Design a combinational circuit that generates the 10’s complement of a BCD (Binary Coded Decimal) digit.
(i)Built the truth table of your circuit
my understanding is that, the 9's complement of 0 is 9,the 9's complement of 1 is 8.....and 10's complement equals to 9's complement plus 1. but someone told me " 10's compliment is similar to 2's compliment in binary system.we can find 2's compliment by adding 1 to 1's compliment.1's compliment of 0001=1110...add 1 to 1110 to get 2's compliment.1110+1=1111 " so...what is the correct answer
Your understanding is correct: 10's complement is done by taking 9's complement and adding 1.
On better reading of your question, I see that the explanation given of how to do 10's complement by the other person is wrong. However, there is a similarity: in both cases you subtract each digit from the largest digit in the number base and then add 1.
The other similarity in behavior is that they can both be used to add signed numbers using the exact same algorithm as addition of unsigned numbers.
In binary: decimal 3 is 0011; to get -3 in 2's complement, subtract each digit from 1 to make the 1's complement (1100) then add 1 to get the 2's complement (1101). Non-negative numbers are unchanged in these complements, so decimal 2 is 0010 in binary 2's complement. Adding 1101 to 0010 gives 1111, which you can show is the 2's complement of -1.
Likewise, in decimal one can get the 10's complement for -12, by subtracting each digit from 9 (9987) then adding 1 (9988). As in binary, non-negative numbers are unchanged in 10's complement so the 10's complement of 15 is 15. Adding 9988 to 15, gives (1)0003 [you drop the carry out] giving 3, which is the answer to -12+15.
The Wikipedia article on 2's complement, gives more details about why 2's complement is used in computers. 10's complement in decimal has analogous properties to 2's complement in binary.