Page 35 - ComputerScience_Class_11

Note: An addition table for octal numbers can also be used to do the same. Add row value with column
value. The intersection cell is the sum. If it is greater than 7, then the right digit is taken as sum and 1 is
carry to the previous digit the next more significant column.

Example 1: (3452) + (167) +1 +1
8
8
Answer: 3 4 5 2
+ 1 6 7
(3641) 8 3 6 4 1

Example 2: (46.71) + (152.6) 8 +1 +1 +1
8
Answer: 4 6 . 7 1
+ 1 5 2 . 6

(221.51) 8 2 2 1 . 5 1

1.4.2 Octal Subtraction
Octal subtraction can be done in three different methods which are as follows:
• Borrow method
• 7’s complement method
• 8’s complement method

Octal Subtraction by Borrow Method
Octal subtraction can be performed by the borrow method in the same way as decimal subtraction.

The steps to be followed are:
1. Subtract each digit of minuend and subtrahend starting from the rightmost column (LSB).
2. If the minuend digit is smaller, borrow 8 from the previous digit.
Example 1: (456) - (173) 8
8
Answer: +8
4 3 5 6
- 1 7 3
(263) 8 2 6 3

Example 2: (362.4) - (76.7) 8 +8 +8 +8
8
Answer: 3 2 6 5 2 1 . 4
- 7 6 . 7
(263.5) 8 2 6 3 . 5

Octal Subtraction by 7’s complement method
7’s complement of a number is obtained by subtracting all bits from 7. For example, the 7’s complement of 26501 is
calculated as:
7 7 7 7 7
- 2 6 5 0 1
5 1 2 7 6

The steps to be followed are:
1. Make the number of digits of the subtrahend equal to minuend by adding leading 0’s in the integer part of the
subtrahend and trailing 0’s in the fractional part if required.

System of Numeration 33