Final answer:
Octal numbers are a base-8 number system with digits ranging from 0 to 7. Each octal digit represents three bits in binary. Conversion from decimal to octal involves dividing the number by 8 and using remainders to form the octal digits.
Step-by-step explanation:
Octal Number Representation
Octal numbers are a radix-8 number system, meaning they are based on eight distinct symbols or digits. The digits used in the octal system are 0 through 7. Each octal digit represents three bits in binary, since 2³ (2 to the power of 3) equals 8, which is the total number of values a three-bit number can have (from 000 to 111 in binary).
To convert a decimal number to octal, you divide the number by 8 and use the remainder as the least significant digit in the octal representation. Then, you take the quotient and repeat the process until the quotient is zero. The octal number is written using only the base-8 digits (0-7), without any symbols from hexadecimal notation like A-F.
For example, to convert the decimal number 65 to octal:
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- Divide 65 by 8. The quotient is 8, and the remainder is 1.
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- Write down the remainder (1).
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- Divide the quotient (8) by 8. The new quotient is 1, and the remainder is 0.
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- Write down the new remainder (0) to the left of the previous remainder. This gives you 01.
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- The last quotient is 1, so write it to the left of the remainders. This gives you 101 in octal.
Therefore, the decimal number 65 is represented as 101 in octal notation.