Question

The octal numeral system is a base 8 positional system that uses the symbols 0,1,2,3,4,5,6,7. Write each base 8 number as a base 10 number. 12 and 117

Answer 1

Step-by-step explanation:

(12) in base 8

= (1 * 8¹ + 2 * 8⁰) in base 10

= (8 + 2) in base 10

= 10 in base 10.

(117) in base 8

= (1 * 8² + 1 * 8¹ + 7 * 8⁰) in base 10

= (64 + 8 + 7) in base 10

= 79 in base 10.

Answer 2

Using octal numeral system, 12₈ number as 10₁₀ and (117)₈ number as (79)₁₀.

What is octal numeral system?

Octal numeral system has "a base of 8 and uses the number from 0 to 7".

According to the question,

a) (12)₈

          = (1 * 8¹ + 2 * 8⁰)₁₀

          = (8 + 2)₁₀

          = 10₁₀.

b) (117)₈

        = (1 * 8² + 1 * 8¹ + 7 * 8⁰)₁₀

        = (64 + 8 + 7)₁₀

        = (79)₁₀

Hence, using octal numeral system, 12₈ number as 10₁₀ and (117)₈ number as (79)₁₀.

Learn more about octal numeral system here

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