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Let's see if
we can convert some numbers from one base to another. There are many
ways to work with number base conversions. We will be discussing only
one method. Please feel free to use any conversion system with which
you are comfortable.
Don't panic! Yes, it is math. But you can do it! |
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Example 1:
Convert 510
(read 5 base 10) into base 2.
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The Process:
1. Divide the "desired" base (in this case base 2)
INTO the number you are trying to convert.
2. Write the quotient (the answer) with a remainder like you
did in elementary school.
3. Repeat this division process using the whole number from
the previous quotient (the number in front of the remainder).
4. Continue repeating this division until the number in
front of the remainder is only zero.
5. The answer is the remainders read from the bottom up.
510 =
1012 (a
binary conversion) |
Example 2: Convert
14010 to base 8.
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The process is the same as in example
1. The answer is:
14010
= 2148
(an octal conversion)
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Example 3: Convert
11010 to base 16.
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The process remains the same. BUT
there is one problem in base 16 that did not appear in the
examples above. One of the remainders in this division
contains 2 digits (14). You CANNOT allow 2 digits to reside
in one of the place holdings in a number. For this reason,
base 16, which can have six 2-digit remainders (10, 11, 12, 13,
14, 15) replaces these values with alphabetic representations
(10-A, 11-B, 12-C, 13-D, 14-E, 15-F). The answer is:
11010
= 6E16
(a hexadecimal
conversion) |
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