Number System | Conversion of Number System

Number System:

The method of writing and expressing numbers using different symbols or basic symbols or numbers (digits) is called the number system. With the help of this number can be easily counted and expressed. In a word, the method of describing and calculating numbers is called the number system.

The number system is a specific expression of numbers.

The number system is a set of rules for expressing numbers that must have the following -

Exact rules for expressing numbers with specific symbols.

Different rules for determining addition, Subtraction, multiplication, division, etc., of numbers.

Precise or complete rules for expressing different forms of numbers such as fractions, positives, negatives, etc.

The total number of digits used to represent a number in the number system is the base of the number. The basis of a number system refers to the total number of numbers or symbols used in that number system.

Types of Number System :

There are two types of number systems based on presentation method -

1. Non-positional number system: 
2. Positional number system:

Non-positional number system: 

A number system that has no local value for numbers. And the value of that number does not change depending on the position. It is called a non-positional number. Although some quality places change over short distances, they do not have a sequence in non-positional numbers.

Non-positional numbers such as v = 5 are captured. So here v is a non-positional number. Again x = 10, l = 50 c = 100 D = 500 M = 1000 etc. Non-positional numbers.

Positional number system:

The positional number system is the number that has a local value and changes value when the place changes. For example, 123 represents the value up to the century, and 3 replaces the deal. The value is changed to decimal, and the actual number changes to 132. 

The positional number system is further divided into 4 parts-

 1. Binary

 2. Octal

 3. Decimal

 4. Hexadecimal

Conversion of Number:

Conversion from decimal to binary/octal/hexadecimal (in case of fractions)

Step-1- First, you have to multiply the number by binary base 2.

Step-2- You have to separate the whole part and the fraction.

Step-3- Multiply the new fraction by base 2 again and separate the whole part and the fraction.

Step-4- Step-1 and step-2 will continue till the fractional part is complete. 1 (00 will come in the fractional part).

Step-5- If the number is repeated, then the work of multiplication has to be done there.

Step-6- If the multiplication process continues indefinitely (even if the fraction is not 1 even after multiplying the base by the base again and again), then after the decimal, it is necessary to take a maximum of 5 cells or as many cells as asked in the question.

Step-7- The desired value or number can be obtained by arranging the whole numbers from top to bottom side by side.

Binary Number:

The binary number system is a variant of the decimal (10-base) number system that we are all familiar with. Binary numbers are significant because they simplify the design of computers and related technologies compared to the decimal system. The binary number system is a system of numbering that employs only two digits—0 and 1—to represent numbers, rather than the digits 1 through 9 plus 0. 

Notice how the numbers 0 and 1 are the same in both systems, but things start to alter at 2. In the binary system, decimal 2 corresponds to the number 10. The 0 symbolizes zero, as you might assume, whereas the 1 indicates two. Here's how to convert from binary to digital. The first digit on the right side of any number can be either 0 or 1. If the second digit is 1, however, the number 2 is shown. If it's zero, it's just zero. The third digit might be either 4 or 0, depending on the situation.

Signed Number :

The use of Positive and negative numbers to solve various mathematical problems. The sign (+ or -) is usually used before the number to indicate whether the number is positive or negative. When a positive or negative sign precedes a number, that number is called a significant number. An additional bit is added before the actual value to denote the number marked in the binary method. This extra bit is called a sign bit. When the symbol bit is 0, the number is considered positive, and if the symbol bit is 1, the number is deemed harmful.

Representation of Marked Numbers: 

There are three methods for representing numbers with negative (-) marks or negative numbers in computer systems. 

Signed magnitude form

 1's Complement form

 2's Complement form

1's Complement:

The number obtained by complementing or reversing each bit of a binary number is called the Complement of 1. The representation of positive numbers in this process is similar to the formation of actual values. In the case of positively marked numbers, the symbol bit 0 is used for the positive symbol, and the remaining 8-bit is used for the data bit. To determine the value of a negatively marked number, one has to select a positively marked number. The value of the negatively marked number is determined by inverting all the bits, including the symbol-bit (i.e. 1 if 0 and 0 if 1). This process also yields different values of +0 and -0, which are inconsistent with reality. 

