9's complement of a 4-bit binary number
I don't understand how to calculate the 9's complement of a binary number. I can apply it to decimal ones, example 15 = (9-1)(9-5) ) 84 then I thought to proceed with a binary -> decimal -> 9's complement -> binary conversion but I guess it's not the right way to act.
Answer
Not sure if you're still looking for help on this, I see it's been two months. But I couldn't find how to do the 9's compliment of a BCD (Binary-Coded Decimal, which is stored in 4 bits up to 1001) anywhere on the front page of google, without converting the binary to decimal. This doesn't work if you only work in binary, like in an ALU.
After a bit of scratching around with 9's compliment on paper in binary, I found the answer.
You need to take 9 (1001), and add the 2's compliment of the 4-bit binary number that you want the 9's compliment of:
To find the 9's compliment of 2 (0010) for example
1. 1's compliment of 0010 = 1101
2. Add 0001 to get the 2's compliment = 1110
3. Add this to 1001 (9) = (1) 0111
This can be tested in decimal: 0111 = 7, and 9 - 2 = 7.
Note that there was a carry bit (1) to the left. This indicates that the final answer is positive. For every 9's compliment up to 9, this carry bit will be 1.
The 9's compliments for 10 and above requires an extra step: you need to calculate the two's compliment again on the result of step 3. In the following example, I work out the 9's compliment for 13:
1. 1's compliment of 1101 = 0010
2. Add 0001 to get the 2's compliment = 0011
3. Add this to 1001 (9) = (0) 1100 (note that the carry bit = 0)
4. 1's compliment of 1100 = 0011
5. Add 0001 to get 2's compliment = 0100
In decimal: 9 - 13 = -4.
Note that there was no carry bit to the left (0). This means that the final answer is a negative value: -4.
Whether or not there is a carry bit to the left, will determine whether you need to do a second 2's compliment calculation at step 3, and also whether the final answer is a positive or a negative value.