[<higher16bits>.]<lower16bits>The part [<higher16bits>.] is only given out if it is not zero. This has the effect of not changing asn16 asnumbers in any way and making real as4 very obvious. But you potentially have to work on your regular expressions, i.e. if you used _[0-9]+_ in the asn16 world you have now to cope with _[0-9\.]+_ or similar.
<higher16bits>.<lower16bits>The higher 16 Bit value is always given out.
<32bits>This is just an unsigned 32 bit integer. As with asdot, as2 numbers are not changed, but you have to realize yourself that you crossed the 65535 and are in the true as4 world (if that matters to you). But your regexps like _[0-9]+_ have not to be changed (if they do not depend on as numbers having no more than 5 digits).
<highest8bits>.<8bitsbelowthat>.<8bitsfurtherdown>.<lowest8bits>This is looks like an ip address. This format should never be used and is only there for testing purposes.
Asdot and asdot+ are defined in draft-michaelson-4byte-as-representation-02.txt, even if they are not called such. Asdot+ is supposed to be used after the transition period, i.e. when all bgp speakers worldwide can handle as4 - something which may well be decades in the future.
The configure command for setting the asnumber format which is used is
bgp asnum format (asdot|asdot+|asip|asplain)and it will show up in the configuration if you do not use asdot because the is the default format and will be used when you define nothing.
This was the situation when I wrote this patch. I have no strong support for one or the other - if I do not count that I have seen as4 first on RIPE meetings, and there they have been presented in asdot. Not surprisingly because the presentations were done by RIR people. But: just having seen them written one way is no reason to choose that way as the only reasonable one.
So I decided to implement all formats, and make this runtime-configurable. You have to (hard!) reset your bgp sessions if you switch, because regular expressions are influenced by this (and remember to actually have your regexps in the right format!). The decision to make asdot the default is based on the fact that this is already in use by the RIRs (which would have been reason enough) and cisco. asip is more a joke than anything else, do not take that one seriously.