15's Complement Subtraction Example A1052

5. Find Subtraction of A1052 and 15B07 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 = A1052, B = 15B07.
Find A - B = ? using 15's complement
First find 15's complement of B = 15B07

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

Step-1: 15's complement of 15B07 is obtained by subtracting each digit from F



	F	F	F	F	F
-	1	5	B	0	7

	E	A	4	F	8

Step-2: Now Add this EA4F8 to A1052

			1
	A	1	0	5	2
+	E	A	4	F	8

1	8	B	5	4	A

Step by step solution of A1052 + EA4F8 = 18B54A

Write the numbers, so that each digit lines up vertically


	A	1	0	5	2
+	E	A	4	F	8

Step-1 :
`=2_16+8_16`
`=2_10+8_10`
`=10_10`
`=A_16`
Write the A in the sum place


	A	1	0	5	2
+	E	A	4	F	8

					A

Step-2 :
`=5_16+F_16`
`=5_10+15_10`
`=20_10`
`=16xx1+4`
`=14_16`
Write the 4 in the sum place and carry the 1 to the next carry place

			1
	A	1	0	5	2
+	E	A	4	F	8

				4	A

Step-3 :
`=1+0_16+4_16`
`=1+0_10+4_10`
`=5_10`
`=5_16`
Write the 5 in the sum place

			1
	A	1	0	5	2
+	E	A	4	F	8

			5	4	A

Step-4 :
`=1_16+A_16`
`=1_10+10_10`
`=11_10`
`=B_16`
Write the B in the sum place

			1
	A	1	0	5	2
+	E	A	4	F	8

		B	5	4	A

Step-5 :
`=A_16+E_16`
`=10_10+14_10`
`=24_10`
`=16xx1+8`
`=18_16`
Write the 18 in the sum place

			1
	A	1	0	5	2
+	E	A	4	F	8

1	8	B	5	4	A

The left most bit (1) of the result (18B54A) is called carry and add it to the rest part of the result (8B54A)


	8	B	5	4	A
+					1

	8	B	5	4	B

So answer is 8B54B

This material is intended as a summary. Use your textbook for detail explanation.
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5. Example A1052 - 15B07