# Decimal to Octal and Octal to Decimal Conversion with Example

Numbers are the arithmetical symbols used to represent a particular quantity, for counting and making calculations. Over the world, different cultures have introduced and used different symbols for representing numbers. The Tally system was popular for many centuries. The numbers we use today are from the decimal number system. These are also known as Hindu-Arabic numerals. This number system was introduced by Indians. With the coming of Arabs to India for trading, this number system was spread to the outer world and European nation. With the advent of time, many other numerical systems such as the Binary system, octal system, hexadecimal system are introduced. In this article Decimal to Octal Conversion is explained.

## What is a Decimal Number System?

The decimal number system is also known as Denary. It is the extension of the Hindu-Arabic number system. A decimal number system can represent integer and non-integer numbers. It uses ten symbols for representing numbers. They are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. The way of denoting decimal numbers is called ‘decimal notation’.

Decimals are also represented using a decimal separator’.’ example ‘4.5’. By using the infinite sequence of digits after the decimal separator, we can represent the real numbers. It is a positional numerical system also known as the base-10 number system.

### Uses of Decimal Number System

For our day-to-day counting, we use decimal numbers. The decimal number system is the standard system used worldwide for representing numbers. For counting money, physical quantities, etc.. we use the decimal number system. Decimal numbers represent whole numbers in an easy format. It is easy to perform arithmetic calculations using decimal number systems.

These numbers can also be counted and calculated on fingers easily. These numbers are mostly preferred in situations where precise calculations are required. Using the decimal system, numbers such as fractions, real numbers, integers, non-integers, etc.. can be represented.

## What is an Octal Number System?

The octal number system is also known as the base-8 number system. It uses eight different symbols for representing numbers. They are 0, 1, 2, 3, 4, 5, 6, 7. Octal numbers can also be written from binary numbers by grouping the binary digits as groups of three.

It is also a positional number system. In the octal number system, each place value of the digits is the power of eight. Usage of octal numbers can be found in the texts of native Americans and Europeans dating back to the 15th century. Scottish economist, James Anderson coined the term Octal in 1801.

### Uses of Octal Number System

The octal number system was widely used by computer programmers and developers. It is used for programming the processors with a bit size of 24, 16, 36. Compared to binary, octal numbers use less number of bits for representing a number. The octal number system is used within file permission for UNIX systems.

Digital displays also use the octal number system for representing numbers. Octal numbering is also preferred for digital electronics for the error-free and shorter representation of data. As word length of modern computers is not multiple of three, the hexadecimal system is preferred nowadays.

## Decimal to Octal Conversion Method

Decimal and Octal number system both are the positional numerical. As the decimal number system is a standard system for representing numbers, we use this system for writing instructions to a computer. But machines are unable to understand the decimal numbers. Computers can only understand the instructions in binary format. So, it is important to convert the decimal numbers into an octal format for communicating with computers.

To convert a decimal into octal format some steps have to be followed. Firstly, the decimal number has to be divided with 8. Its quotient is written below and the remainder is also noted. Resume the division using the quotient as the dividend until the quotient becomes zero. Note all the remainders from the bottom-up. The number thus formed will be the octal representation of the given decimal number.

### Decimal to Octal conversion Example

To understand the Decimal to Octal conversion let us look at an example. Let us convert the decimal number 256 into octal.

Step1: Divide the number with 8. Until the quotient becomes zero

Step2: Write the remainders from bottom-up to from the octal number.

Thus the Octal format of the decimal number 256 is 400.

## Octal to Decimal Conversion Method

The octal number system is most popular among electronic systems and digital displays. But in our daily life, we use decimal numbers for counting and arithmetics. So, to perform the arithmetic calculations on the Octal number, it has to be converted into decimal format. It is important to know the conversion of octal numbers into decimal numbers.

For conversion of Octal to decimal numbers, some steps have to be followed. As the octal number system is the base-8 number system, each place value is the power of eight. For converting it into a decimal format, each decimal digit has to be multiplied with 8 raised to the power equal to the place value. Then sum all the multipliers.

### Octal to Decimal Conversion Example

To understand the octal to decimal conversion let us look at an example. Let us convert the octal number (234)_{8} into a decimal format.

The first step in the conversion is to multiply the decimal digits with the powers of eight according to their place values.

= 2×8^{2} + 3×8^{1} +4×8^{0}

= 2×64 + 3×8 + 4×1

= 128 + 24 + 4

=156

Thus the decimal representation of the given octal number is (156)_{10}

The octal numbers are represented with a radix 8 whereas the decimal numbers are represented with a radix 10.

The roots of various number systems used today lie in the Hindu-Arabic number system. As the languages used by human interpretation and that of machines are different, various formats of number systems are introduced for easy communication between the machines and humans. Some of the other number systems are the binary number system, hexadecimal number system, ASCI representations, etc…

Though the numbers are written in different formats, internally computers convert them into a binary format using encoders. All the data in the electronic systems is stored in the form of binary digits. Many online converters are also available. Convert the given octal number 67 into decimal number format.