I have this waveform and I would like to have the Y.
I know that the equation is
Y = D' + E' + F'.
Where it has
' it means NOT.
As I see it, the only thing I did, and I am not sure if it is right, was this:
If I got it right, this is it:
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The exercise shows the application of DeMorgan's Theorem. Stated simply,
In this case, you have three inputs. Doesn't matter, DeMorgan's Theorem extends to any number of inputs:
that is, the NAND of the three inputs.
Y will be low when all three inputs are high. Based on the sequence, Y will pulse low only at the end, when DEF are all high.
More about DeMorgan's Theorem here: https://www.electronics-tutorials.ws/boolean/demorgan.html
Do a truth table for both (D' + E' + F') and (DEF)'. They will be the same.
Since Y is equal to the sum of (not D), (not E) and (not F), it will be true whenever any one of D, E and F is not true. For then at least one of the three terms will be true. Thus, in your diagram, Y will be true or high whenever any of D, E and F is not true or low. It will only be not true or low whenever all of D, E and F are true or high. You should be able to construct Y from this information.
The easiest way to read the boolean equation
D is false OR E is false OR F is false.
If you understand how to translate from your boolean to my English equivalent, the correct answer should be obvious. If any of D, E, or F are false, the output will be true. So it's always high, except when all three inputs are true.