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Number conversion is the process of converting a numerical value from one number system to another. The two main number systems mentioned in the keywords are binary and decimal.
It plays a crucial role in computer science, digital electronics, and mathematics, ensuring seamless data processing and communication between machines and humans. Various conversion techniques, including division, multiplication, and positional notation, make it easier to switch between number systems efficiently.
Number System Conversion is the process of changing a number from one numerical system to another, such as decimal to binary, binary to octal, or hexadecimal to decimal. Number System Conversion involves changing a number from one base to another, such as binary (base 2), decimal (base 10), octal (base 8), and hexadecimal (base 16).
This conversion is essential in computer science, digital circuits, and data processing to ensure compatibility between different systems.
Some common number conversions include:
Each system has its unique way of representation, and conversions follow specific rules to maintain accuracy. Learning these number system conversions helps in coding, electronics, and mathematical calculations, making it a fundamental concept in technology and engineering.
| Binary Numbers | Octal Numbers | Decimal Numbers | Hexadecimal Numbers |
| 0000 | 0 | 0 | 0 |
| 0001 | 1 | 1 | 1 |
| 0010 | 2 | 2 | 2 |
| 0011 | 3 | 3 | 3 |
| 0100 | 4 | 4 | 4 |
| 0101 | 5 | 5 | 5 |
| 0110 | 6 | 6 | 6 |
| 0111 | 7 | 7 | 7 |
| 1000 | 10 | 8 | 8 |
| 1001 | 11 | 9 | 9 |
| 1010 | 12 | 10 | A |
| 1011 | 13 | 11 | B |
| 1100 | 14 | 12 | C |
| 1101 | 15 | 13 | D |
| 1110 | 16 | 14 | E |
| 1111 | 17 | 15 | F |
Number system conversion is essential for computer processing, programming, and digital electronics. It helps in translating numbers between binary, decimal, octal, and hexadecimal systems, ensuring smooth communication between humans and machines.
The base 2 number system, also known as the binary number system, uses only two digits: 0 and 1. It is widely used in computers and digital circuits for data processing and storage.
The eight types of numbers in mathematics are Natural Numbers, Whole Numbers, Integers, Rational Numbers, Irrational Numbers, Real Numbers, Complex Numbers, and Prime Numbers. Each type has unique properties used in different calculations.
To convert 987 into binary, divide the number by 2 repeatedly and note the remainders:
987 ÷ 2 = 493 remainder 1
493 ÷ 2 = 246 remainder 1
246 ÷ 2 = 123 remainder 0
123 ÷ 2 = 61 remainder 1
61 ÷ 2 = 30 remainder 1
30 ÷ 2 = 15 remainder 0
15 ÷ 2 = 7 remainder 1
7 ÷ 2 = 3 remainder 1
3 ÷ 2 = 1 remainder 1
1 ÷ 2 = 0 remainder 1
Thus, 987 in binary is 1111011011₂.
The five common number systems are: