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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?
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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.
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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.
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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 |
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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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