1. (20 points) Use a K-map to find the simplest POS expression for Pi (A, B, C, D)- M(0.24,8.10.1 1.15) 2. Given the expression P2 (A, B, C,D) - Im(2,4,5,6,7,9,10,12,13) a. (20 points) Use a K-map to show that P2 (B C+D)CABD)(BC+D)(A B C). b. (20 points) Implement P2 using only NOR gates. Assume that the complemented inputs are available (i.e. you do not need a NOT gate to produce the complement of each input since it will be provided beforehand) 3. (20 points) Use a K-map to derive the simplest POS expression for Pa(w,q2.91o)- (1,5,6,7,11,12,13,15) 4. (20 points) Given the expression Ps (x3, x2, xi, xo) = (x3 + X2)(X1 + x) (x2+ x2+ x1 + xo), which type of implementation will produce a circuit with a lower overall transistor cost: the simplest implementation that uses only NAND and NOT gates or the simplest implementation that uses only NOR and NOT gates? What is the transistor cost of the resultant circuit