Public vs. Private IP address?

Hello,
I have been told that my router needs to allocate private IP addresses to the public one (the one I receive from my university) in order to not disturb the funcionality of the network in the building where I am currently. Would you be able to help me understand this better:

The appliances which are connected to my router have the following public IP addresses (found by: "what is my IP" on the web):
144.8.4.11
144.8.4.12
etc.

The private IP addresses (got them e.g. through Terminal:isconfig) look like the following:
144.8.127.175
144.8.127.176
144.8.127.166
etc.

Now are these really private addresses?

My internet works fine now but I need to make sure the setting is right (otherwise I will get trouble from IT people)
I have also found the following information: ranges and the amount of usable IP's are as follows:

10.0.0.0 - 10.255.255.255
Addresses: 16,777,216
172.16.0.0 - 172.31.255.255
Addresses: 1,048,576
192.168.0.0 - 192.168.255.255
Addresses: 65,536

If this is true, then my private IP addresses are not really private? And if so, what are the problems that I could cause exactly in this regard?
Can I set up private address in a router manually? How?

Thanks for helping me make sense of this!

Talmy, Sevoneone, Monokakata and Brentmore,

I am thankful to your responses - all of you really helpful. Let me clarify a few things and respond to some of your posts, hopefully you'll be able to explain this better to me:

The situation with my router (I think it must be the reason for the confusing situation). I am currently using a device which is very weirdly configured. It is a device which you will receive here in Japan from one of the large internet when you use their cable.
See here for the scheme:
https://www.google.com/search?q=RV-...catalog%2Ffaq_nqa%2Fqid_12242%2F1.htm;456;402

If I plug the Ethernet cable into one of the LAN ports (LAN1 to LAN4), I am able to receive a wifi signal for all my devices and use them (there's an internal cable that connects VSDL with LAN ports-setting by the company). The trouble is that the IP addresses look at the follows:

Mac PC:
public address: 144.8.4.11 (www my IP)
IPv4 address: 144.8.127.168
Subnet Mask 255.255.255.192
Router: 144.8.127.129

Ipad:
public address: 144.8.4.19 (www my IP)
IP Address: 144.8.127.177
Subnet Mask 255.255.255.192
DNS: 144.1.5, 144.8.1.6


Now if insert the Ethernet cable into the VSDL plug (i.e. the way it normally shoud be), I get the following:
Mac PC:
Public: none
IPv4 address: 192.168.1.2
Subnet Mask 255.255.255.0
Router: 192.168.1.1

Here you see that finally the router is assigning the proper Private Address to my laptop. The trouble is that now, even though connected to the router, I cannot download anything.
I get the following messages in my broswers:

1. server not found (after trying to connect for a long time)
2. unable to find the proxy server (this is after I try to connect with the proper proxy setting...the only way how to connect to the network and start using the web is through a 8080 port, a proxy server and a html log-on website).

In sum, with a weird setting (Ethernet into lan1), internet works, can connect my devices but the setting is not right and if I understand it correctly, this could cause trouble to the network.
With the Ethernet cable inserted properly I cannot use the internet.

I was explained that the setting has to be right (one Public address...and then the router assigns many private ones to the necessary devices), but I am unable to set it up this way. One of the people who lived in this apartment before told me that he managed to do it only after buying a modem and flashing it with the following software:
http://www.dd-wrt.com/site/index

I would be most grateful to hear your advice.
Kristina.

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brentmore said:

Kristina,

Your university gave you 1 public IP address. Your job is to use your own router to divvy up your network so that all of your devices can 'share' that 1 public IP address and get their own private address. You router will most likely do this using Network Address Translation (NAT). It will assign a private IP like 192.168.1.x to each of your devices. As far as the rest of the world is concerned, you only have one address (the public one), but YOU know that you have lots of other (private) addresses on your network.

So if you do "what's my ip" from any of the devices on your personal network, you should get the same answer from all of them. If that's not the case, it's incorrectly configured and IT will probably let you know about it.

Click to expand...

Brentmore, that's absolutely correct. Yes, I am trying to get it set up the way you have suggested, but not able to do so. please see below and let me know what you think.

talmy said:

I see now -- you don't have a router but a combination modem/router. The modem part is why it doesn't work when connected to the VSDL port. If you just use the LAN ports, it's nothing more than a Ethernet switch and won't do the address translation. Pure routers seem to be hard to find -- you may need to get a "wireless router" which is a combination of router and wireless access point, and then turn the wireless access point off.

Click to expand...

Talmy、
once again, thank you for your response.
I am glad to report that I have managed to set up everything properly now.
There are additional questions though I hoped to get help from you.

1.my devices are properly connected now (having private addresses in the proper range with one public address). However, Ipad + Iphone + Iphone share one private address while my two Macs share another.
Is this normal?
It looks something like this:
144.8.4.11 (for Ipad, iphone)
144.8.4.19 for my two PCs.
I thought that it should be one public address for all devices?

2. I managed to set up my network on a router (a Japanese setting) I bought second hand. There were no instructions as to what the SSID should be, neither the password.
I connected to the router through an ethernet cable..and the following: http://192.168.11.1/ in a browser. Looking at the maker's instructions, it was enough to enter "root" and no password ..and I could get into the router settings. There I found both SSID for the wireless connection + a range of four keys...and one of them, the first, worked. It is a WEP64 key..but I am confused as to the security of the whole thing. Is this normal to be set up in this way? Can someone from the outside connect to my router? (i.e. through wifi..and see the settings in this way as well?)

3. This is a university network..and they allow us to use it by loging a proxy..and 8080 port (I've heard that this is rare..but this is the proxy's port I need to enter in order for all my devices to work).

4. Last but not least, I am confused as to how things get updated in Itunes (maybe you will not know), especially when it comes to podcasts. I can update on this network my podcasts on my Mac, but trying to do the same on an Ipad (using Podcast application) I am unable to do so. It's constantly refreshing..though it is capable to download the latests titles of the podcasts (i.e. not data, but at least the information that there is a new one). Can this be somehow related to the fact that I am connecting to the network through 8080 port?

One again, thank you for your help.