Number System

The number system is the way of representing numbers using symbols and a set of rules. It is a mathematical notation used to represent data in a computer system. In a computer, all data, like text, images, and videos, is stored in the form of Binary as 0s and 1s.

In our daily life, we use Decimal Numbers for calculation, but in the digital system Binary numbers are used to represent the information.

Decimal Number System

The Decimal number is the standard form of denoting numbers. It has bases/ radix because it uses 10 digits from 0 to 9.

• It is also called the base-10 system.
• Digits used in it are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
• Each digit in the number is at a specific place value that is a power of 10.
• From right to left – units have the place value as 10⁰, Tens have the place value as 10¹, Hundreds as 10², Thousands as 10³, and so on.

1457 is written as

1×10³ + 4×10² + 5×10¹ + 7×10⁰

1×1000 + 4×100 + 5×10 + 7×1

1000 + 400 + 50 + 7

1457

Binary Number System

The binary number system is also called the Base-2 number system because it consists of only two digits, 0 & 1. This makes it less complicated than other number systems since it comprises only two digits. Binary digits are useful for computation result of devices that have two states, ON and OFF.

Note: Binary digits are called bits 

• The numbers are formed using the two digits 0 and 1.
• It is useful in electronic devices and computer systems because it can be easily performed using just two state i.e., 0 and 1. 
• Each digit in the number is at a specific place value that is a power of 2.
• From right to left – as powers of 2, i.e., 2⁰, 2¹, 2², etc.

Binary Numbers can be converted to a decimal value by multiplying each digit by the place value and then adding the result.

Example

(1010) is written as

1×2³ + 0x2² + 1×2¹ + 0×2⁰

1×8 + 0x4 + 1×2 + 0x1

8+0+2+0

10

Octal Number System

The Octal Number system consists of 8 digits, i.e., from 0 to 7. It is easier to handle octal numbers in comparison to Binary numbers because if we present any number in binary, that will be long, while in the case of an octal number, that array of numbers will be shorter.

• The numbers are formed using 8 digits, i.e., 0, 1, 2, 3, 4, 5, 6, 7.
• It is useful for representing file permissions in Unix/Linux operating systems.
• Each digit in the number is at a specific place value that is a power of 8.
• From right to left – as powers of 8, i.e., 8⁰, 8¹, 8², etc.

(741) is written as

• 7x8² + 4x8¹ + 1x8⁰
• 7x64 + 4x8 + 1x1
• 448+32+1
• 481

Hexadecimal Number System

The hexadecimal number system consists 10 letters and 6 alphabets. Where digits are used from 0 to 10 and alphabets like A, B, C, D, E, and F, in which these alphabets represent 10, 11, 12, 13, 14, & 15 respectively. The hexadecimal number is used mostly in the case of Microprocessors and Microcontrollers.

• The hexadecimal is formed using 16 digits, i.e.,0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, and F.
• Hexadecimal Numbers are useful for handling memory address locations. 
• The digits from 0 to 9 are used as in the decimal system, but the numbers 10 to 15 are represented using the letters A to F as follows: 10 is represented as A, 11 as B, 12 as C, 13 as D, 14 as E, 15 as F.
  ii. Place Value: the position of the digit. Each digit in the number is at a specific place value that is a power of 16. (from right to left – as powers of 16 i.e., 16⁰, 16¹, 16², etc)

 (4F)₁₆ can be written as
(4F)₁₆ = 4 × 16¹ + F × 16⁰
(4F)₁₆ = 4 × 16 + 15 × 1
(4F)₁₆ = 48 + 15
(4F)₁₆= 63 (in decimal)

Also check

Conversion of Number Systems

1. Decimal to Other Number System
2. Binary to Other Number System
3. Octal to Other Number System
4. Hexadecimal to Other number system