(Solved): Design a controller for the LED labeled "8" in a 7 segment LED display to display digits \( 0-9 \) ...

Design a controller for the LED labeled "8" in a 7 segment LED display to display digits \( 0-9 \) using the patterns shown in the figure. The LED will light up when \( Z \) equals 1 . \( Z \) is a function of 4 variables, \( Z=f(A, B, C D) \). Where variable \( D \) is the least significant bit. 1 and 2. Find the Sum of Minterms and the Sum of Don't Cares. \[ Z=\sum m i \] 3. Find the simplest Boolean \( 5 O P \) expression (SOP = Sum of Products) Format Note: Place this answer in order by the number of inputs to the AND gates. For example, to write WXY \( +Z \) \( +X Z+Z Y \); then answer \( Z+X Y+X Z+W X Y \) or \( Z+X Z+X Y+W X Y \) are in correct format order and will be marked correct and \( X Y+W X Y+Z+X Z \) will be marked wrong by the computer. So order the sum with the terms with the smallest. number of variables first, the terms with highest number of variables last. \[ Z= \]