Conversion from any Base Number to Base 10 || Lesson 21 ||Digital Electronics || Learning Monkey ||

2.3K views on YouTube

Wisdomers - Computer Science and Engineering 154 tutorials here

Electronics

Here we will try to understand the Conversion from any Base Number to Base 10.

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 this discussion, we will understand the Conversion from any Base Number to Base 10.

Conversion from any Base Number to Base 10

In our previous discussions on the conversion of a binary number to decimal, the method used to convert binary to decimal is used here also.

Any Base X Number can be converted into Decimal Number by the Sum of the positional weights of each bit in the Base X number.

Not only the Binary, Octal, or Hexadecimal Number any base number can be converted to Base 10.

How to find the positional weights of a digit or bit in base X?

To understand this concept we convert the following bases to base 10.

( 10101 )2
( 675 )8
( 1AF )16
( 022 )3
( 176 )9

Example 1:

( 1010 )2

To convert a Base 2 Number to Base 10 we have to sum the positional weights of every digit (or) bit in the given number.

The conversion of the ( 1010 )2 to Base 10
Example 2:

( 675 )8

To convert a Base 8 Number to Base 10 we have to sum the positional weights of every digit (or) bit in the given number.

The conversion of the ( 675 )8 to Base 10

Example 3:

( 1AF )16

To convert a Base 16 Number to Base 10 we have to sum the positional weights of every digit (or) bit in the given number.

The conversion of the ( 1AF )16 to Base 10 i

Example 4:

( 022 )3

To convert a Base 3 Number to Base 10 we have to sum the positional weights of every digit (or) bit in the given number.

The conversion of the ( 022 )3 to Base 10
Example 5:

( 176 )9

To convert a Base 9 Number to Base 10 we have to sum the positional weights of every digit (or) bit in the given number.

The conversion of the ( 176 )9 to Base 10

Link for playlists:
https://www.youtube.com/channel/UCl8x4Pn9Mnh_C1fue-Yndig/playlists

Link for our website: https://learningmonkey.in

Mail us @ learningmonkey01@gmail.com