What is the octal representation of the decimal number 431?

The octal representation of the decimal number 431 is 667.

To convert a decimal number to octal, we need to divide the decimal number by 8 and record the remainder. This process is repeated until the quotient is zero. The octal number is then formed by reading the remainders in reverse order.

Let's convert the decimal number 431 to octal.

First, divide 431 by 8. The quotient is 53 and the remainder is 7.

Next, divide the quotient 53 by 8. The new quotient is 6 and the remainder is 5.

Finally, divide the quotient 6 by 8. The new quotient is 0 and the remainder is 6.

Now, read the remainders in reverse order to get the octal number. So, the octal representation of the decimal number 431 is 667.

This method is known as the 'repeated division by 8' method. It's a simple and effective way to convert decimal numbers to octal. It's important to remember to read the remainders in reverse order, as this gives the correct octal number.

This is a fundamental concept in computer science, as different number systems are often used in different computing contexts. For example, octal numbers are commonly used in programming, particularly with some older systems. Understanding how to convert between these systems is a key skill for any computer scientist.