A 7-segment LED has seven lights arranged as shown in the image below. It can be

Question

A 7-segment LED has seven lights arranged as shown in the image below. It can be used to display the numbers 0-9. For example, to display a 3, you would turn on the top, middle, bottom, and both right-hand segments and turn off the two left-hand segments. Try covering up the two left-hand segments with your hand to see what we mean. Consider any one segment of a 7-segment LED display. Say that two different people each design their own version of a circuit to control that segment. They agree on which input bit patterns (patterns of T and F) represent which of the inputs 0-9. They also agree on when the LED should turn on given each of those inputs. However, the circuits they produce use very different gates. Could two such different circuits both be correct? If so, can the circuits be logically equivalent? If so, must the circuits be logically equivalent? (No yes-or-no answers, please. Muse and pontificate!) NOTE: We're using "short answer boxes" here to work around a Vista quiz bug. We don't need you to keep your answers short, however! Write big long wonderful answers in some other window and then paste them into the teeny little boxes that are limited to 100 characters. Sorry about that last!)

Explanation / Answer

Say that two different people each design their own version of a circuit to control that segment. They agree on which input bit patterns (patterns of T and F) represent which of the inputs 0-9. They also agree on when the LED should turn on given each of those inputs.Problems arise there only.It cannot be compatible.

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