In multiplication of octal numbers a simple rule for multiplication of two digits in any radix is to multiply them in decimal. If the product is less than the radix, then we take it as the result. If the product is greater than the radix we divide it by the radix and take the remainder as the least significant digit. The quotient is taken as carry in the next significant digit.

For example, (3)

To multiply two octal numbers we use the rule given above. The process for multiplication of octal numbers is illustrated with the help of the following examples:

(i) 6

We have 6 × 3 = 18 in decimal, which when divided by 8 gives a remainder 2 and carry 2. Again 6 × 2 = 12 in decimal, and 12 + 2 = 14. This when divided by 8 gives a remainder 6 and a carry 1.

Hence 6
_{8} × 23_{8} = 162_{8} |
6 × 3 = 18 18/8 = 2 with remainder 2 → l,s,d, 6 × 2 = 12 + 2 (carry) = 14 14/8 = 1 with remainder 6. |

(ii) 15

Since 15

15

Now 7 × 44 = 374

6 × 44 = 330

Taking octal addition, we have 374

- Number System

- Decimal Number System

- Why Binary Numbers are Used

- Binary to Decimal Conversion

- Conversion of Numbers

- Hexa-decimal Number System

- Conversion of Binary Numbers to Octal or Hexa-decimal Numbers

- Octal and Hexa-Decimal Numbers

- Signed-magnitude Representation

- Radix Complement

- Diminished Radix Complement

- Arithmetic Operations of Binary Numbers

**Binary Addition****Binary Subtraction****Subtraction by 2’s Complement****Subtraction by 1’s Complement****Addition and Subtraction of Binary Numbers****Binary Addition using 1’s Complement****Binary Addition using 2’s Complement****Binary Multiplication****Binary Division****Addition and Subtraction of Octal Numbers****Multiplication of Octal Numbers****Hexadecimal Addition and Subtraction**

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