It is necessary to design an adder for two decimal digits represented in the excess-3 code (Table 3-6). 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.

Table 3-6

TABLE 3-6 Four Different Binary Codes for the Decimal Digit Excess-3 gray Decimal BCD digit 8421 0 1 2 6789SAWN 3 4 5 9 2421 0000 0000 0001 0001 0010 0010 0011 0011 0100 0100 0101 1011 0110 1100 0111 1101 1000 1110 1001 1111 1010 0101 Unused 1011 0110 bit 1100 0111 combi- 1101 1000 nations 1110 1001 1111 1010 Excess-3 0011 0100 0101 0110 0111 1000 1001 1010 1011 1100 0000 0001 0010 1101 1110 1111 0010 0110 0111 0101 0100 1100 1101 1111 1110 1010 0000 0001 0011 1000 1001 1011