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“Question: is the 555 complete in the Boolean sense? That is, can any Boolean function be realized as a network of 555 chips? Answer: yes. Tie the threshold pin high—-this essentially disables the 555’s internal latch. Now provide inputs to the reset and trigger pins and take the output from either the totem-pole output or the open-collector output with a suitable external load. This is a somewhat unusual gate—-it can be interpreted as the negation of the conditional operator, or as an AND gate with one of the inputs inverted. But it is complete: an inverter can be obtained by tying reset high; now using this inverter, invert the reset input and one has a NOR gate made from two 555s; the NOR gate is known to be complete. Of course a given Boolean function will be implemented most efficiently by telling the logic synthesis tool (or human designer) to map directly onto the “555 gate” rather than use the NOR-gate construction; but the NOR is a convenient route to the completeness proof. Storage elements can be made from cross-coupled gates or, as we will see below, from 555s configured to use their internal latch, which is slightly more efficient.”

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