Binary Subtraction using Complement Numbers:

Binary numbers can be subtracted in two ways with the help of complementary numbers. 

1's Complement and

2's Complement method.

CODE: 

The unique code used to represent different characters, numbers, and several special symbols used in a computer separately to the computer's processor (CPU) is called code. Code is created through encoding. Coding is required for data input. After processing, the output is decoded again. In this way, the code is again converted into letters, numbers or symbols.

This code is formed according to the binary calculation of the electric pulse. When people work, they work in their language using letters or symbols. But the computer does not understand human language, so the computer performs the work by calculating the binary number determined behind this symbol. This is why code is used to make human language helpful to computers. The following are some of the most commonly used codes -

Octal Code

Hexadecimal Code

BCD Code

Alphanumeric Code

ASCII Code

EBCDIC Code 

Unicode

Morse Code

Gray Code etc.

BCD Code: 

BCD means Binary Coded Decimal. We know that a computer is an electrically powered device in the form of a machine. The computer does its internal work in binary. This binary is a symbol of power on means 1 and ability off means 0. The computer understands nothing but this power on and off or 1 and 0. If you write your name, the computer does not know it at all. The computer thinks he is calculating 01010101. But people can't run computers with 010101. For this reason, human languages like abcd or a a a k b have to be converted to binary. 

This sets a binary number for a sound on a computer as opposed to our language. Some of the basic things for running a computer are coded in a limited way of 8 bits. This 8-bit coding system is called BCD code. A total of 256 are in the BCD system. It was later extended.

Alphanumeric Code:

Alphanumeric code is used for many special symbols, including letters, numbers, and various mathematical symbols used in computers. Such as +,>, @, #, &, etc., also numbers like 1,2, 3 ৭, 9, etc, and the letter a i g f a b c d are used. The use of various circuits in digital electronics and modern microcomputers is not limited to numerical characters but also requires the expression, printing, and transmission of alphabets, numbers, special symbols, etc. To meet all these needs, one or more code methods are introduced in computers to express alphabets, numbers, special characters, etc. These are called alphanumeric codes. 

Before Unicode, other digital devices, including computers, had special codes for use, then the most widely used. Because then there was no Unicode system to code all language symbols. This is why alphanumeric codes have emerged for the necessary work and were used the most.

ASCII Code:

The complete form of the word ASCII is American Standard Code for International Interchange,

In 1975, Robert Beamer invented the seven-bit ASCII code. ASCII is a widespread code. It consists of 6 bits with 3 bits on the left as zones and 4 on the right as numeric bits. However, by adding a parity bit to the far left, ASCII is converted to a 4-bit code.

Parity bit

7

3 zone bits

6 5 4

Numeric bits

3 2 1 0

By adding a parity bit to the left of the ASCII-6 code, ASCII is converted to an 8-bit code, known as ASCII-6. The ASCII-8 code can be used to specify 256 unique symbols. At present, ASCII code means ASCII-6.

ASCII code is widely used in various types of computers, especially microcomputers. 

For example, ASCII code transfers alphanumeric data between keyboards, mice, monitors, printers, etc.

EBCDIC Code: 

EBCDIC means Extended Binary Coded Decimal Interchange Code.  

A particular type of alphanumeric code is used in IBM mainframe equipment and large computing systems that deal with large amounts of alphanumeric data. This code differs from ASCII code. This coding method uses eight 8 bits, and the ninth bit is added as a parity bit. The EBCDIC code uses 1111 for numbers 0 to 9, 1100, 1101, and 1110 for letters A to Z and 0100, 0101, 0110, and 0111 for special symbols as zone bits. 28 = 256 letters, numbers, and special characters have been coded through this code.

This code is commonly used on IBM and IBM equivalent computers. For example, IBCM code is used in IBM, mainframe, and minicomputers.