Complete the following problems. Show all work. 1) Complete the following truth table. The first two inputs (A,B) represent a 2-bit unsigned binary number in the range 010 to 310. The last two inputs (CD) represent a second 2-bit unsigned binary number in the same range. The output, Z, is 1 if and only if the sum of the two input numbers is prime. (010 and 110 are not prime). Once your truth table is filled out, complete the sum of minterm expression below the truth table by filling in the proper minterm numbers. A B C D Z Z(A, B, C, D) = Eml ) 2) Simplify the following (minimum shown in parenthesis. Must reach minimum for full credit): a. X'x + xyz + xyz (1 term, 1 literal) b. X'X'z' + x'x's + x'x2 + xyz' (3 terms, 7 literals) 3) Give a NAND gate implementation for the following function. Do not simplify. You may assume all inputs are available complemented and uncomplemented. a. g = a(c + bd") + b(ac + d')