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In number system,

the is very important to have actually a an excellent knowledge of just how to transform numbers native one basic to an additional base. Here, we will learn how to convert any kind of given number from base 10 to basic 8.

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Decimal come Octal Conversion-

A given number have the right to be convert from basic 10 to any type of other base using division method and multiplication method.


Following two cases are possible-

Case-01: because that Numbers carrying No fractional Part-

division Method is provided to transform such number from basic 10 to another base. The division is performed v the required base.

Steps To convert From basic 10 to basic 8-

division the given number (in base 10) v 8 till the an outcome finally left is much less than 8. Traverse the remainders from bottom to peak to obtain the forced number in base 8.

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

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

For genuine Part-

The steps connected in converting the real component from base 10 to an additional base are exact same as above.

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For spring Part-

Multiplication an approach is used to convert fractional part from basic 10 to an additional base. The multiplication is performed with the required base.

Steps To convert From basic 10 To basic 8-

multiply the given fraction (in basic 10) through 8. Create the real part and fractional component of the an outcome so obtained separately. Main point the fractional component with 8. Compose the real part and fractional part of the an outcome so obtained separately. Repeat this procedure till the fractional component remains 0. If fractional part does not terminate to 0, discover the result up come as numerous places together required.

Required Number in base 8

= collection of real component of multiplication results derived 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 complying with numbers from basic 10 to basic 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 actual Part-

The real part is (1032)10 We transform 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 convert the fractional part from basic 10 to basic 8 using 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 through 8. An outcome = 5.5. Compose 5 in real part and 0.5 in spring part.

Step-02:

multiply 0.5 through 8. Result = 4.0. Compose 4 in real component and 0.0 in fractional part.

Since fractional component becomes 0, so we stop.

The fractional part terminates to 0 after ~ 2 iterations. Traverse the real component column from height to bottom to attain the forced number in basic 8.

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

Combining the an outcome of real and 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, we treat the real component and fractional part separately-

For actual Part-

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

So, (172)10 = (254)8

For fractional Part-

The fractional component is (0.878)10 We convert the fractional component from basic 10 to basic 8 making use of 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, permit us find the value as much as 4 decimal places. Traverse the real component column from height to bottom to attain the compelled number in base 8.