Q6Digital Electronics

We must aggressively minimize the Boolean expression: $Y=(A+B{)}^{\prime }\cdot (A^{\prime }+B^{\prime }{)}^{\prime }$. We first apply De Morgan's laws strictly to each parenthetical term to invert them. The first term $(A+B{)}^{\prime }$ becomes $(A^{\prime }\cdot B^{\prime }).$ The second term $(A^{\prime }+B^{\prime }{)}^{\prime }$ becomes $(A\cdot B)$. Multiplying them together yields $Y=A^{\prime }\cdot B^{\prime }\cdot A\cdot B$. Since $A\cdot A^{\prime }=0$ and $B\cdot B^{\prime }=0$, the entire equation collapses. $Y=0$.