A hierarchical component with the function is to be used along with inverters to implement the following equation:

The overall circuit can be obtained by using Shannon’s expansion theorem,

where F₀(X) is F evaluated with variable X = 0 and F₁(X) is F evaluated with variable X = 1. This expansion F can be implemented with function H by letting Y = F₀ and Z = F₁. The expansion theorem can then be applied to each of F₀ and F₁ using a variable in each, preferably one that appears in both true and complemented form. The process can then be repeated until all F_i ’s are single literals or constants. For G, use X = A to find G₀ and G₁ and then use X = B for G₀ and G₁. Draw the top-level diagram for G using H as a hierarchical component.

H = XY + XZ G = ABC + ABD + ABC + ABD