If you haven’t been exposed to this little scamp before, then it’s well worth your taking the time to ponder this poser. On the bright side, we can use as many AND and OR gates as our hearts desire. Also, before you ask, we aren’t allowed to use any NAND, NOR, XOR, or XNOR gates. Sad to relate, there’s a problem in that we are informed we have only two NOT gates at our disposal. If we were permitted to use any logic gates we desired, then we would need only three NOT gates to do the job. Our task is to specify the contents of the black box. The three outputs are the logical inversions of their corresponding inputs (when A is 0, NotA is 1 when A is 1, NotA is 0 when B is 0, NotB is 1… etc.). We start with a black box that has three inputs, A, B, and C, along with three outputs NotA, NotB, and NotC. Speaking of logic, before we dive headfirst into the BCD fray with gusto and abandon (and aplomb, of course), let’s take a moment to remind ourselves of one of my favorite logical conundrums. In fact, may I make so bold as to say that, even if you’re a digital logic guru boasting a size-16 brain with go-faster stripes on the sides, if you don’t learn something new in this column then my name isn’t Max the Magnificent! The more I delve into this sort of thing, the more I say to myself, “Wow! I would never have thought of that!” A great example is binary coded decimal (BCD) because there’s a lot more to this topic than one might, at first, suppose. I love learning how logic designers of the past solved tricky problems with innovative solutions.
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