Service manual

STP 11-25R13-SM-TG
Q - 8
binary can quickly result in numbers with 20 or more digits. This leads to the use of decimal, octal, and
hexadecimal numbers for the purpose of converting the large binary numbers to shorter, easier-to-use
expressions. Converting a number to a different base is often necessary. A great number of
conversional methods exist, but only a few are useful in practice. The methods used in this text were
selected for their simplicity and practical application.
b. The Decimal System
.
(1) When humans first began counting, 10 fingers were the most convenient means available. It is
reasonable to assume that the 10-digit or decimal system used throughout the civilized world was
developed using man’s 10 fingers. Any number, regardless of how large or small, can be written with just
10 different symbols. These symbols are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
(2) One important feature of all modern number systems is the concept of place value. As you may
recall, the value of a digit depends not only upon the numerical value of that digit, but also upon its place
relative to the decimal point. Look, for example, at the number 42,337. The second digit from the
decimal point is "3" and has the value of 30. The third digit from the decimal point is also "3” but has the
value of 300. See the place value of each digit in the number 42,337 in this explanation.
4 x 10,000 = 40,000
2 x 1,000 = 2,000
3 x 100 = 300
3 x 10 = 30
7 x 1 = 7
42,337 Total
(3) The previous example would have been easier to write using powers of 10. You are already
familiar with powers of 10, but refer to Table Q-7 as necessary.
Table Q-7. Powers of Ten
(4) 10,000 may be written as 10
4
, which means 10 x 10 x 10 x 10. The raised number "4", called
the exponent, indicates how many times to use the base number 10 as a factor. The expression 10
4
is
read as "ten to the fourth power" or simply, "ten to the fourth".
10
5
= 100,000
10
4
= 10,000
10
3
= 1,000
10
2
= 100
10
1
= 10
10
0
= 1