In 2007, I submitted a letter-to-the-editors (AmSci, May/Jun2007, Vol. 95 Issue 3, p195). I suggested that the "half-life" decay of a mole of radioactive element should end with a whole atom; thus 20=1. Going in reverse, the current value of Avogadro’s Number is approximated by 279 = 604 462 909 807 314 587 353 088.
In a 1996 copyrighted pamphlet, “Mole, Bits, and Cubes” (TXu000593728), I submitted that this Binary definition should be the value of Avogadro’s Number. It is invariant, free of dimensionality, and free of all the physical measurements currently being used to “hone in” on a value that seems far too prejudiced considering it is all tangled up with a chunk of metal that needs periodic cleaning that removes few bits of matter in the process and is subject to experimental errors in measurements (80 parts in a billion? and at what accuracy).
With No = 279, the kilogram is as good as measurements can determine the purity, number, and atomic mass of the units of whatever material (e.g., the silicon-28 sphere that is being proffered) is being measured and the standard on which the standards folks make the reference point. Thus, a binary mole of absolutely pure carbon-12 would currently weight precisely 12.0· grams and always be so until they changed the reference point from C-12. At least Avogadro’s “Number” would finally be a “constant” – one and the same.
What I see is a great effort (by those who will be making a decision) not to alter the massive weights and measurements structure that is in place throughout the world of commerce. In that realm, Avogadro’s Number/constant is not a factor - only the size of the “king’s foot”; in this case “Le Gran K” or an article representing it. Science takes second place in this realm; but, then it is scientists who are doing the "defining"!
See http://pages.swcp.com/~jmw-mcw/binary_mole.htm for definition of the binary mole.