A number system is a method of representing numbers using a set of digits or symbols. In computer science, number systems are very important because computers understand only binary language (0 and 1).
The main types of number systems used in computing are:
- Binary Number System
- Decimal Number System
- Octal Number System
- Hexadecimal Number System
Introduction to Number System – Binary, Decimal, Hexadecimal
Binary Number System
A binary number is a fundamental number system digital circuit. The digital circuit only uses two values, 0 and 1. Normal digits are not used in digital circuits because normal numbers have different levels and sizes. Each digit of a binary number is called a ‘bit’ and represents an off/on state in electronic circuits, meaning 0 is off and 1 is on. A binary number is a base-2 number system.
Advantages of binary code
- Only two digits are used: 0 and 1.
- Different types of logic can be applied to this two-digit number.
- It is easy to use in mathematical operations like addition, subtraction, etc.
- It is easy to convert binary to decimal or decimal to binary.
- It is a more accurate and readable number system.
Position and negative logic system
The positive denotes high voltage, meaning 1, and the negative denotes no voltage, meaning 0. This combination makes the digital circuit more powerful for calculation.
RADIX (Base of Number System)
RADIX is an alphabet size of a number system which tells how many unique digits are used by the system to represent numbers. For example, suppose one number is 6834; then it is represented as (6834)₁₀. The subscript 10 indicates that the number is a decimal number and its value is calculated as follows:
Binary Counting System
Binary counting means counting numbers using only two digits, 0 and 1. The binary has a base-2 system, which means each place value represents a power of 2.
Binary to Decimal Conversion
To convert a binary number to a decimal number, follow the given procedure.
Decimal to Binary Conversion
To convert a decimal number to binary, follow the following methods.
To find the binary number, the decimal number should be divided by only 2 until the remainder comes to 0 or 1. After converting, read the remainders from bottom to top, and then you will find the binary number.
Example: Convert Decimal 25 to Binary
- 25 ÷ 2 = 12 remainder 1
- 12 ÷ 2 = 6 remainder 0
- 6 ÷ 2 = 3 remainder 0
- 3 ÷ 2 = 1 remainder 1
- 1 ÷ 2 = 0 remainder 1
Now, reading remainders upwards: 11001
Hexadecimal Number System
The hexadecimal number system is another way to represent numbers; the hexadecimal number system has a base 16. Digits range from 0 to 15, but we have only single symbols from 0 to 9, and from 10 to 15 we use letters.
Hexadecimal conversion
1. Decimal to Hexadecimal conversion
To convert the decimal number into hexadecimal, use the hex-dabble method, like the double-dabble method, where the given number is divided by 16.
2. Hexadecimal to decimal conversion
To convert a given hexadecimal number into decimal, each number is multiplied by 16ⁿ. For example, if the hexadecimal number is 9AE, then you have to convert it in the following method.
Octal Number System
In the octal number system, eight symbols from 0 to 7 are used, and its radix is 8. To convert an octal number into decimal, follow the given method.
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