Not supporting double is not a matter of storage format like you said (RR.GG.BB.TT) but having native intrinsics (and so dedicated hardware) for handling operations on double (add, mul, madd, etc).
Anyway, most GPU supports only single precision because where most of the GPU market lies is in the gaming market and gamers don't need double precision. Also most of gamers are looking for good performance/price ratios. Implementing DP is costful in term of transistor budget (and TDP), and if games don't use double precision this is meaningless.
This is why you see high-end ATI GPUs supporting double (HD 59xx and HD 58xx, but not mid and entry-level GPUs such as HD 57xx and less).
@karlphillip:
Yes you're right, IEEE754 (kind of) for GPUs like GTX 260, but current ATI and NVIDIA generation is supporting IEEE 754-2008 on high-end parts.
About hardware implementation, this are secrets IHVs usually don't tell :)