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Example 3: Perform the following binary multiplication (10101) × (11011) 2
2
Answer: 1 0 1 0 1
x 1 1 0 1 1
+1 +1 +1 +1 +1 +1
1 0 1 0 1
1 0 1 0 1 x
0 0 0 0 0 x x
1 0 1 0 1 x x x
1 0 1 0 1 x x x x
1 0 0 0 1 1 0 1 1 1
(1000110111) 2

1.3.4 Binary Division
Binary numbers are also divided in a manner similar to decimal numbers. The division is done by the repeated process
of subtraction. In binary division, the following rules are followed:
1 0 1 Quotient
0 / 1 = 0
1 / 1 = 1 101 1 1 0 1 1
For example, let us divide (11011) by (101) . 1 0 1
2
2
1 1 1
1 0 1

1 0 Remainder

1.4 OCTAL ARITHMETIC
The arithmetic of octal numbers involves octal addition, octal subtraction, octal multiplication and octal division. Octal
arithmetic operations start from its rightmost least significant bit.

1.4.1 Octal Addition
The steps to be followed are:
1. The sum of the digits of the addends is calculated starting from the rightmost digit to the leftmost.
2. If the sum is less than 8, write the octal value as the result in that column.
3. If the sum exceeds 7, then subtract 8 from the result. The difference is taken as sum and 1 is carried to the next
more significant column.

+ 0 1 2 3 4 5 6 7
0 0 1 2 3 4 5 6 7

1 1 2 3 4 5 6 7 10
2 2 3 4 5 6 7 10 11
3 3 4 5 6 7 10 11 12

4 4 5 6 7 10 11 12 13
5 5 6 7 10 11 12 13 14

6 6 7 10 11 12 13 14 15
7 7 10 11 12 13 14 15 16

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