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so I have this expression and I have to simplify it to minimum SoPs

$(x+(y'(z+w)')')'$

so my final answer is $x'y'z'w'$

but I think there is something wrong or trick can some one help me or tell me if my answer is right or wrong .

thank you

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  • $\begingroup$ That looks correct. $\endgroup$ – Marconius Oct 6 '15 at 19:24
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Your answer is correct. Using DeMorgan's theorem:

$$(X + (Y^{'} \cdot (Z + W)^{'})^{'})^{'} $$

$$= (X + (Y + (Z + W))^{'}$$

$$= (X + Y + Z + W)^{'}$$ $$= X^{'} Y^{'} Z^{'}W^{'}$$

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  • $\begingroup$ but in the question they asked for Sum of product so it is still correct ? $\endgroup$ – D.k Oct 6 '15 at 21:28
  • $\begingroup$ It is in SOP form, in this case, there is just 1 minterm. You can check by setting up the Karnaugh Map for this boolean expression and extracting the only minterm which is when X and Y and W and Z are 0. $\endgroup$ – Kevin Zakka Oct 7 '15 at 4:38

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