Which of the following is not a valid octal number?
Octal numbers, also known as base-8 numbers, are a numeric system that uses eight digits ranging from 0 to 7. These numbers are commonly used in various computing applications, including file permissions and octal file paths. However, not all combinations of digits can form a valid octal number. In this article, we will discuss which of the following options is not a valid octal number and why.
One of the options provided is 123. To determine if it is a valid octal number, we need to check if all its digits fall within the range of 0 to 7. In this case, the digit 3 is greater than 7, which is not allowed in an octal number. Therefore, 123 is not a valid octal number.
Another option is 456. Similar to the previous example, we need to verify if all digits are within the range of 0 to 7. The digit 6 exceeds the limit, making 456 an invalid octal number.
The third option is 789. Once again, we need to check the digits to ensure they are within the valid range. Unfortunately, all three digits exceed the maximum allowed value of 7, so 789 is not a valid octal number.
The fourth option is 1024. In this case, we need to look at the digits and determine if they are within the valid range. The digits 1, 0, and 2 all fall within the range of 0 to 7. However, we must also consider the placement of the digits in the number. In octal, the digit 8 does not exist, so the number 1024 cannot be represented in octal form. Therefore, 1024 is not a valid octal number.
In conclusion, all the options provided—123, 456, 789, and 1024—are not valid octal numbers. This is because they contain digits that exceed the maximum allowed value of 7 or are not representable in the octal system. Understanding the properties of octal numbers is essential for anyone working with computing systems that utilize this numeric base.
