Explanation:
The use of numerical systems arose from the need of man to improve certain mathematical calculations as time goes.
Several factors demanded the study and application of mathematical operations using decimal numbers. Among these factors, technological advancement essentially from the first experiments in the use of electronics.
There are several numeric systems, but four of them stand out: decimal, binary, octal and hexadecimal.
The decimal system is used every day in countless ways and, no doubt, is the most important number system. He has ten digits with which can form any number through the law.
Non-decimal systems such as binary, octal and hexadecimal are critical in the areas of digital and computer techniques. Through these systems is possible to perform logical combinations and working with computer programming languages. This article will show the link between the logical circuits and these numbering systems.
2 - The Binary Numbering System
The binary numbering system is composed of only two digits:
Zero (0)
One (1)
To represent zero amount using the number 0; to represent a quantity, use the digit 1.
Assuming you need to represent the number two. Which digit you can use, if there is no number 2 in that system?
We have the following response. In the decimal system, we do not have the number ten and represent the amount of ten using the digit 1 followed by the digit 0. In this case, the number 1 means that we have a group of ten and the digit 0, no drive, which means ten.
In the binary system, do likewise. For you the amount of two, we use the digit 1 followed by the digit 0. The figure 1 means that there is a group of two elements and 0, a group of any unit, thus representing the number two.
The table below helps us to understand the differences between the decimal and binary system, using this rule. The number sequence displayed to the number nine.
Decimal
Binary
0
0
1
1
2
10
3
11
4
100
5
101
6
110
7
111
8
1000
9
1001
2.1 - System Conversion binary to Decimal System
To better understand the conversion we use a decimal number either, for example, 356. This number means:
3 x 100 + 5 x 10 + 6 x 1 = 356
Hundred ten unit
3 x 10 � + 5 x 10 � 6 x 10 + 10 = 356
We realize that the least significant digit (6) multiplies the unit (1), the second digit (5) multiplies the ten (10) and the most significant (3) multiplies the hundred (100). The sum of these results will represent the number.
In General, the formatting rule of a number is the sum of each digit multiplied by the corresponding base (in the example, the number ten) high for an index as the positioning of the digit in the number.
In another situation, we will use a binary number, for example, the number 101. We can conclude that it is equivalent to number 5 in the decimal system. Using the concept of a number, we will convert the number to the decimal system as follows:
1 0 1
1 x 2� + 0 x 2� + 1 x 2