(Solved): all the same part a b and c plz help  Design a controller for the LED labeled "D" in a 7 segmen ...

Design a controller for the LED labeled "D" in a 7 segment LED display to display digits \( 0-9 \) using the patterns shown in the figure. The LED witt iggt up when \( Z \) equals \( 1 . Z \) is a function of 4 variables, \( Z=1(A, B, C D) \), where variable \( \mathrm{D} \) is the least significant bit, 1 and 2. Find the Sum of Minterms and the Sum of Don't Cares. \[ Z=\sum m l \quad 1+\sum d l \] 3. Find the simplest Boolean SOP 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.