Number System in Computer: UGC NET Paper 1 and Study Material
A number system may be defined as a way to write to express numbers. Using digits or other symbols to represent numbers consistently is known as a number system. A number system is used in computers to represent data and carry out machine-level operations. Binary, octal, decimal, and hexadecimal systems are commonly used by computers. It is a mathematical notation for depicting numbers of a particular set by using numbers and alphabets in a prescribed manner. It gives a distinct graphical representation also of each number and represents the arithmetic and algebraic structure of the figures.
The number system is a topic that is surely asked in the UGC-NET Paper 1 examination. The number system uniquely depicts every number representing the different combinations of numbers.
In this article, learners will be able to understand the following:
- Number System Meaning
- What is Number System in Computers?
- Types of Number Systems in Computer
- Relationship Between Several Number Systems
- Number System Conversion
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Number System Meaning
A number system is a form of representing or naming numbers. There are several kinds of number systems in math, such as decimal numbers, binary numbers, octal numbers, and hexadecimal number systems.
The digit's value depends on three aspects, the digit, its position in the number, and the base of the number system. Number system can be used for mathematical reasoning codes.
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What is Number System in Computers?
The Number System in computers is also called an ICT number system. Numbers or letters are entered into the computer and translated into numbers. There is a conversion taking the place of the data entered by individuals and its interpretation by the computer's decoding method.
Types of Number Systems in Computer
There are several types of number systems in a computer that is operated, and all have a specific purpose. The computer supports four types of number systems: binary, octal, decimal, and hexadecimal.
Decimal Number System
The decimal number system is the most commonly used. It has 10 digits from right to left, 0-9, where the value increase exponentially by increasing the power with the consecutive rise in the power of 10.
For, eg.
9632
= (9*(10^3))+(6*(10^2))+(3*(10^1))+(2*(10^0)
= 9000+600+30+2
Binary Number System
There are several facts necessary to know about the binary system to understand about binary number system better.
- This is the most basic unit of storage in a device, represented by a bit.
- This is used to represent any information in a computer.
- The numbers we recognize in a computer are represented by an electric signal that is either on or off, known as transistors.
- 1 or 0 in a binary number system represents on and off. 0 and 1 describe every number, where 0 is the lower rate, and 1 is the higher rate.
Conversion of a Binary Number to a Decimal System
11010
={1*(2^4)}+{1*(2^3)}+{0*(2^2)}+{1*(2^1)}+{0*(2^0)}
=16+8+0+2+0
=2610-Ans.
Explanation
- Starting from the left to the right corner, every single digit is multiplied by the powers of 2, increasing consecutively.
- The same is then solved to get the numeric representation of the binary number.
Conversion of Decimal to Binary Number
2610
|
number |
Divided by |
remainder |
|
112 |
2 |
0 |
|
56 |
2 |
0 |
|
28 |
2 |
0 |
|
14 |
2 |
0 |
|
7 |
2 |
1 |
|
3 |
2 |
1 |
|
1 |
- |
- |
Ans. 1110000
Octal Number System
As the name suggests, the base of these numbers is eight numbers. The digits present in this are 0,1,2,3,4,5,6,7.
Every place in the octal number has the power of base as 0, where the last digit has the x power of command. It is applied when the number of bits is a multiple of 3. It was introduced to make the binary number system more compact.
Conversion from Octal to Binary
125708
= {(1*84)+(2*83)+(5*82)+(7*81)+(0*80)}*10
=(4096+1024+320+56+0)*10
=549610
Conversion of Binary to Octal
1010111100
=(1010111100)*2
=(001 010 111 100)*2
= 1274*8
Hexadecimal Number System
The hexadecimal number is distinct from the rest of the number systems. It is a much more compact way of representing numbers on a computer using only 4 bits. It uses 16 symbols, of which 10 are numbers from 0-9, and letters A, B, C, D, R, and F are taken as extra symbols.
