Having problem with 10's complement subtraction From what I've found, to find A - B using 10's complement; where A and B are decimals
Let A = 215 , B = 155


*

*Find 10's complement of B = (1000 - 155) = 845

*Add 10’s complement of B to A

*If it produces end carry; carry is ignored

*If it doesn't produces a carry then the answer = –(10's complement of the sum obtained)



But I'm having problem applying that to the particular problem below:
Find the differences by using tens complement
2 15 743 - 56 100

10's complement of 56100 = (1 00 000 - 56 100) = 43 900
2 15 743 + 43 900 = 2 59 643
Here I'm not sure if 2 is a carry or not. And the answer should be 1 59 643
So how do we solve that kind of problems? 
 A: Jack M is basically right about what he says in the comments. The idea of the method seems to be that if we want to find $A-B$ by applying $C=10^n-B$ we get
$$
A+C=A-B+10^n
$$
so we have to subtract the $10^n$ to get $A-B$ alone. Normally this is done by disregarding the $1$ that is carried. Now, since you have used $10^5=100000$ to calculate 10's complement, then that is what you should subtract to get the answer, namely
$$
259643-100000=159643
$$
and we are good.

But to follow Jack M's suggestion right from the start you could have used $1000000-56100=943900$ and then have $215743+943900=\color{red}{\not 1}159643$ to get the answer straight away.

The other cases for the algorithm is when the result of $A+C$ is less than $10^n$. Then it seems tricky to immediately subtract $10^n$. But then we can subtract $A+C$ from $10^n$ and change the sign since
$$
\begin{align}
-[10^n-(A+C)]&=-10^n+(A+C)\\
&=-10^n+A-B+10^n\\
&=A-B
\end{align}
$$
this is practical since it is easy to find 10's complement of $A+C$ and then add the negative sign.
