(i) Give the truth table and equations for sum and carry for half-adder and implement a halfadder using an XOR gate and a 2-input AND gate. (ii) Give the truth table and equations for sum and carry for full-adder and show how you could implement a full-adder using two half-adders and a 2-input OR-gate. (iii) Implement a half-adder using 2-to-4 decoder with inverted (active low) outputs and two 2-input NAND gates. (iv) Implement a full-adder using a 3-to-8 decoder with active high outputs, two 4-input NOR gates and two 2-input NOR gates.