A machine word mathematical formulation is applied to analysis and synthesis of circuits for signed binary number multiplication. The circuits are related to each other and to contemporary circuit algorithms in the course of the syntheses and in a comparative discussion. Circuits with complemented multiplier/multiplicand (M̄) or complemented partial product word (P̄) corrections offer advantages in circuit symmetry and algorithmic structure.

A restraint-pair formulation for system equality and inequality restraints in both state and control variables is synthesised using ``zero-zone'' function forms. The resulting unification of different categories of algebraic restraints leads to simplified problem representations and to systematic programming routines for problems in restrained optimization.

In optimal resource allocation problems the Dynostat algorithm separates the overall optimization task into less complicated optimum seeking techniques working in parallel. A hybrid computer implementation is shown to provide a much faster optimizer than was previously the case using a digital computer. Solution accuracies are considered adequate for many practical applications. The improved formulation presented of gradient search is advantageous for high-speed optimization. Confidence is increased in analog computer solutions by introducing auxiliary algorithms that check on solution feasibility and also improve accuracy.