The computer logic appears to take into account the actual tyre temperature when recommending the current pressure as opposed to what is on the label (in the US anyway) on the door post. One of the things I did with Bimmercode was to set the pressure display to also show the temperature.
In some markets, on some BMWs, they utilize the antilock wheel rotation sensors to estimate when a tire pressure is low, so any recommendation on desired pressure could be off, if it displays it at all.
But, in general, I've found the TPMS values to match up pretty closely to an external gauge when checking.
I've opted for a 12vdc powered compressor, then I don't have to worry about whether the battery in the thing is charged or not.
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