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You are watching: Convert from base 10 to base 8


In number system,

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

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Decimal come Octal Conversion-

A offered number can be convert from basic 10 to any other base using department method and also multiplication method.


Following two situations are possible-

Case-01: for Numbers transporting No spring Part-

department Method is provided to convert such numbers from base 10 to one more base. The division is performed through the forced base.

Steps To convert From basic 10 to basic 8-

division the offered number (in basic 10) v 8 until the result finally left is much less than 8. Traverse the remainders indigenous bottom to optimal to acquire the compelled number in basic 8.

Case-02: for Numbers carrying A fountain Part-

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

For real Part-

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

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For fountain Part-

Multiplication technique is supplied to convert fractional component from basic 10 to another base. The multiplication is performed v the required base.

Steps To convert From basic 10 To basic 8-

main point the given fraction (in basic 10) with 8. Create the real part and fractional part of the an outcome so derived separately. Main point the fractional component with 8. Compose the real component and fractional component of the an outcome so obtained separately. Repeat this procedure until the fractional part remains 0. If fractional component does no terminate to 0, discover the result up to as plenty of places together required.

Required Number in basic 8

= series of real component of multiplication results derived in the over steps from peak 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 basic 8-

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

Solution-

1. (1032)10

(1032)10(?)8

Using department method, we have-

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

2. (1032.6875)10

(1032.6875)10 → ( ? )8

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

For genuine Part-

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

So, (1032)10 = (2010)8

For spring Part-

The fractional part is (0.6875)10 We convert the fractional part from basic 10 to basic 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:

main point 0.6875 v 8. Result = 5.5. Compose 5 in real part and 0.5 in spring part.

Step-02:

main point 0.5 through 8. Result = 4.0. Write 4 in real component and 0.0 in fountain part.

Since fractional part becomes 0, so us stop.

The fractional component terminates to 0 after ~ 2 iterations. Traverse the real part column from height to bottom to attain the forced 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 division method, we 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 component separately-

For actual Part-

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

So, (172)10 = (254)8

For fractional Part-

The fractional component is (0.878)10 We transform the fractional part from base 10 to base 8 making use of multiplication method.

Using multiplication method, we 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 not terminates come 0 after number of iterations. So, allow us uncover the value as much as 4 decimal places. Traverse the real part column from optimal to bottom to attain the required number in basic 8.