# Simplify Boolean Expression

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

• That looks correct. – Marconius Oct 6 '15 at 19:24

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

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

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

• but in the question they asked for Sum of product so it is still correct ? – D.k Oct 6 '15 at 21:28
• 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. – Kevin Zakka Oct 7 '15 at 4:38