The upward compatibility of binary Boolean algebra with Post algebra was examined. There exists in a Post algebra, P(m), a single two-element Boolean algebra, B(2) {4}. If the complement operation in P(m) is the pseudo-complement or strong negation, then more than one B(2) to P(m) mapping is possible. For m = 2('N), N an integer greater than one, there are 2('N-1) homomorphic mappings of B(2) into P(m). Standard B(2):P(4) building blocks were designed and constructed with integrated injection logic to demonstrate the practical aspects of the dual radix concept. An algorithm for finding the maximum compatible mapping from B(2) to P(m) for completely and incompletely specified functions was developed. Finally, memory elements, bus design, and basic architecture to support a B(2):P(4) processor were considered and comments concerning a B(2) machine operating in a P(m) host were made.