Avichal said:In BCD addition when the number exceed 9 we add 6 as the correction value. Although I tried all the cases and saw tthat 6 was indeed the asnwer, how do I prove that? Suppose that instead of BCD I had a 6-bit number, what would be the correction value for that coding?
Avichal said:What is x in 0x09. Anyways for 9 representation is 1001 and for 10 its 1010 in binary.
In BCD representation for 9 is the same but for 10 its 0001 0000 instead of 1010.
We need to add 6 for that - I get that but how to prove it?
In BCD addition, we add 6 because it is the binary equivalent of the decimal number 2. This is because in BCD (Binary-coded decimal) representation, each decimal digit is represented by a 4-bit binary code. And the binary code for the decimal number 2 is 0110. Therefore, we add 6 to ensure that the carryover from each digit does not exceed 9 (the highest decimal number that can be represented by a 4-bit binary code).
No, adding 2 instead of 6 in BCD addition would result in incorrect calculations. This is because the binary code for the decimal number 2 (0010) does not match with the binary equivalent of the decimal number 2 in BCD representation (0110). Therefore, adding 2 would not prevent the carryover from exceeding 9, and the resulting sum would be incorrect.
No, adding 6 is not a universal rule in BCD addition. It is specific to BCD representation, where each decimal digit is represented by a 4-bit binary code. In other forms of binary addition, such as pure binary or 2's complement, there is no need to add 6 as the carryover is determined by the highest binary number that can be represented by the number of bits being used.
Yes, there is a reason why we add 6 and not another number in BCD addition. As mentioned earlier, the binary code for the decimal number 2 (0110) is the only one that matches with its BCD representation. Other decimal numbers have different binary codes, which would result in incorrect calculations if used as the carryover number in BCD addition.
If we add a number other than 6 in BCD addition, the resulting sum would be incorrect. This is because the carryover number is crucial in BCD addition to ensure that the carryover from each digit does not exceed 9. Using any other number would not guarantee this, and the final result would be inaccurate.