Problems with 7400 series floating high

Hi, I'm quite new to electronics, in the penultimate year at school,
quite good with computers and wanting to teach myself electronics. I
have made a binary adder circuit on Crocodile Clips which works. I'm
now trying to put it together on a breadboard. Unfortunately the fact
that the 7400 series chips float at a high voltage is causing me some
problems.

Here is a picture of what I have so far:
http://heldtogether.co.uk/adder.png
As you can see if both switches are off the 'carry' LED lights, which
is clearly wrong, if one is on, the correct LED lights, and if both
switches are on neither LED lights. It has crossed my mind to put in
an inverter, but it seems awfully wasteful, and inelegant!

Could someone help me to sort this out, and continue my studies?!?

Thanks
Josh

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