The author considers binary sequences (i.e. having letters from the set \(\{0,1\})\), and defines binary cumulants for joint probability distributions on binary sequences of finite length. Distributions on binary sequences of finite length are related to solve some fundamental mathematical problems (e.g. Hilbert's 17th problem). This is because these distributions map injectively into their moments and into their classical cumulants, evaluated for all subsets of the letter positions. The main results exposed within this article are as follows: (1) The binary cumulant is bounded in magnitude, by the unity, and is shown to vanish if there exists any bipartitions of the letter positions into statistically independent blocks. (2) The probability distributions on binary \(n\)-sequences are proved to map injectively into their binary cumulants for all subsets of the set of letter positions. (3) An inversion algorithm is established, deriving the joint distribution from its collection of binary cumulants.