1.3 Digital Number System
Many number systems are in use in digital technology. The most common are the decimal, binary, octal, and hexadecimal systems. The decimal system is clearly the most familiar to us because it is a tool that we use every day. Examining some of its characteristics will help us to better understand the other systems.
Decimal System
Decimal System The decimal system is composed of 10 numerals or symbols. These 10 symbols are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9; using these symbols as digits of a number, we can express any quantity. The decimal system, also called the base-10 system because it has 10 digits.
|
103 |
102 |
101 |
100 |
|
10-1 |
10-2 |
10-3 |
|
=1000 |
=100 |
=10 |
=1 |
. |
=0.1 |
=0.01 |
=0.001 |
|
Most Significant Digit |
|
|
|
Decimal point |
|
|
Least Significant Digit |
Binary System
In the binary system, there are only two symbols or possible digit values, 0 and 1. This base-2 system can be used to represent any quantity that can be represented in decimal or other number system.
|
23 |
22 |
21 |
20 |
|
2-1 |
2-2 |
2-3 |
|
=8 |
=4 |
=2 |
=1 |
. |
=1/2 |
=1/4 |
=1/8 |
|
Most Significant Bit |
|
|
|
Binary point |
|
|
Least Significant Bit |
Binary Counting
The
Binary counting sequence is shown in the table:
