
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
235_{8} 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 8^{0 }= 5
3 x 8^{1} = 24
2 x 8^{2} = 128 
Now simply add
these values together.
5 + 24 + 128 = 157
Answer: 235_{8} = 157_{10} 
**Remember:
any number to the zero power equals
one. 
Example 2: Let's
do the problem at the top of this lesson.
Convert 1011_{2} to base 10.
The process is the same as in example
1.
1 x 2^{0 }=
1
1 x 2^{1} = 2
0 x 2^{2} = 0
1 x 2^{3} = 8 
1 + 2
+ 0 + 8 = 11
Answer: 1011_{2} = 11_{10} 

Example 3: Convert
1C4_{16} to base 10.
4 x 16^{0
}= 4
C x 16^{1} = 12 x 16^{1} = 192
1 x 16^{2} = 256 
4 +
192 + 256 = 452
Answer:
1C4_{16} = 452_{10}

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