A method for finding out the simplest two-stage expression for a given multiple-output switching function requiring minimum number of AND-blocks is presented in this paper. The different component functions of the given multiple-output function are plotted on a chart. A knowledge of the weights of the minterms, prime implicants and the essential prime implicants of the individual component functions enables one to determine easily from the chart the multiple-output prime implicants (or Mopi's(which are essential. In the next step, those Mopi's are selected which satisfy the condition for being included in one of the minimal covers. Finally, other Mopi's are selected by trial for the coverage of the still uncovered terms. A procedure has also been suggested for finding out a cover requiring minimum number of diodes for two-level circuit realization of the given multiple-output function starting from a minimal Mopi cover. The method can be suitably modified for simplification of functions incorporating a certain number of ‘ don't care ’ states. © 1964 Taylor and Francis Group, LLC.