Overview of Summa seriei binariae [1676 (?)]
In this manuscript, Leibniz shows that every sum in the form $2^e+2^{e-1}...+2^{e-e}$ is equal to $2^{e+1}-1$. On a surface level, this fragment might not appear related to dyadics, because no use of the binary notation is involved. However, some hints suggest its strong relation to the work on the binay system: first of all, the identity expressed is valid only for base two powers, meaning that Leibniz was searching here for properties unique to the base two system. Even more, thanks to the work on these unpublished manuscripts, it is known nowadays that Leibniz’s work on dyadic was strongly related to his work on transcendental numbers and their properties. Since, according to Leibniz, transcendental numbers are generated through a manipulation of series of powers having an indefinite number of exponents, a property like the one demonstrated in this manuscript, which can be applied to any series written in this form regardless of the value assigned to e, must have been interpreted by Leibniz as an encouraging hint that the work on the base two system could have led to the mastering of transcendental numbers.
For these reasons, it is safe to assume that this manuscript is dated around 1679: around that time in fact Leibniz’s interest towards irrational and transcendental numbers was merging with his interest in dyadic.