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Is 0.0.0.0 a valid IP address? I want my program to be able to store it as an indication that no address is in use, but this won't work if it's actually valid.
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In the Internet Protocol Version 4, the address 0.0. 0.0 is a non-routable meta-address used to designate an invalid, unknown or non-applicable target. It may also be used for when the client is offline. This address is assigned specific meanings in a number of contexts, such as on clients or on servers.
The message "Invalid IP Address" indicates a problem with your computer's network setup. Every computer that uses an Ethernet-type network, such as the Internet, has an Internet Protocol address that lets other computers communicate with it. Without a valid IP address your computer cannot use the network.
The default route in IPv4 is designated as 0.0. 0.0/0 or simply 0/0. Similarly, in IPv6, the default route is specified as ::/0. The subnet mask /0 specifies all networks, and is the shortest match possible.
According to RFC 1700 - "Assigned Numbers", "Special Addresses" section, a network number of 0 can only be used as a source address, and represents a host on the same network. Therefore it is invalid to assign an address of this type to an interface.
It is valid inasmuch as it contains four octets, each within the range 0 through 255 inclusive. However, it is not usable as a real IP address.
RFC1700 (a) states that 0.0.0.0/8 (0.<anything>.<anything>.<anything>) is reserved as a source address only. You can get into situation where it appears you have this address but that's normally because no address has been assigned to you (by DHCP, for example).
See also Wikipedia entry on IPv4.
(a) Although this RFC is now considered obsolete, it is still correct in terms of the given behaviour. Its replacement, https://www.iana.org/assignments/iana-ipv4-special-registry/iana-ipv4-special-registry.xhtml, still has the same text detailing use of the 0.0.0.0 address.
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Lets look at the Question being asked here by the OP.
Is 0.0.0.0 a valid IP address?
Yes. This is technically a valid IP address, and the other answers describe many various uses of it (I am not going to repost wikipedia links here ... or maybe I am).
As such I believe paxdiablo's answer above is the most correct, but lets look at the context of your question as well.
I want my program to be able to store it as an indication that no address is in use, but this won't work if it's actually valid.
This entirely depends on your use case. Given that this is a programmers forum, lets consider that perspective.
If your software is storing actual internet addresses - server locations, visitors to your website, replication/mirror or backup sites, web service or database servers etc. - then this will be perfectly valid. No machine on the internet will ever have this address assigned, nor will it ever resolve to a valid connection.
If on the other hand you are writing firewall or router firmware, then this address does take on special meaning; default route, accept any IP source/destination, block all IP source/destination, fall-trough catch-all, etc. as outlined by everyone else. However, let me point out that if you are coding on this level you should have a good enough understanding of network protocols so as to not need to ask this question in the first place.
I am therefore going to assume that most people viewing this question fall into the first category, and suggest that this is a perfectly valid way of storing a null, empty or missing IP address, if there is some reason that an actual null value cannot be used. Even if you neglect validation checking and your software does try to connect to this IP address, it will simply not be able to make a connection.
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