It is necessary to design an adder for two decimal digits represented in the excess-3 code. Show that the correction after adding two digits with a 4-bit binary adder is as follows:

a. The output carry is equal to the uncorrected carry.

b. If output carry=1, add 0011.

c. If output carry=0, add 1101 and ignore the carry from this addition. Show that the excess-3 adder can be constructed with seven full-adders and two inverters.

Please give a correct answer and explain it. Thank you!