From Lessons in Electric Circuits, consider the truth table below.

a$.(10$ points$)$ Create and fill in a Karnaugh map as shown below. Note that the order is slightly different than usual $(00011110).$

b$.(10$ points$)$ Find the Boolean expression for the truth table based on the Karnaugh map.

$\backslash$table$[[$A$,$B$,$C$,$D$,$Out$],[0,0,0,0,0],[0,0,0,1,1],[0,0,1,0,0],[0,0,1,1,0],[0,1,0,0,0],[0,1,0,1,1],[0,1,1,0,0],[0,1,1,1,0],[1,0,0,0,0],[1,0,0,1,1],[1,0,1,0,1],[1,0,1,1,1],[1,1,0,0,0],[1,1,0,1,1],[1,1,1,0,0],[1,1,1,1,1]]$

$\backslash$table$[[$K$-$map,CD$,],[,00,01,11,10],[$AB$,00,,,,],[,01,,,,],[,11,,,,],[,10,,,,]]$