13. A circuit has four inputs A, B, C and D encoded in a natural binary form where D is the least significant bit and A is the most significant bit. The inputs can take values ranging from 0000 (0 in decimal) to 1011 (11 in decimal) which represents the months of the year from January (0) to December (11). Input in the range 1100-1111(i.e. 12 to 15) cannot occur. The output of the circuit is high if the month represented by the input has 31 days. Otherwise, the output is low. The output for inputs in the range 1100 to 1111 is undefined. i. Write the truth table ii. Simplify it using K-map iii. Draw the circuit for the simplified Boolean expression of output using NOR gates only.