The logical operation of two-input bubble gates is described. All logical interactions use bubble repulsion to prevent bubbles from transferring to an adjacent path. This principle unifies the gate design and is intended to facilitate hardware development. The serial nature of bubble technology is used to best advantage with pipeline structures. Two-input gates are employed to produce relatively simple pipeline designs for serially adding, subtracting, multiplying, and dividing binary integers. The size of the division unit is reduced by adapting the pipeline circuit for recursive operation. The compactness of these designs is demonstrated by a circuit layout exercise using standard propagation patterns for 6 μ bubbles. The small areas required for the bubble arithmetic units should make them competitive with semiconductors for a class of real time signal processing applications requiring modest throughput rates.