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Change a number from any base
back to base 10:

The computer is representing a number from the keyboard by a pattern of ON and OFF signals represented by 1011.  What number was typed at the keyboard to produce this pattern?

Let's see how we can quickly convert numbers back to base 10 so that they will have more meaning to us humans.

 

Example 1:  Convert 2358 into base 10.

The Process:
Above each of the digits in your number, list the power of the base that the digit represents.  See the example on the left.  It is now a simple process of multiplication and addition to determine your base 10 number.  In this example you have
5 x 80 = 5  
3 x 81 = 24
2 x 82 = 128
Now simply add these values together.
5 + 24 + 128 = 157
Answer: 2358 = 15710 

**Remember: any number to the zero power equals one.

 

Example 2:  Let's do the problem at the top of this lesson.
                     Convert 10112 to base 10.

The process is the same as in example 1.  

1 x 20 = 1  
1 x 21 = 2
0 x 22 = 0
1 x 23 = 8 
  1 + 2 + 0 + 8 = 11

  Answer:  10112 = 1110

 

Example 3:  Convert 1C416 to base 10.

4 x 160 = 4  
C x 161 = 12 x 161 = 192
1 x 162 = 256
4 + 192 + 256 = 452

Answer: 1C416 = 45210

 

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