How to Convert Decimal to Octal: Simple Techniques and Examples

Converting decimal numbers to octal numbers can be a bit tricky for those who are new to the process. Decimal numbers are base 10 numbers, meaning they use 10 digits (0-9), while octal numbers are base 8 numbers, meaning they use 8 digits (0-7). In this article, we will discuss some simple techniques and examples to help you convert decimal numbers to octal numbers with ease.

Technique 1: Division Method

The division method is one of the simplest techniques for converting decimal numbers to octal numbers. The process involves dividing the decimal number by 8 and writing down the remainder. Then, the quotient is divided by 8 again, and the remainder is written down. This process is repeated until the quotient becomes 0.

Let's take an example to better understand this technique:

Convert the decimal number 158 to octal.

Solution:

Step 1: Divide 158 by 8, and write down the remainder. The quotient is 19.

158 ÷ 8 = 19 remainder 6

Step 2: Divide 19 by 8, and write down the remainder. The quotient is 2.

19 ÷ 8 = 2 remainder 3

Step 3: Divide 2 by 8, and write down the remainder. The quotient is 0.

2 ÷ 8 = 0 remainder 2

Therefore, the octal equivalent of the decimal number 158 is 236.

Technique 2: Binary Method

The binary method involves converting the decimal number to binary and then converting the binary number to octal. The binary number is divided into groups of three digits, starting from the right, and each group is converted to its octal equivalent.

Let's take an example to better understand this technique:

Convert the decimal number 247 to octal.

Solution:

Step 1: Convert the decimal number 247 to binary.

247₁₀ = 11110111₂

Step 2: Divide the binary number into groups of three digits, starting from the right.

111 101 11₂

Step 3: Convert each group to its octal equivalent.

111₂ = 7₈

101₂ = 5₈

11₂ = 3₈

Therefore, the octal equivalent of the decimal number 247 is 375.

FAQs

What is a decimal number?

A decimal number is a base 10 number, meaning it uses 10 digits (0-9) to represent numbers.

What is an octal number?

An octal number is a base 8 number, meaning it uses 8 digits (0-7) to represent numbers.

What is the easiest way to convert decimal to octal?

The easiest way to convert decimal to octal is by using the division method. Divide the decimal number by 8 and write down the remainder. Then, divide the quotient by 8 again and write down the remainder. Repeat this process until the quotient becomes 0. The octal equivalent is the remainders read from bottom to top.

Can I convert decimal to octal using the binary method?

Yes, you can convert decimal to octal using the binary method. Convert the decimal number to binary and then divide the binary number into groups of three digits, starting from the right. Each group is then converted to its octal equivalent. The final answer is the combination of the octal equivalents of each group.

Conclusion

Converting decimal numbers to octal numbers is a simple process once you understand the techniques involved. The division method is the easiest and quickest technique, while the binary method is useful for those who prefer working with binary numbers. By following the examples given in this article, you should be able to convert decimal numbers to octal numbers with ease.