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With decimal you have 10 digits 0-9 and each digit place represents a 10^n*digit, binary is 0-1 digits with each digits place represents 2^n*digit. Binary requires fewer digits to memorize than decimal, but more places to represent the same value compared to decimal. If you are trying to find the most efficient base for balancing the number of digits to memorize vs the number of places a value requires to represent you get a graph like this showing the minimum approaching e (~2.718):
https://www.wolframalpha.com/input/?i=beta%2Flog%28beta%29+from+1.5+to+5
And the derivative approaching e:
https://www.wolframalpha.com/input/?i=derivative+beta%2Flog%28beta%29
That comes into play when you're doing something like picking a base for computer architecture. Almost all computers theses days are binary, but some were base 3 trinary for a bit. But you don't need to pick an integer value and can pick pi or e as a base too. Here's a better write up with an explanation of radix and bases:
https://web.archive.org/web/20160324100419/http://www.americanscientist.org/issues/pub/2001/11/third-base/2