Tag: From Decimal to Octal

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

 

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