The sum of the elements of an integer-valued array recursively calculated as follows: the sum of an array of size 0 is 0; otherwise, the sum is the value of the first element added to the sum of the rest of the array. write an int-valued function named sum that accepts an integer array, and the number of elements in the array and returns the sum of the elements of the array.

7. design a circuit with three inputs (x, y, and z) representing the bits in a binary number, and three outputs (a, b, and c) also representing bits in a binary number. when the input is 1, 2, or 3, the binary output should be one lesser than the input. when the input is 4, 5, or 6, the binary output should be one greater than the input. when the input is 0, the output is 0, and when the input is 7, the output is 7. show your truth table, all computations for simplification, and the final circuit.