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Questions and Answers
What is the base of the number system with the digits 0, 1, 2, 3, 4, 5, 6, and 7?
What is the decimal equivalent of the octal number 4372?
When adding octal numbers, what do you do if the sum of a column is greater than 7?
In octal subtraction, what do you do if you cannot subtract a smaller digit from a larger digit?
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How is octal multiplication similar to decimal multiplication?
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How is octal division performed?
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Study Notes
Octal Number System
- The octal number system is base-8 and consists of the numbers: 0, 1, 2, 3, 4, 5, 6, and 7.
Structure of Octal Systems
- A four-digit octal number is assessed in a weighted system to find the decimal equivalent.
- Each digit in the octal number is multiplied by a power of 8 (8^3, 8^2, 8^1, 8^0) to find the decimal equivalent.
Base 8 (Octal) Representation
- Example of an octal number: 4372(8) = 2298 (10)
Operations in Octal System
Addition
- To add octal numbers:
- Write down the numbers vertically and align them by their rightmost digits.
- Add the numbers column by column, starting from the right.
- If the sum of a column is greater than 7, subtract 8 from the sum and carry over 1 to the next column.
Subtraction
- To subtract octal numbers:
- Write down the numbers with the larger one on top.
- Subtract the numbers column by column, starting from the right.
- If you cannot subtract a smaller digit from a larger digit, borrow 1 from the next left column, which is equivalent to borrowing 8 in decimal.
Multiplication
- Octal multiplication is similar to decimal multiplication:
- Multiply each digit of the bottom number by the entire top number.
- Write each resulting product one row lower than the previous, shifted one place to the left.
- Add all the products together.
Division
- Octal division is performed like decimal division:
- Divide the dividend by the divisor to find the quotient.
- Write down the remainder if any.
- Continue the process with the next digit of the dividend.
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Description
Learn about the basics of the octal number system, including its structure, representation, and operations such as addition. Understand how to convert octal numbers to decimal equivalents.
