The Logic of Bidirectional Binary Counters

The counters without short-time internal memory, conceived by Bigelow, disclosed by Ware, and extended by Brown, are discussed from the standpoint of their respective logic. It is shown that the (self-instructed) bidirectional1 counter of Brown has a more rigorous logic than the unidirectional counter of Ware; the operation of Brown's bidirectional counter being subjected to the only restriction that its speed be compatible with the operating speed of its individual toggles, whereas the operation of Ware's counter is predicated upon the existence of unspecified buffering states in the input of each stage, to prevent run-away conditions. These buffering states, which occur naturally in Brown's bidirectional counter, can be provided explicitly in unidirectional counters by replacing the two transfer circuits of Ware's counter stage, which are controlled only by one toggle of the preceding stage, by two of the four transfer circuits of Brown's bidirectional counter stage, all four of which are controlled by both toggles of the preceding stage. This paper introduces the viewpoint that a bidirectional counter of Brown's type is a counter in which the state of one toggle of each stage determines which toggle of the next stage is master, while the state of the other toggle of each stage determines whether the slave of the next stage shall be like or unlike the master. This viewpoint permits a succinct discussion of the several possible interstage connections, and of the several counting codes obtained for each connection.