2. Find Subtraction of 342 and 614 using 8's complement

Solution:

8's complement subtraction steps :

1. At first, find 8'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 8's complement of the sum is the final result and it is negative.

Here A = 342, B = 614.
Find A - B = ? using 8's complement
First find 8's complement of B = 614


Step-1: 7's complement of 614 is obtained by subtracting each digit from 7

	7	7	7
-	6	1	4
	1	6	3

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Step-2: Now add 1 :
163 + 1 = 164

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Step-3: Now Add this 164 to 342

	1
	3	4	2
+	1	6	4
	5	2	6

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Step by step solution of 342 + 164 = 526

Write the numbers, so that each digit lines up vertically

	3	4	2
+	1	6	4

Step-1 :
`=2_8+4_8`
`=2_10+4_10`
`=6_10`
`=6_8`
Write the 6 in the sum place

	3	4	2
+	1	6	4
			6

Step-2 :
`=4_8+6_8`
`=4_10+6_10`
`=10_10`
`=8xx1+2`
`=12_8`
Write the 2 in the sum place and carry the 1 to the next carry place

	1
	3	4	2
+	1	6	4
		2	6

Step-3 :
`=1+3_8+1_8`
`=1+3_10+1_10`
`=5_10`
`=5_8`
Write the 5 in the sum place

	1
	3	4	2
+	1	6	4
	5	2	6

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Here there is no carry, answer is - (8's complement of the sum obtained 526)


Step-1: 7's complement of 526 is obtained by subtracting each digit from 7

	7	7	7
-	5	2	6
	2	5	1

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Step-2: Now add 1 :
251 + 1 = 252

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So answer is -252

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