Octal to binary

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Looking to convert octal to binary? Look no further! Our Octal converter is here to save the day. You can use this to convert your data from octal format to binary format in real time. 

Overview

Octal to Binary converter is a very useful tool required by many professionals in the fields of computer engineering, computer science, programming, academia and information technology. 

What exactly are Octal and Binary systems?

Octal number system is the numeral system with base-8. It uses 8 digits to represent data (0-7) while Binary on the other hand, uses two alternating states to code and process data. 

Binary is the default language in which computers process information.  By now, you might be getting the hunch as to why octal is converted into binary. 

Yes! The primary reason is that computers inherently don’t process information in octal format and so if a computer engineer wants to check whether the system he/she designed is working properly, they might feed it data to process directly in binary to keep tabs on its functionality during trials.

Conversion from Octal to Binary number system

There are various direct or indirect methods to convert a octal number into binary number. In an indirect method, you need to convert an octal number into other number system (e.g., decimal or hexadecimal), then you can convert into binary number by converting each digit into binary number from hexadecimal system and using conversion system from decimal to binary number.

Example 1

Let’s convert octal number 205 into a binary number.

First, convert this number into decimal or hex format,
\(= (205)_8\)
\( = (2\times8^2+0\times8^1+5\times80)^8\) or \((010  000  101)_2 \)

Since octal and hex bases are 8 and 16 respectively.
= \((133)_{10}\)   or   \((0  1000  0101)_2\)
= \((133)_{10}\)   or   \((85)_{16}\)

Now, convert it into binary format.
= \( (1\times2^7+0\times2^6+0\times2^5+0\times2^4+0\times2^3+1\times2^2+0\times2^1+1\times20)_2\)   or   \((1000  0101)_2\)
= \((10000101)_2\)

Hold your horses though, there is an elegant direct approach to convert octal numbers to binary format as well. Since there are only 8 numbers \((i.e., 0, 1, 2, 3, 4, 5, 6, \mathrm{and} 7)\) in octal system and its base (i.e., 8) is equivalent to 23=8. So, you can characterize each number of octal in groups of 3 bits in binary format.

Octal to Binary Table

Octal Binary
0 000
1 001
2 010
3 011
4 100
5 101
6 110
7 111

This approach is simple and can also be used to convert binary to octal. The algorithm is broken down below.

  • Use Octal number as input
  • Convert each individual number of octal into binary.
  • There’s your output in binary.

Example 2

Convert octal number \(540\) into a binary number.

According to the algorithm we formulated above, the corresponding binary number will be,

\(= (540)8\)
\(= (101  100  000)2\) 
\(= (101100000)2\)

This is a rather elegant conversion, you can use this for integer and fractional octal numbers too.

If you are also looking for other converters, you can check out our octal to hex converter.

 

 

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Octal to binary

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