A corporation with four shareholders having shares: A: 60, B: 100, C: 160, D: 180. We want to build a machine that allows automatic voting at meetings. Each shareholder, whose voting weight is proportional to the number, presses a button bearing his name (A, B, C, D). If a shareholder votes YES, his variable (for example A) is 1; if he votes NO, it is 0. A resolution will be voted (V = 1) if the sum of the shares corresponding to the YES votes represents at least half of the shares plus one. (a) Construct the truth table of V according to the four Boolean variables A, B, C, D. (b) Give the raw (that is, not simplified) expression of the function in the form of SOP (Sum Of Product, that is, sum of products). (c) Draw a logical circuit (flowchart) that perform the function with doors AND, OR and NOT. (d) Build the Karnaugh table for this function (AB variables for different rows and CD for different columns). (e) Simplify this expression if possible and give the simplified form as a SOP. (f) Give the logical circuit associated with this simplified function.