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You are watching: How to convert base 10 to base 8


In number system,

that is an extremely important to have a good knowledge of exactly how to convert numbers from one basic to another base. Here, we will learn just how to convert any given number from basic 10 to base 8.

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Decimal to Octal Conversion-

A offered number have the right to be convert from basic 10 to any other basic using department method and multiplication method.


Following two instances are possible-

Case-01: for Numbers transferring No fractional Part-

division Method is provided to transform such numbers from base 10 to an additional base. The division is performed v the forced base.

Steps To convert From basic 10 to base 8-

division the offered number (in basic 10) v 8 till the an outcome finally left is less than 8. Traverse the remainders indigenous bottom to height to get the required number in base 8.

Case-02: because that Numbers delivering A spring Part-

To convert such numbers from basic 10 to an additional base, real part and fractional component are treated separately.

For actual Part-

The steps affiliated in converting the real component from basic 10 to one more base are very same as above.

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For fountain Part-

Multiplication an approach is supplied to transform fractional part from basic 10 to an additional base. The multiplication is performed through the forced base.

Steps To transform From base 10 To basic 8-

multiply the given portion (in basic 10) v 8. Create the real part and fractional part of the result so acquired separately. Multiply the fractional component with 8. Compose the real part and fractional part of the an outcome so derived separately. Repeat this procedure until the fractional part remains 0. If fractional component does no terminate to 0, discover the an outcome up come as countless places as required.

Required Number in basic 8

= series of real component of multiplication results obtained in the over steps from top to bottom

Also Read- Conversion to base 10


PRACTICE PROBLEMS based on DECIMAL come OCTAL CONVERSION-

Problems-

Convert the complying with numbers from base 10 to base 8-

(1032)10 (1032.6875)10 (172)10 (172.878)10

Solution-

1. (1032)10

(1032)10(?)8

Using department method, us have-

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

2. (1032.6875)10

(1032.6875)10 → ( ? )8

Here, us treat the real part and fractional component separately-

For genuine Part-

The real component is (1032)10 We convert the real component from base 10 to basic 8 using department method exact same as above.

So, (1032)10 = (2010)8

For fractional Part-

The fractional component is (0.6875)10 We transform the fractional part from base 10 to base 8 making use of multiplication method.

Using multiplication method, us have-

Real part Fractional Part
0.6875 x 8 5 0.5
0.5 x 8 4 0.0

Explanation

Step-01:

multiply 0.6875 with 8. Result = 5.5. Compose 5 in real part and 0.5 in spring part.

Step-02:

main point 0.5 with 8. Result = 4.0. Write 4 in real part and 0.0 in spring part.

Since fractional part becomes 0, so us stop.

The fractional component terminates to 0 after 2 iterations. Traverse the real part column from optimal to bottom to acquire the compelled number in base 8.

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

Combining the an outcome of real and also fractional parts, we have-

(1032.6875)10 = (2010.54)8

3. (172)10

(172)10 → ( ? )8

Using department method, us have-

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From here, (172)10 = (254)8

4. (172.878)10

(172.878)10 → ( ? )8

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

For genuine Part-

The real part is (172)10 We convert the real part from basic 10 to basic 8 using department method very same as above.

So, (172)10 = (254)8

For spring Part-

The fractional component is (0.878)10 We transform the fractional component from basic 10 to basic 8 utilizing multiplication method.

Using multiplication method, us have-

Real part Fractional Part
0.878 x 8 7 0.024
0.024 x 8 0 0.192
0.192 x 8 1 0.536
0.536 x 8 4 0.288

The fractional component does no terminates come 0 after numerous iterations. So, let us find the value approximately 4 decimal places. Traverse the real part column from top to bottom to achieve the forced number in basic 8.