2. Find Subtraction of 670 and 831 using 10's complement

Solution:

10's complement subtraction steps :

1. At first, find 10's complement of the B(subtrahend).
2. Then add it to the A(minuend).
3. If the final carry over of the sum is 1, then it is dropped and the result is positive.
4. If there is no carry over, then 10's complement of the sum is the final result and it is negative.

Here A = 670, B = 831.
Find A - B = ? using 10's complement
First find 10's complement of B = 831


Step-1: 9's complement of 831 is obtained by subtracting each digit from 9

	9	9	9
-	8	3	1
	1	6	8

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Step-2: Now add 1 :
168 + 1 = 169

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Step-3: Now Add this 169 to 670

	1
	6	7	0
+	1	6	9
	8	3	9

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Step by step solution of 670 + 169 = 839

Write the numbers, so that each digit lines up vertically

	6	7	0
+	1	6	9

Step-1 :
`=0+9`
`=9`
Write the 9 in the sum place

	6	7	0
+	1	6	9
			9

Step-2 :
`=7+6`
`=13`
Write the 3 in the sum place and carry the 1 to the next carry place

	1
	6	7	0
+	1	6	9
		3	9

Step-3 :
`=1+6+1`
`=8`
Write the 8 in the sum place

	1
	6	7	0
+	1	6	9
	8	3	9

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Here there is no carry, answer is - (10's complement of the sum obtained 839)


Step-1: 9's complement of 839 is obtained by subtracting each digit from 9

	9	9	9
-	8	3	9
	1	6	0

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Step-2: Now add 1 :
160 + 1 = 161

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So answer is -161

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