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Hexadecimal (Base 16)
(Page 2 of 2)
Hexadecimal to Binary Conversion
To convert a Base16 number
into its binary equivalent, simply convert each Base16
digit into its 4-bit binary equivalent, and then add
up the value of the 1bits. Remember, all four bits
must be used even if the binary number begins with zeros. Follow
the example below to understand this conversion better.
As you can see, so long as you can
convert a Base16 number into its binary equivalent and
then add up the base 10 numbers that the 1-bits represent,
you can easily convert any Base16 number into its Base10
equivalent.
![[spacer]](1p.gif)  A Hex Shortcut
Of course we could let you go away from hexadecimal math without showing you a quicker way of doing base 16 to base 10 conversions. This method requires a bit more understanding of exponents. As you learned about binary math, each column that binary number represents from right to left increases in value by power of 2. Therefore the first column represents 2^0, or 1. The next column represents 2^1, or 2. The column after that represents 2^2, or 4. The same kind of "conversion chart" can be made with Base 16. Instead of using powers of 2, we will instead use powers of 16. Building our chart from right to left our first column would have a value of 16 ^0, or 1. Our next column would have a value of 16 ^1, or 16. Our third column would have a value of 16^2, or 256. Refer to the charts to see how this should be constructed.
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To perform a conversion, we start
with a blank hex conversion chart, like Table 6.
Base 10 values are shown in ( ) for each place column.
Table 6: Blank Hexadecimal Conversion Chart
Place
|
16^3 (4096)
|
16^2 (256)
|
16^1 (16)
|
16^0 (1)
|
Value
|
|
|
|
|
For example, if we needed
to convert the Base 16 number CC3Fh into Base 10, we would begin by
placing each digit into the chart from right to left, as shown in Table 7.
Table 7: Conversion of Hexadecimal Value CC3F
Place
|
16^3 (4096)
|
16^2 (256)
|
16^1 (16)
|
16^0 (1)
|
Value
|
C
|
C
|
3
|
F
|
Now, we multiply each digit’s
Base 10 value by its Base 16 column value, then add the results, like
so:
(12 x 4096) + (12 x 256)
+ (3 x 16) + (15 x 1) = 52,287
The Trick Explained
Now, to convert a hexadecimal number we simply place our digits starting from right then moving to the left. We then use the same method that we learn about in binary math. This time we will take the base 10 values of the digits and multiply by the value of the column. You then add up all of these values. And Viola’! You have the Base10 equivalent of your Base16 number. |
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