Converting Hexadecimal to Binary
27FB*16
=2*163+7*162+15*161+10*16
=8192+1792+ 240+10
=1023410
Relationship Between Several Number Systems
The relationship of the few number systems is the relationship of the different number systems, for example, binary, decimal, octal, and hexadecimal; these differ from each other and can be easily converted from one to another. The knowledge of relations between them is very important in computer science and engineering, wherein more than one number system is applied for the representation, processing, and storage of data.
|
Hexadecimal(base 16) |
Decimal (base 10) |
Octal(base 8) |
Binary(base 2) |
|
0 |
0 |
0 |
0000 |
|
1 |
1 |
1 |
0001 |
|
2 |
2 |
2 |
0010 |
|
3 |
3 |
3 |
0011 |
|
4 |
4 |
4 |
0100 |
|
5 |
5 |
5 |
0101 |
|
6 |
6 |
6 |
0110 |
|
7 |
7 |
7 |
0111 |
|
8 |
8 |
10 |
1000 |
|
9 |
9 |
11 |
1001 |
|
A |
10 |
12 |
1010 |
|
B |
11 |
13 |
1011 |
|
C |
12 |
14 |
1100 |
|
D |
13 |
15 |
1101 |
|
E |
14 |
16 |
1110 |
|
F |
15 |
17 |
1111 |
Conversion of the Number System in Computer Organization
Number system conversion refers to the process of converting a number from one base to another, such as from binary to decimal or hexadecimal to binary. This conversion is important in fields like computer science and digital electronics, where different number systems are used to represent data in various formats.
Binary to Decimal
To convert from **binary to decimal**, start by writing down the binary number and identifying each digit's position (starting from the right). Multiply each digit by 2 raised to the power of its position, then sum all the results to get the decimal equivalent. For example, the binary number 1101 converts to decimal as \( 1 \times 2^3 + 1 \times 2^2 + 0 \times 2^1 + 1 \times 2^0 = 13 \).
Decimal to Binary
To convert from **decimal to binary**, divide the decimal number by 2 and record the remainder. Repeat the division for the quotient until it reaches 0, then write the remainders in reverse order to get the binary equivalent. For instance, to convert 13 to binary, divide 13 by 2 (remainder 1), 6 by 2 (remainder 0), 3 by 2 (remainder 1), and 1 by 2 (remainder 1), resulting in binary 1101.
Decimal to Hexadecimal
To convert from **decimal to hexadecimal**, divide the decimal number by 16 and record the remainder, which will be a value between 0 and 15. If the remainder is 10 or higher, use the corresponding letter (A for 10, B for 11, etc.). For example, to convert 254 to hexadecimal, divide 254 by 16 (remainder 14, which is E) and 15 by 16 (remainder 15, which is F), so the hexadecimal equivalent is FE.
Hexadecimal to Decimal
To convert from **hexadecimal to decimal**, expand the hexadecimal number by multiplying each digit by 16 raised to the power of its position, starting from 0 on the right. Sum all the results to get the decimal value. For example, the hexadecimal number 1A3 converts to decimal as \( 1 \times 16^2 + 10 \times 16^1 + 3 \times 16^0 = 1 \times 256 + 10 \times 16 + 3 = 419 \).
Computers can comprehend and manipulate numbers thanks to the number system. It enables computers to store information, perform mathematical operations, and obey our commands.
The System of Binary Numbers
There are just two numbers in the binary number system: 0 and 1. Similar to a light switch that is either on (1) or off (0), computers use this system because it is straightforward and corresponds to how they turn things on and off.
System of Decimal Numbers
With digits ranging from 0 to 9, this is the number system we utilize on a daily basis. In order to make binary numbers easier for people to understand, computers occasionally convert them to decimal numbers.
System of Octal Numbers
Numbers 0 through 7 are used in the octal system. It makes long binary numbers shorter and makes computer programs easier to read and use.
The System of Hexadecimal Numbers
This system displays values using letters A through F and numbers 0 through 9. Computer programmers frequently use it because it's a fast way to write big binary numbers.
The Significance of Number Systems
Computers rely on number systems to help them understand what needs to be done. The computer wouldn't be able to play games, save images, or solve math problems without them!
Conclusion
The number system, although not directly applicable in our daily lives but the knowledge about the conversions and several number systems, helps develop various technologies. This helps in coding and developing multiple applications through the coders. There are four types of the number system, binary number system, hexadecimal number system, decimal number system, and octal number system, which need to be studied.
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Major Takeaways for UGC NET Aspirants
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Number System in Computer Previous Year Questions
- Consider the given number (45)y where y is the base of the number. Some of the possible values of y are given below.
Options. A. 5
- 6
- 7
- 8
Ans. B, C, and D only