4. Find Subtraction of B25C and C3B1 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 = B25C, B = C3B1.
Find A - B = ? using 16's complement
First find 16's complement of B = C3B1


Step-1: 15's complement of C3B1 is obtained by subtracting each digit from F

	F	F	F	F
-	C	3	B	1
	3	C	4	E

---

Step-2: Now add 1 :
3C4E + 1 = 3C4F

---

Step-3: Now Add this 3C4F to B25C

			1
	B	2	5	C
+	3	C	4	F
	E	E	A	B

---

Step by step solution of B25C + 3C4F = EEAB

Write the numbers, so that each digit lines up vertically

	B	2	5	C
+	3	C	4	F

Step-1 :
`=C_16+F_16`
`=12_10+15_10`
`=27_10`
`=16xx1+11`
`=1B_16`
Write the B in the sum place and carry the 1 to the next carry place

			1
	B	2	5	C
+	3	C	4	F
				B

Step-2 :
`=1+5_16+4_16`
`=1+5_10+4_10`
`=10_10`
`=A_16`
Write the A in the sum place

			1
	B	2	5	C
+	3	C	4	F
			A	B

Step-3 :
`=2_16+C_16`
`=2_10+12_10`
`=14_10`
`=E_16`
Write the E in the sum place

			1
	B	2	5	C
+	3	C	4	F
		E	A	B

Step-4 :
`=B_16+3_16`
`=11_10+3_10`
`=14_10`
`=E_16`
Write the E in the sum place

			1
	B	2	5	C
+	3	C	4	F
	E	E	A	B

---

Here there is no carry, answer is - (16's complement of the sum obtained EEAB)


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

	F	F	F	F
-	E	E	A	B
	1	1	5	4

---

Step-2: Now add 1 :
1154 + 1 = 1155

---

So answer is -1155

---

---