Hi I'm a student and I got stuck on a problem.
I need to create a logic circuit only using AND gates or NOT gates. But the question in boolean form includes the OR operator and i'm having difficulty figuring out how to get rid of the OR in the expression.
The boolean expression is ABC + A~B~c + AB~C
I know I'll probably have to use the boolean properties to expand/simplify, i've been trying different things but I have no ideas and completely lost.
You just need to know that \$A+B=\overline{\overline{A+B}}=\overline{\overline{A}\cdot\overline{B}}\$. So:
$$\begin{align*} A\cdot B\cdot C + A\cdot\overline{B}\cdot\overline{C} + A\cdot B\cdot\overline{C} &\\\\ &=\overline{\overline{A\cdot B\cdot C + A\cdot\overline{B}\cdot\overline{C} + A\cdot B\cdot\overline{C}}}\\\\ &=\overline{\overline{A\cdot B\cdot C}\cdot\overline{A\cdot\overline{B}\cdot\overline{C}}\cdot\overline{A\cdot B\cdot\overline{C}}} \end{align*}$$
Of course, you could have first simplified your equation. It's just \$A\cdot B + A\cdot\overline{C}\$.
\$ABC + A\overline{B}\overline{C} + AB\overline{C} \$
\$ABC + \color{Red}{AB\overline{C}} + A\overline{B}\overline{C} + AB\overline{C} \$ (Idempotent)
\$AB(C + \overline{C}) + A\overline{C} (\overline{B} + B) \$ (Distributive)
\$AB + A\overline{C}\$ (Complement)
\$\overline{\overline{AB} \cdot \overline{A\overline{C}}}\$ (DeMorgan's)
More NAND than all AND/NOT, but it works.
