Problem. You are designing a simple black and white image processing algorithm. It needs to detect the darkness or lightness of an area in the image. For every 2 pixels x 2 pixels matrix, the color of the pixels are observed. The area is considered dark if at least half of the pixels are black, Otherwise, the area is considered light. The pixels under observation are labeled A, B,C, and D as shown below. Let A 0, B 0, C =0, or D=0 if the corresponding pixel of the label is color black. Let X =0 if the 2 x 2 matrix is considered dark. Example scenarios are also shown below. B D Example scenarios: Matrix is considered light Matrix is considered dark B. C D C D A = 0, B = 1, C 1, D 1 A = 1, B = 0, C 0, D 0 Part 1. Specify the input and output variables and the binary states of each. 1. What are the input variables and what do their binary values represent? 2. What are the output variables and what do their binary values represent? Part 2. Construct the truth table showing the desired output for each combination of inputs. (Please arrange your variables in alphabetical order with the MSB as the first letter in alphabetical order) Part 3. Write the Boolean expression for the truth table you constructed in Part 2. Simplify the final expression such that there are only 3 variables per term. Partial points will be given if the final expression is not simplified.