# Multiplication of Octal Numbers

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)4 × (1)4 = (3)4 but (3)4 × (2)4 = (12)4 since 3 × 2 = 6 is decimal and division of 6 by 4 has the remainder 2 and quotient 1.

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:

Evaluate:

(i) 68 × 238

Solution:

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 68 × 238 = 1628 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) 158 × 448

Solution:

Since 158 = 78 + 68, We write

158 × 448 = (78 + 68) × 448 = 78 × 448 + 68 × 448

Now 7 × 44 = 374

6 × 44 = 330

Taking octal addition, we have 3748 + 3308 = 7248

Hence 158 x 448 = 7248

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• 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