Draw the circuit and the truth table full using paper and pen $..$

Question$2$: BCD adder

Consider a $4$ bit Adder given the following figure, where A and B are $4$ bit numbers:

$1-$ Dress the corresponding truth table

$2-$ To realize a BCD adder, we need to:

Step $1$: First add the two binary numbers A and B

Step$2$: If the sum is less or equal than $9,$ then the value of BCD sum and binary sum will be the same otherwise we will add $6(0110$ in binary$).$ If a carry results from this addition, add it to the next higher$-$order BCD digit.

Thus to implement BCD Adder Circuit we require :

$4-$bit binary adder for initial addition

Logic circuit to detect sum greater than $9$ and

One more $4-$bit adder to add $01102$ in the sum if sum is greater than $9$ or carry is $1.$

a$)$ Dress the truth table for the BCD sum $($from decimal numbers $0$ to $15)$

b$)$ Give the conditions from the truth table where we need to add $6$ to the binary sum? Give a logic equation

c$)$ Design a BCD adder using two $4$ bits' adder and gate AND and OR