1. The Decimal System.

a. General. In digital technology there are many numbering systems in use. The most common

systems are decimal, binary, octal, and hexadecimal. The decimal system is clearly the most familiar to

us since we use it every day. Reviewing some of its characteristics will help us to better understand the

other numbering systems.

b. Characteristics. The decimal system, also called the base 10 system, is composed of ten numerals

or digits. They are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 and can be used to express any quantity. Decimal numbers

greater than nine are formed by placing numbers in columns to the left of the first digit. Each column has

10 times the value of the column immediately to its right. This method of representing decimal numbers

is called positional notation. The value of a digit depends on its position. For example, consider the

decimal number 357. This number can be written as 300 + 50 + 7 or in scientific notation:

In essence the three carries the most weight and is considered the most significant digit (MSD). The

seven carries the least weight and is called the least significant digit (LSD). Consider as another example

the number 29.35. This number is actually equal to 20 + 9 + .3 + .05 or in scientific notation:

Consider another example, the digit 3 has a different value in each of the following base 10 numbers:

463

731

302

In the right hand position, 3 has the value of 3. In the middle position, 3 has the value 30. In the left

position, 3 has the value 300. 3, 30, and 300 can all be represented by multiplying 3 by the base 10 raised

to a power: