Information Technology Reference
In-Depth Information
3 x 10 to the 2nd power + 2 x 10 to the 1st power plus 8 x 10 to the 0 power
or
300 + 20 + 8.
This will be the makeup of our number in base 10 and it will apply to any number we can
consider in the decimal system. But the same makeup will apply to other bases, whether it
is base 2, base 8, base 16 or base 62 for that matter.
Looking at our process of counting from 0 to 23 in the other three bases, you may
have noticed the makeup of each of these number systems. Base 2 has only two elements,
0 and 1 while base 8 uses the 8 elements 0, 1, 2, 3, 4, 5, 6 and 7. Finally hexadecimal
needs 16 characters so we have to add a few more that are not familiar to us, namely A,
B, C, D, E and F. The A would be the equivalent of 10 in base 10, B would stand for 11,
C would represent 12 and you can figure out the other 3 symbols. Thus base 16 uses in
order the 16 elements
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E and F.
If we were to think of a base 62 system, you might realize that we need 62 symbols and
we might use the 10 familiars numbers 0 through 9, the capital letters of the alphabet and
lower case letters and we would have our 62 elements. We won't get into this system but
you can see how different bases systems rely on different combinations of symbols.
Let us now look at three numbers, one in each of our other base systems. These
are
10111 (base 2),
27 (base 8)
and
17 (base 16).
These are all equivalent or equal to 23 in base 10.
10111
can be broken down into
1 x 2 to the 4th power +
0 x 2 to the 3rd power +
1 x 2 to the 2nd power +
1 x 2 to the 1st power +
1 x 2 to the power of 0.
This gives us
16 + 0 + 4 + 2 + 1 = 23.
The number in base 8 of 27 can be broken down into
2 x 8 to the 1st power +
7 x 8 to the power of 0.
This translates into
16 + 7 = 23.
Lastly our number in hexadecimal of 17 is equivalent to
1 x 16 to the 1st power +
7 x 16 to power of 0.
This also becomes
16 + 7 = 23.
