Abstract: Circuitry is disclosed for allocating requests for demand-shared bus access among a plurality of requesting ports. During bus contention time, each requesting unit synchronously and sequentially applies the digits of its unique priority code to the bus beginning with the most significant digit. Each requesting unit remains in contention only so long as each digit it applies is greater than or equal to the digit applied by any other unit. After the application of all digits, only the requesting unit having the highest code remains in contention and it seizes the bus. A polarity control conductor is provided, selectively altering the preference that is normally specified by the assigned priority codes. The application of a reversal signal to this conductor for a given interval of time causes each requesting unit to invert each bit of its priority code it applies to the bus during this time interval.