Decimal to Octal Conversion | Base 10 to Base 8

Number System Conversions-

 

Before you go through this article, make sure that you have gone through the previous article on Basics of Number System.

 

In number system,

  • It is very important to have a good knowledge of how to convert numbers from one base to another base.
  • Here, we will learn how to convert any given number from base 10 to base 8.

 

 

Decimal to Octal Conversion-

 

A given number can be converted from base 10 to any other base using division method and multiplication method.

 

Following two cases are possible-

 

Case-01: For Numbers Carrying No Fractional Part-

 

  • Division Method is used to convert such numbers from base 10 to another base.
  • The division is performed with the required base.

 

Steps To Convert From Base 10 to Base 8-

 

  • Divide the given number (in base 10) with 8 until the result finally left is less than 8.
  • Traverse the remainders from bottom to top to get the required number in base 8.

 

Case-02: For Numbers Carrying A Fractional Part-

 

To convert such numbers from base 10 to another base, real part and fractional part are treated separately.

 

For Real Part-

 

The steps involved in converting the real part from base 10 to another base are same as above.

 

For Fractional Part-

 

  • Multiplication Method is used to convert fractional part from base 10 to another base.
  • The multiplication is performed with the required base.

 

Steps To Convert From Base 10 To Base 8-

 

  • Multiply the given fraction (in base 10) with 8.
  • Write the real part and fractional part of the result so obtained separately.
  • Multiply the fractional part with 8.
  • Write the real part and fractional part of the result so obtained separately.
  • Repeat this procedure until the fractional part remains 0.
  • If fractional part does not terminate to 0, find the result up to as many places as required.

 

Required Number in Base 8

= Series of real part of multiplication results obtained in the above steps from top to bottom

 

Also Read- Conversion to Base 10

 

PRACTICE PROBLEMS BASED ON DECIMAL TO OCTAL CONVERSION-

 

Problems-

 

Convert the following numbers from base 10 to base 8-

  1. (1032)10
  2. (1032.6875)10
  3. (172)10
  4. (172.878)10

 

Solution-

 

1. (1032)10

 

(1032)10  (?)8

 

Using division method, we have-

 

 

From here, (1032)10 = (2010)8

 

2. (1032.6875)10

 

(1032.6875)10 → ( ? )8

 

Here, we treat the real part and fractional part separately-

 

For Real Part-

 

  • The real part is (1032)10
  • We convert the real part from base 10 to base 8 using division method same as above.

 

So, (1032)10 = (2010)8

 

For Fractional Part-

 

  • The fractional part is (0.6875)10
  • We convert the fractional part from base 10 to base 8 using multiplication method.

 

Using multiplication method, we have-

 

Real partFractional Part
0.6875 x 850.5
0.5 x 840.0

 

Explanation

 

Step-01:

 

  • Multiply 0.6875 with 8. Result = 5.5.
  • Write 5 in real part and 0.5 in fractional part.

 

Step-02:

 

  • Multiply 0.5 with 8. Result = 4.0.
  • Write 4 in real part and 0.0 in fractional part.

 

Since fractional part becomes 0, so we stop.

 

  • The fractional part terminates to 0 after 2 iterations.
  • Traverse the real part column from top to bottom to obtain the required number in base 8.

 

From here, (0.6875)10 = (0.54)8

 

Combining the result of real and fractional parts, we have-

(1032.6875)10 = (2010.54)8

 

3. (172)10

 

(172)10 → ( ? )8

 

Using division method, we have-

 

 

From here, (172)10 = (254)8

 

4. (172.878)10

 

(172.878)10 → ( ? )8

 

Here, we treat the real part and fractional part separately-

 

For Real Part-

 

  • The real part is (172)10
  • We convert the real part from base 10 to base 8 using division method same as above.

 

So, (172)10 = (254)8

 

For Fractional Part-

 

  • The fractional part is (0.878)10
  • We convert the fractional part from base 10 to base 8 using multiplication method.

 

Using multiplication method, we have-

 

Real partFractional Part
0.878 x 870.024
0.024 x 800.192
0.192 x 810.536
0.536 x 840.288

 

  • The fractional part does not terminates to 0 after several iterations.
  • So, let us find the value up to 4 decimal places.
  • Traverse the real part column from top to bottom to obtain the required number in base 8.

 

From here, (0.878)10 = (0.7014)8

 

Combining the result of real and fractional parts, we have-

(172.878)10 = (254.7014)8

 

Also Read- Decimal to Binary Conversion

 

To gain better understanding about Decimal to Octal Conversion,

Watch this Video Lecture

 

Next Article- Decimal to Hexadecimal Conversion

 

Get more notes and other study material of Number System.

Watch video lectures by visiting our YouTube channel LearnVidFun.

Summary
Decimal to Octal Conversion | Base 10 to Base 8
Article Name
Decimal to Octal Conversion | Base 10 to Base 8
Description
Decimal to Octal Conversion- We use division method to convert a given decimal number to octal form. Decimal to Octal Conversion Examples. Convert the given numbers from base 10 to base 8.
Author
Publisher Name
Gate Vidyalay
Publisher Logo
Liked this article? Share it with your friends and classmates now-