Decimal Number System
Overview - Number Systems
Probably the biggest stumbling block most beginning programmers
encounter when attempting to learn assembly language is the common use of the
binary and hexadecimal numbering systems. Understanding these numbering systems
is important because their use simplifies other complex topics including boolean
algebra and logic design, signed numeric representation, character codes, and
packed data.
Microcontrollers don't use the decimal system to read and write
numbers. Instead, they use a binary or two's
complement numbering system. To understand the limitations of computer
arithmetic, you must understand how computers represent numbers.
There are three number bases commonly used in PICBASIC. These
are:
| Name |
Base |
Symbol |
| Binary |
Base 2 |
% |
| Decimal |
Base 10 |
none |
| Hexadecimal |
Base 16 |
$ |
The Decimal Number Base Systems
The Decimal Number System uses base 10. It includes the digits
from 0 through 9. The weighted values for each position is as follows:
| Power of 10: |
107 |
106 |
105 |
104 |
103 |
102 |
101 |
100 |
| Value: |
10000000 |
1000000 |
100000 |
10000 |
1000 |
100 |
10 |
1 |
You have been using the decimal (base 10) numbering system for
so long that you often take it for granted. When you see a number like
"123", you don't think about the value 123. Instead, you generate a
mental image of how many items this value represents. In reality, however, the
number 123 represents:
-
|
(1 * 102) + (2 * 101) + (3 * 100) =
(1 * 100) + (2 * 10) + (3 * 1) =
100 + 20 + 3 =
123
|
| 
