Subtraction of Octal number, Hexadecimal and Decimal can be done using compliments too. Therefore, a few examples are given below for Octal - 7 and 8 compliment, Hexadecimal - 15 and 16 compliments and for Decimal - 9 and 10 compliments.
Octal Number
Example : Using 7 Compliments
(1546)8 - (467)8
Minuend : 1546 and Subtrahend : 467. Minuend contain 4 digits where Subtrahend having 3, so add a leading 0 to Subtrahend 0467. Now 7'th compliment mean subtract the Subtrahend from 7's.
7 7 7 7
0 4 6 7
-------------
7 3 1 0
-------------
Now add the Subtrahend to the minuend
1
1 5 4 6
+ 7 3 1 0
-------------
-------------
1 0 5 6
1 ( Adding Carry digits [Refer to Binary subtraction])
-------------
1 0 5 7
Result of : (1546)8 - (467)8 = (1057)8
Example : Using 8 Compliments
(1546)8 - (467)8
Minuend : 1546 and Subtrahend : 467. Minuend contain 4 digits where Subtrahend having 3, so add a leading 0 to Subtrahend 0467. Now 7'th compliment mean <> subtract the Subtrahend from 7's.
7 7 7 7
0 4 6 7
-------------
7 3 1 0
+ 1 (Add one to the 7 compliment)
-------------
7 3 1 1 Now add the Subtrahend to the minuend
-------------
1
1 5 4 6
+ 7 3 1 1
-------------
-------------
Result of : (1546)8 - (467)8 = (1057)8
Hexadecimal Number
Subtraction of Hexadecimal number can be done with with 15 or 16 compliments
Example : Using 15 Compliments(15CB)16 - (2BC)16 = 1 5 12 11 - 2 11 12
Minuend : 15CB and Subtrahend : 2BC Minuend contain 4 digits where Subtrahend having 3, so add a leading 0 to Subtrahend 0 2 11 12. Now 15'th compliment mean subtract the Subtrahend from 15's.
15 15 15 15
0 2 11 12
-------------
15 13 4 3 Now add the Subtrahend to the minuend
-------------
1 1
1 5 12 11
15 13 4 3
---------------
1 ( Remove the extra carry digits and add it to the remainder)
-------------
1 3 0 15 = 130F
Result of : (15CB)16 - (2BC)16 = (130F)16
Example : Using 16 Compliments
(15CB)16 - (2BC)16 = 1 5 12 11 - 2 11 12
Minuend : 15CB and Subtrahend : 2BC Minuend contain 4 digits where Subtrahend having 3, so add a leading 0 to Subtrahend 0 2 11 12. Now 15'th compliment mean subtract the Subtrahend from 15's.
15 15 15 15
0 2 11 12
---------------
15 13 4 3
+ 1 (Add 1 [16 Compliment])
---------------
15 13 4 4 Now add the Subtrahend to the minuend
---------------
1 1
1 5 12 11
15 13 4 4
--------------
--------------
1 3 0 15 = 130F
Result of : (15CB)16 - (2BC)16 = (130F)16
Decimal Number
We can do it for our (yes our) Decimal number system too. Subtraction of decimal number can be done with with 9 or 10 compliments
Example : Using 9 Compliments
(1497)10 - (879)10
Minuend : 1497 and Subtrahend : 879 Minuend contain 4 digits where Subtrahend having 3, so add a leading 0 to Subtrahend 0879 . Now 9'th compliment mean subtract the Subtrahend from 9's.
9 9 9 9
0 8 7 9
----------
9 1 2 0 Now add the Subtrahend to the minuend
----------
1
1 4 9 7
9 1 2 0
--------------
1 ( Remove the extra carry digits and add it to the remainder) +1
---------------
6 1 8
Result of : (1497)10 - (879)10=(618)10
Example : Using 10 Compliments
(1497)10 - (879)10
Minuend : 1497 and Subtrahend : 879 Minuend contain 4 digits where Subtrahend having 3, so add a leading 0 to Subtrahend 0879 . Now 9'th compliment mean subtract the Subtrahend from 9's.
9 9 9 9
0 8 7 9
----------
9 1 2 0 (add 1 to make it 10 compliment)
+ 1
----------
9 1 2 1 Now add the Subtrahend to the minuend
----------
1
1 4 9 7
9 1 2 1
--------------
-------------
6 1 8
-------------
Result of : (1497)10 - (879)10= (618)10
We yet to finish with number system, but promise you, next one will be the last
in these series!.
1 comment:
thanks :)) it helped me a lot.....
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