Conversion of Numbers from One Base to Other || Lesson 23 || Digital Electronics || Learning Monkey

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Here we will try to understand the Conversion of Numbers from One Base to Other.

In our discussion on Different Types of Number System Conversions, we have discussed that in order to convert a number in Base X to Base Y first we have to convert Base X number to Base 10, and then we have to convert Base 10 number to Base Y.

In our discussion on Conversion from any Base Number to Base 10 we have converted Base X to Base 10.

We also discussed the second part of the Base X to Base Y conversion where Base10 Number is converted into Base Y.

Conversion of Numbers from One Base to Other:

To understand the conversion of Base X Number to Base Y we will consider the following examples.

1. ( 022 )3 to ( ) 5

2. ( 422 )5 to ( )9

3. ( 57 )8 to ( )2

Example 1:

( 022 )3 to ( ) 5

To convert ( 022 )3 to ( ) 5 first we have to convert ( 022 )3 to ( ) 10 then we have to convert ( )10 to ( ) 5.

Conversion of ( 22 )3 to ( ) 10.

Conversion of ( 8 )10 to ( ) 5
Example 2:

( 422 )5 to ( )9

To convert ( 422 )3 to ( ) 5 first we have to convert ( 422 )5 to ( ) 10 then we have to convert ( )10 to ( ) 9.

Conversion of ( 422 )3 to ( ) 10.

Conversion of ( 112 )5 to ( ) 9.

Example 3:

( 57 )8 to ( )2

To convert ( 57 )8 to ( ) 2 first we have to convert ( 57 )8 to ( ) 10 then we have to convert ( )10 to ( ) 2.

Conversion of ( 57 )8 to ( ) 10.

Conversion of ( 47 )10 to ( ) 2.

This is how a Base x Number is converted into Base Y.

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