Hi all, I was wondering if anyone could help with the following question.
For the function, F(A, B, C, D) = (0, 2, 4, 5, 8, 10, 12, 13) give the minimised sum-of-products solution. Devise a realisation that uses a decoder with active-low outputs and one other gate.
I have a solution of (NOT B AND NOT D) OR (B AND NOT C) but I dont know how to use a decoder in this situation. Can I use a 3-line-to-8-line one for this? Any suggestions?
Also very quickly, why are general purpose encoders not very useful?
As you end up with three terms in your solution, (and I am not sure of the terminology above to help with your minimisation - is D the least significant bit?) then a three to eight decoder (such as the '138) would work, but then you'd have to OR the various outputs together.
I answered a post yesterday that used a '156 decoder, which would be perfect in this particular case, as you have two two product terms and the '156 has two 2-4 decoders. You'll still have to OR some outputs together (but don't be foled by the term OR - a NAND is just as usefully an OR and a NOR an AND if you know how to do it - see DeMorgan's theorem).
As decoders decode minterms by definition, the tough stuff is done in hardware. You'll have to figure out the rest (I could, but someone else beat you to my 'help with the homework on the season of goodwill' quota).
Datasheet at:
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Who says? They have their uses, although they are not generally as useful as decoders, in terms of the issues we come up against. Great for encoding banks of switches (although there are other methods) amongst many other things.
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