15's Complement Subtraction Example 1234

3. Find Subtraction of 1234 and ABC using 15's complement

Solution:

15's complement subtraction steps :

1. At first, find 15'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 1 is added to the result.
4. If there is no carry over, then 15's complement of the sum is the final result and it is negative.

Here A = 1234, B = 0ABC.
Find A - B = ? using 15's complement
First find 15's complement of B = 0ABC

Note : 15's complement of a number is obtained by subtracting each digit from F

Step-1: 15's complement of 0ABC is obtained by subtracting each digit from F



	F	F	F	F
-	0	A	B	C

	F	5	4	3

Step-2: Now Add this F543 to 1234


	1	2	3	4
+	F	5	4	3

1	0	7	7	7

Step by step solution of 1234 + F543 = 10777

Write the numbers, so that each digit lines up vertically


	1	2	3	4
+	F	5	4	3

Step-1 :
`=4_16+3_16`
`=4_10+3_10`
`=7_10`
`=7_16`
Write the 7 in the sum place


	1	2	3	4
+	F	5	4	3

				7

Step-2 :
`=3_16+4_16`
`=3_10+4_10`
`=7_10`
`=7_16`
Write the 7 in the sum place


	1	2	3	4
+	F	5	4	3

			7	7

Step-3 :
`=2_16+5_16`
`=2_10+5_10`
`=7_10`
`=7_16`
Write the 7 in the sum place


	1	2	3	4
+	F	5	4	3

		7	7	7

Step-4 :
`=1_16+F_16`
`=1_10+15_10`
`=16_10`
`=16xx1+0`
`=10_16`
Write the 10 in the sum place


	1	2	3	4
+	F	5	4	3

1	0	7	7	7

The left most bit (1) of the result (10777) is called carry and add it to the rest part of the result (0777)


	0	7	7	7
+				1

	0	7	7	8

So answer is 0778

This material is intended as a summary. Use your textbook for detail explanation.
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3. Example 1234 - ABC