Mixed Bases
It is sometimes convenient to consider positional numeral systems where the weights associated with the positions do not form a geometric sequence 1, b, b2, b3, etc., starting from the least significant position, as given in the polynomial form. In a mixed radix system such as the factorial number system, the weights form a sequence where each weight is an integral multiple of the previous one. Other sequences can be used, but then every integer may not have a unique representation. For example, Fibonacci coding uses the digits 0 and 1, weighted according to the Fibonacci sequence (1, 2, 3, 5, 8, ...); a unique representation of all non-negative integers may be ensured by forbidding consecutive 1's.
For calendrical use, the Mayan numeral system was a mixed radix system, since one of its positions represents a multiplication by 18 rather than 20, in order to fit a 360-day calendar. Also, giving an angle in degrees, minutes and seconds (with decimals), or a time in days, hours, minutes and seconds, can be interpreted as mixed radix systems.
Read more about this topic: Non-standard Positional Numeral Systems
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