The weights associated with these 8 positions are 80, 40, 20, 10, 8, 4, 2 and 1. Uniqueness is ensured by requiring that, in each group of four bits, if the first bit is 1, the next two must be 00. Asymmetric numeral systems are systems used in computer science where each digit can have different bases, usually non-integer. In these, not only are the bases of a given digit different, they can be also nonuniform and altered in an asymmetric way to encode information more efficiently. They are optimized for chosen non-uniform probability distributions of symbols, using on average approximately Shannon entropy bits per symbol.