What I find the neatest is that it's not just showing hexadecimals, but the binary representation at the same time. In the Birkana symbol for 9 it's very easy to recognize the binary 1001: it has the top and bottom 'bits' set.
It also made me aware that I never thought about the symbols we use for numbers. Our digits 0 through 9 suddenly seem very arbitrary, looking at Birkana. Though ten digits are more difficult than sixteen to represent this way, they could certainly have had logic in them.
As for the logic behind our decimal digits, there was an explanation going around for it, but at best it's probably reaching very hard. I'll let you decide: http://message.snopes.com/showthread.php?t=49183
Once upon a time, the digit for 0 was a dot, the digit for 1 was (close to) ι, the digit for 2 was (close to) μ, the digit for 3 was close to w with a leading descender like μ has. The digit for 4 might have been closer to a + sign that eventually morphed to look more like a backwards 2. It was the number of vertical lines which encoded 1, 2, or 3; with 4 and 5 and 6 there was more need to come up with more-abstract symbols.
In Arabic these first 4 digits have actually survived relatively unmolested, ٠ - ١ - ٢ - ٣, while the backwards 2 for 4 started hooking down to become a ٤ and some other stuff happened with the next 5 digits.
In English the digits for 2, 3, and 4 all rotated about 90 degrees counterclockwise while the tail disappeared for the 3 and the 4 didn't close up on the top until relatively late.
It also made me aware that I never thought about the symbols we use for numbers. Our digits 0 through 9 suddenly seem very arbitrary, looking at Birkana. Though ten digits are more difficult than sixteen to represent this way, they could certainly have had logic in them.