authority (IANA) developed the IPv4 address classes (A, B, and C), it designated a range in each class to serve as private addresses. So, a private address is an IP address taken from one of the private ranges designated by IANA.