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How to Convert a Binary Number to a Decimal Number

Converting a Binary Number to a Decimal Number

In order to find topics for articles, I quite often review my site searches to determine those topics that are of interest to my site visitors. During my most recent review, I noticed that quite a number of searches were done on the topic of converting a binary number to a decimal number. So, for those of you who are interested in this topic, I've provided some basic steps in performing the conversion.

1.      Start with the last digit and multiply that digit with 2^0. Note that the power of 0 of any number is always 1.

2.      Continue working from right to left multiply each digit with an incremental increasing power of 2 (i.e. 2^1, 2^2, 2^3, 2^4, etc). 

3.      Repeat step 2 until all digits have been multiplied.

4.      Add the end result of each worked power of 2 for a final answer.

Example: Convert Binary 1010 to a Decimal

Multiply

Result

0 * (2^0)

  0

1 * (2^1)

  2

0 * (2^2) or 2*2   

  0

1 * (2^3) or 2*2*2 

  8

Answer

10

 

Example: Convert Binary 11011 to a Decimal

Multiply

Result

1 * (2^0)           

  1

1 * (2^1)           

  2

0 * (2^2) or 2*2    

  0

1 * (2^3) or 2*2*2  

  8

1 * (2^4) or 2*2*2*2

16

Answer

27

 

Example Convert Binary 111010 to a Decimal

Multiply

Result

0 * (2^0)

  0

1 * (2^1)             

  2

0 * (2^2) or 2*2      

  0

1 * (2^3) or 2*2*2    

  8

1 * (2^4) or 2*2*2*2  

16

1 * (2^5) or 2*2*2*2*2

32

Answer

58

 

Example Convert Binary 1010010 to a Decimal

Multiply

Result

0 * (2^0)

  0

1 * (2^1)             

  2

0 * (2^2) or 2*2      

  0

0 * (2^3) or 2*2*2

  0

1 * (2^4) or 2*2*2*2  

16

0 * (2^5) or 2*2*2*2*2

0

1 * (2^6) or 2*2*2*2*2*2

64

Answer

82

 
Now, that you have a good grasp on the process of the conversion, practice converting binary numbers to decimal numbers. Once you have your answers, you can check those answers with the Decimal/Binary Conversion Tool at http://acc6.its.brooklyn.cuny.edu/~gurwitz/core5/nav2tool.html or take the Decimal/Binary Conversion Quiz at http://acc6.its.brooklyn.cuny.edu/~gurwitz/core5/binquiz.html.


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