Question 1.12: Use De Morgan's theorem to express Y= A+B, the OR operation,...

The conversion could be performed directly but when used on more complicated expressions it is easy to ‘forget’ an inversion as mentioned above. We therefore firstly invert both sides of the expression giving \overline{Y}=\overline{A+B} . Applying De Morgan’s theorem gives \overline{Y}=\overline{A}\cdot \overline{B } , with both sides again inverted to give the final expression \overline{Y}=\overline{\overline{A} \cdot \overline{B} }

Finally we note that one way of interpreting De Morgan’s theorem is that any AND/OR operation can be considered as an OR/AND operation as long as NOT gates are used as well (see last example). This approach will be considered later on in this chapter when we look at the principle of duality in Section 1.6.