# Binary to Octal and Octal to Binary Conversion with Example

A numerical system gives the mathematical notation for representing the numbers using digits, symbols, etc…Hindu-Arabic Numerical System is widely accepted today all over the world for representing numbers. This system was developed in India. Making this numerical system as basic many positional numbering systems such as Binary Number System, Octal Number System, Hexadecimal Number System, etc.. are invented. Al these numbering systems have there own advantages and applications. The binary number system is widely used in digital electronics. The working of the electrical circuits can be explained using binary numbers. It is useful to know the relationship between all these positional systems. In this article Binary To Octal conversions are explained.

## What is a Binary Numbering System?

The binary number system is also known as the base-2 number system. It uses two symbols to represent the numbers. They are 0 and 1. It was developed from the Hindu-Arabic numerals. It is a positional numbering system. Each digit in binary representation is known as a bit. A combination of four bits is called a Nibble. Eight bits form a Byte.

### Uses of Binary Number System

Binary Numbers system is very useful in digital computers. It helps in the easy implementation of electronic circuits using logic gates. As computers can only understand o’s and 1’s, this number system is used to implement electronic circuits using ON and OFF logic.

Computer programmers and developers use binary numbering for programming. In modern computers, all the data is stored in the form of binary representation. For digital communication, data is transmitted in the form of binary bits. Digital electronics, CDs, Displays, etc.. uses data in the form of binary bits.

## What is an Octal Numbering System?

Emanuel Swedenborg discovered octal Numbering in 1716. The term octal was coined by James Anderson, in 1801. It is also known as the base-8 numbering system. It uses 8 symbols to represent numbers. They are 0, 1, 2, 3, 4, 5, 6, 7 . Three binary bits form an octal digit.

### Uses of Octal Numbering System

The octal number system was derived from the binary number system. It showed an easy way of representing larger binary numbers. In early computer systems such as IBM Microframes, UNIVAC 1050, etc.. used octal numbering system for computing as they employed 6-bit, 12-bit, and 16-bit words.

This numbering system proved to be very useful for display consoles. For displaying these numbers, low-cost displays such as nixie tubes, seven-segment displays can be used as consoles. Whereas binary displays are complex, decimal displays require extra hardware and hexadecimal displays require extra numerical.

In modern computing, the octal number system is preferred as it uses less number of digits and easy to display on digital screens. This type of representation is also used for floating points.

In Aviation, to distinguish different aircraft on the radar screen, the transponders present on aircraft transmit code in the form of octal digits.

## Binary to Octal Conversion Method

Both binary numbers and octal numbers are positional number systems. Each digit of a binary number is known as a bit. Octal digit is formed by grouping 3 binary bits. Each of the octal digits is represented using 3 bits.

For conversion of Binary number into Octal, the given bitstream should be divided into groups with 3-its in each. After this, the Octal number equivalent to the binary bits is taken from the conversion table. There are many other methods for conversion of Binary number into Octal, but this is the easiest method used.

### Binary to Octal Conversion With Example

To understand this conversion, let us look at an example. Let us convert the binary number ‘01010001110’ into an Octal number.

Step1: Starting from the right-side, group the binary bits with 3-bits in each group. If there are leftover bits at the end, add zeroes.

001 |010 |001 |110

Here, after grouping the bits from the right-side, ’01’ is remained. To make it octal an extra zero is added at the end.

Step2: Refer to the conversion table and note down the octal equivalent of the binary bits.

From the table, the octal equivalents for the given number are-

110 = 6

001 = 1

010 = 2

001 = 1

Thus, the Binary To Octal conversion of the given number is = (1216)_{8}. Octal numbers are represented with a base-8.

## Octal to Binary Conversion Method

For interpretation of the data and storing it in memory, the computer systems convert them into binary format. So, it is important to understand the conversion.

For octal to binary conversion, it is important to know the conversion table. Every octal digit can be represented in a binary format using a 3-bit combination.

### Octal to Binary Conversion With Example

Let us convert an octal number (563)_{8} into binary format. The step in conversion is to write down the 3-bit binary equivalent of each octal digit from the conversion table.

563 = 101 | 110 | 011

Thus, the binary conversion of the given number is ‘101110011’

### Encoder for Code-Conversion

Encoders are the combinational circuits used for the conversion of one form of data into another. Encoders are usually used as code- converters. There are encoders available for the conversion of decimal numbers to binary, Hexadecimal numbers to binary, etc…

For programming, the computer programmer writes the code using the octal numbering format. But computers can only interpret instructions in the form of binary format. So, for the proper functioning of electronic systems, encoders are required. There are many online converters available that are used for easy conversions.

Octal To Binary Encoders are used as code converters. This Encoder consists of 8 input lines and three output lines. Here, when an octal number is given as input, it gives a 3-bit binary converted number as output. At a time only one input is high for this encoder.

The truth Table of the Encoder is given below.

As the processors have 4-bit, 8-bit, 16-bit, 32-bit data buses, and memory cells, the use of the octal number system helps the processor in faster operation. There are inbuilt code converters available for hardware systems. The radix 8 used for denoting a number as Octal. What is the binary representation of the octal number (923)_{8}?