The use of 2 digits for a numbering system may be seen to arise from 3 sources.
Ancient Chinese world view. The development of two forces of energy continually ebbing, flowing, acting and reacting is embodied with the principles of yin and yang. Yang is represented by a solid line and yin by an open line.
These lines are then combined with each other twice to represent 4 phases of energy, strong yang, lesser yang, lesser yin and strong yin.
Then a third line is combined for more precision to represent a trigram of lines, giving a total of 8 possible trigrams representing 8 phases of energy, heaven (complete yang), thunder (strong yang), water (middle yang), mountain (lesser yang), earth (complete yin), wind (strong yin), fire (middle yin), lake (lesser yin)..
Two trigrams are then combined for yet more precision to give the possibility of 64 hexagrams. This is not a formalized numbering system, but the binary logic and counting from 1,2,4,8 to the trigrams and then 8*8 for the two trigrams making 64 hexagrams is evident.
Development of a logical system. The two logic states of true and false were developed into a more formalized numbering system.
Development of computerized logic. The two electrical states of - and + charge readily translated into a logic state of true and false. Each state or bit of information successively combined to give rise to nibbles (4 bits), bytes (8 bits) and more bits (depending on the model being used) to represent extremely large numbers, representations of letters, pictures, etc.