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aito+e) (1o points). 2. For each of the following problems, there are four inputs (A, B,C, D). Show a truth table for the functions (W, X, Y, Z) specified. Show all your work without omitting any details. 2a. The inputs represent a 4-bit unsigned binary number. The output, W, is 1 if and only if the number is a multiple of 2 or 3 but not both. (5 points). 2b. The inputs represent a 4-bit positive binary number. The output, X, is 0 if and only if the input is a prime (where 0 never occurs). Note that a prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. (5 points). 2c. The first two inputs (A, B) represent a 2-bit unsigned binary number (in the range 0 to 3). The last two inputs (C, D) represent a second unsigned binary number (in the same range). The output, Y, is 1 if and only if the two numbers differ by two or more. (5 points). 2d. The inputs represent a BCD number in excess-3 code. Those combinations that do not represent one of the digits never occur. The output, Z, is 1 if and only if that number is a perfect square. (5 points). Note that each question from 2a-2d must not have more than three wrong values per column for any credit. An excess-3 number is shown in the first table below. Use the second table below for solving this problem. Show all your work without omitting any details Decimal Excess-3 Digit Code 0011 0100 0101 0110 0111 1000 1001 1010 1011 1100 0 6 Decimal AB CDW X YZ 0111 1 0 0 0 10 12 13 14 15