converts the result back to a decimal numeral, and then displays that numeral for you. All of
the conversions and calculations, all of the electronic switching actions and manipulations
take place out of your sight, at incredible speed.
Are you confused?
Table 1-2 compares numerical values in the base-ten, base-two, base-eight, and base-sixteen systems from
zero to sixty-four. From this table, you should be able to figure out (with a little bit of thought and scrib-
bling) how to convert larger decimal numerals to any of the other forms. Fortunately, there are plenty of
computer programs and Web sites that will do such conversions for you up to millions, billions, and
trillions!
Here’s a challenge!
Convert the hexadecimal numeral 2D03 to decimal form. Don’t use a computer or go on the Internet to
find a Web site that will do it for you. Grind it out the long way.
Solution
To solve this, you need to know the place values. The digit farthest to the right represents a multiple of one
(that is, just itself ). The next digit to the left represents a multiple of sixteen. After that comes a multiple
of two hundred fifty-six (or sixteen times sixteen). Then comes a multiple of four thousand ninety-six
(sixteen times two hundred fifty-six). Note that D represents thirteen. Thinking in the decimal system,
you can figure it out as follows.
- In the ones place you have 3, so you start out with that
- In the sixteens place you have 0, so you must add zero times sixteen, which is zero, to what you
have so far - In the two hundred fifty-sixes place you have D which means thirteen, so you must add thirteen
times two hundred fifty-six, which is three thousand three hundred twenty-eight, to what you
have so far - In the four thousand ninety-sixes place you have 2, so you must add two times four thousand
ninety-six, which is eight thousand one hundred ninety-two, to what you have so far
Because there are no digits to the left of the 2, you are finished at this point. The final result, expressed as
a sum in decimal numerals, is
3 + 0 + 3,328 + 8,192 = 11,523One more thing ...
Are you getting tired of reading numbers as words? In the rest of this book, we’ll be dealing
in the decimal system exclusively. So we’ll start using numerals to represent specific quantities
most of the time. We won’t have to worry about ambiguity that could result from an alterna-
tive radix such as eight or sixteen. Numerals will also come in handy when numbers get large
or “messy.” That’s one of the reasons why numerals were invented!
The Counting Base 15