[enedil]

Normality of a number is with respect to number bases, so your trick with encoding is invalid. Otherwise, every computable number could be considered normal - take an algorithm for generating of it, supply a random string (this is the encoding), disregard the random string, and you have a perfectly valid normal representation of your number. So it is cheating.

[NieDzejkob]

I agree that normality is a specific formalized concept, but you could always require that an encoding function like this is injective.