16's Complement Subtraction Example A1052

5. Find Subtraction of A1052 and 15B07 using 16's complement

Solution:

16's complement subtraction steps :

1. At first, find 16'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 16's complement of the sum is the final result and it is negative.

Here A = A1052, B = 15B07.
Find A - B = ? using 16's complement
First find 16's complement of B = 15B07

Note : 16's complement of a number is 1 added to it's 15's complement number.

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 1 :
EA4F8 + 1 = EA4F9

Step-3: Now Add this EA4F9 to A1052

			1
	A	1	0	5	2
+	E	A	4	F	9

1	8	B	5	4	B

Step by step solution of A1052 + EA4F9 = 18B54B

Write the numbers, so that each digit lines up vertically


	A	1	0	5	2
+	E	A	4	F	9

Step-1 :
`=2_16+9_16`
`=2_10+9_10`
`=11_10`
`=B_16`
Write the B in the sum place


	A	1	0	5	2
+	E	A	4	F	9

					B

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	9

				4	B

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	9

			5	4	B

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	9

		B	5	4	B

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	9

1	8	B	5	4	B

The left most bit of the result (18B54B) is 1, called carry and it is ignored.

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