Page 30 - Appplied Mathematics for the Petroleum and Other Industries, 5th Edition

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8

Advanced Math Concepts

OBJECTIVES
Upon completing chapter 8, the student will be able to—
1. Identify binary devices that have only two states.
2. Write numbers with value in binary format.
3. Compare various number systems with specific base numbers.
4. Add, subtract, multiply, and divide logic numbers.
5. Create octal numbers from binary numbers.
6. Create hexadecimal numbers from binary numbers.
7. Prepare numbers in ASCII format.
8. Write numbers in BCD and Gray code format.

INTRODUCTION
The first chapter of this manual pointed out that our numbering system is based
on the ten fingers on our hands. Because we have ten fingers and it is easy to count
on them, it is logical that we base our numbering system on 10. Later, Arabic-
speaking scholars developed this primitive system into what we now term the
base 10, or decimal, numbering system. In the base 10 system, characters begin
at 0 and end at 9. To count above 9, we create the double-digit number of 10. In
the number 10, 1 represents the value ten and the 0 represents the value one. Put
another way, the number 10 represents zero ones and one ten. We commonly refer
to this number as representing the quantity ten. When we say the number, we
normally don’t say, “one ten and zero ones”; instead, we abbreviate it simply to ten.
Now, consider the number 203. In this case, 2 is in the hundreds column, 0
is in the tens column, and 3 is in the ones column. So, the number 203 represents
2 hundreds, 0 tens, and 3 ones. However, we simply say that this number is two
hundred-three. Notice that the place of the numbers in the base 10, or decimal,
numbering system shows their relative value.
Thus, the ones are in the right-most column. Then, moving one column
at a time from right to left, come the tens, the hundreds, the thousands, the ten
thousands, and so on. For example, the number 34,895 has 5 ones, 9 tens, 8
hundreds, 4 thousands, and 3 ten thousands. Notice that each succeeding column
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is a multiple of 10—that is, 10 is ten ones, 100 is 10 tens, 1,000 is 10 hundreds,
and so on. Since the base number in the decimal system is 10, number values
can be shown in columns (table 8.1).
The example decimal number is written as 3,634,209 and is read as three
million, six hundred thirty-four thousand, two hundred nine. In reality, this
number results from adding seven numbers: 3,000,000 + 600,000 + 30,000 +
4,000 + 200 + 00 + 9. The placement of the numbers signifies their relative value
in this system. When saying or writing a complete number, we abbreviate it.
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