In addition to the work of \textit{D. Eisenbud} and \textit{B. Sturmfels} [Duke Math. J. 84, 1-45 (1996; Zbl 0873.13021)], the authors present more detailed algorithms for the binomial primary decomposition of a binomial ideal in the ring of polynomials \(K[x_1,x_2, \dots,x_n]\) over an algebraically closed field \(K\). In so doing, decompositions into cellular binomial ideals (different from the ones given in the paper cited above) and after that (in the case of positive characteristic) into unmixed cellular binomial ideals are used. The corresponding algorithms are written out and some examples are presented.