How do you convert a decimal number to its octal equivalent?

To convert a decimal number to its octal equivalent, divide the decimal number by 8 and record the remainder and quotient.

In more detail, the process of converting a decimal number to its octal equivalent involves a series of divisions by 8, where the remainder at each step represents an octal digit. This process is repeated until the quotient is zero. The octal number is then formed by reading the remainders in reverse order, from the last remainder obtained to the first.

Let's take an example to illustrate this process. Suppose we want to convert the decimal number 125 to octal. Here are the steps:

1. Divide 125 by 8. The quotient is 15 and the remainder is 5.
2. Divide the quotient (15) by 8. The new quotient is 1 and the remainder is 7.
3. Divide the new quotient (1) by 8. The final quotient is 0 and the remainder is 1.

Now, read the remainders in reverse order: 175. So, the octal equivalent of the decimal number 125 is 175.

It's important to note that this method works for any decimal number, no matter how large. However, for very large numbers, the process can be quite lengthy. In such cases, it may be more efficient to use a calculator or computer program that can perform the conversion automatically.

Also, remember that octal numbers are often written with a leading '0' to distinguish them from decimal numbers. So, you might write the octal equivalent of 125 as 0175.

In summary, converting a decimal number to octal involves repeated division by 8, recording the remainder at each step. The octal number is then formed by reading the remainders in reverse order.