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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● Binary Numbers