**What is a Number System of Computer**

Today we will tell you about the number system of computers and knowing how many types they are, then let’s start.

The number system is used to display information given by the user instructions. Whenever we write any letter or word on a personal computer, it converts it into numbers because the computer system can understand only numbers.

Digital computers convert all types of data and information into binary numbers. Eg:- Audio, Video, Graphics, and Numbers, etc.

**There are Four Types of the Number system in computers:-**

- Binary Number System
- Decimal Number System
- Octal Number System
- Hexadecimal Number System

Binary Number System:-

As we know that the computer is able to read numbers only, so digital computers represent all their data in binary numbers system. In the binary number are used only two digits (0 and 1) and its base or radix is 2. Because it has only two digits.

**For example-** 110110 is a binary number because only two (0 and 1) digits are used in it, 101001.1101 is also a binary number. In this, the point (.) after 101001 is called the binary point.

Decimal Number System:-

We use these decimal number systems every day in our daily life. In which the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 are used to represent any number systems.

The base or radix of this decimal number system is 10. Radix is the number of quantity digits used in a number system.

Each digit of each number written in the decimal number system has its own place value (weight). It is also called the multiplying factor Multiples are thousands, hundreds, tens and units, etc.

**For example-** 6262.67 can be represented as follows.

(6262.67)10 = 6*10^{3}+2*10^{2}+6*10^{1}+2*10^{0}+6*10^{-1}+6*10^{-2}

Based on the given example. 6 multiplied by 10^{3}, 2 multiplied by ** 10 ^{2}**, 6 multiplied by

**10**

^{1}, and 2 multiplied by 10

^{0}, Similarly, in its decimal part 6 has been multiplied by 1/10

^{1}i.e. 10

^{-1}and 7 by 1/10

^{2}i.e. 10

^{-2}.

Octal Number System:-

Like all these number systems, there is another number system called octal number. They also have some numbers of their own like in the octal number system only 8 digits are from 0 to 7.

These 8 digits are 0, 1, 2, 3, 4, 5, 6, and 7. Similarly, the base or radix of their number system is 8.

Hexadecimal Number System:-

This number system is also similar. Hexadecimal numbers have 10 digits and 6 alphabet letters;- 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F.

In this, 10 represented by A, 11 represented by B, 12 represented by C, 13 represented by D. 14 is represented by E, and 15 is represented by F. Its base or radix is 16 because it has 16 alphanumeric values.

**Number System Relationship**

Binary Number | Decimal Number | Octal Number | Hexadecimal Number |
---|---|---|---|

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 | 8 | 10 | 8 |

1001 | 9 | 11 | 9 |

1010 | 10 | 12 | A |

1011 | 11 | 13 | B |

1100 | 12 | 14 | C |

1101 | 13 | 15 | D |

1110 | 14 | 16 | E |

1111 | 15 | 17 | F |

**We can change the number system in many ways:-**

**Binary to Decimal Conversion:-**

**For Example-** 1010 is a binary number converted to a Decimal number.

1010 – 1*2^{3} + 0*2^{2} + 1*2^{1} + 0*2^{0}

8 + 0 +2 + 0

Sum = 10 is Decimal number

**Decimal to Binary Conversuion:-**

**For Example-** Convert the decimal number 15_{10} to binary.

We will start dividing the given number (15) repeatedly by 2 until we get the quotient as 0. We will note the remainders in order.

**STEP 1-** dividing the given number (15_{10}) repeatedly by 2 until we get the quotient as 0. We will note the remainders in order.

15 ÷ 2 = 7 (Remainder 1)

7 ÷ 2 = 3 (Remainder 1)

3 ÷ 2 = 1 (Remainder 1)

1 ÷ 2 = 0 (Remaindr 1)

**STEP-** write the reainders reverse order 1111

15_{10} is decimal number = 1111 is binary number

**Conclusion:-**

We have tried our best to explain what is a number system of computer blogs, I hope you have understood this blog. If you liked the blog, then share it with your friends too.

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