Modern computers are primarily binary. Proposed in this paper is a new generalized computing system, by which a number system of any arbitrary radix can be manipulated directly without encoders and decoders. The feature of being able to vary the radix is achieved by pulse counting with alterable carry conditions. The architecture and the organization of the new system are also drastically different from those of existing computers. Instead of the adder being the basic functional structure, the heart of the system consists essentially of an adder, subtractor, multiplier and an accumulator integrated into one inseparable unit. Introduced in this paper is a unified system design suitable for all computing systems and also the concept of a universal building block which can be shared both by the arithmetic unit and the memory. As a memory element, the universal building block is capable of storing a digit of any given radix rather than just binary. Instead of communicating between the binary registers and the constituents of the memory or the arithmetic unit as in existing computers, variable pulse train generators and counters are made to communicate with each other. Binary logic is adopted to channel the pulses or the instructions instead of performing the arithmetic operations. A modern computer, however complex, thus becomes a special case of the generalized computing system.