16's Complement Subtraction Example 1234

3. Find Subtraction of 1234 and ABC 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 = 1234, B = 0ABC.
Find A - B = ? using 16's complement
First find 16's complement of B = 0ABC

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

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 1 :
F543 + 1 = F544

Step-3: Now Add this F544 to 1234


	1	2	3	4
+	F	5	4	4

1	0	7	7	8

Step by step solution of 1234 + F544 = 10778

Write the numbers, so that each digit lines up vertically


	1	2	3	4
+	F	5	4	4

Step-1 :
`=4_16+4_16`
`=4_10+4_10`
`=8_10`
`=8_16`
Write the 8 in the sum place


	1	2	3	4
+	F	5	4	4

				8

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	4

			7	8

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	4

		7	7	8

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	4

1	0	7	7	8

The left most bit of the result (10778) is 1, called carry and it is ignored.

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