# How useful is the number system

## Computer number system

When we type some letters or words, the computer translates them into numbers like computers can only understand numbers. A computer can understand the position number of the system, where there are only a few symbols called digits, and these symbols represent different values depending on the position they occupy in the number.

A value of each digit in a number can be determined with

The digit

The position of the digit in the number

The base of the number system (where base is available as the total number of digits in the number system).

### Decimal number system

The number system we use in our day-to-day life is the decimal number system. Decimal number systems have base 10 as it uses 10 digits from 0 to 9. In decimal number system, the consecutive positions to the left of the decimal point represent Units, tens, hundreds, thousands, and so on.

Each position represents a specific achievement from the base (10). For example, the decimal number 1234 consists of the digit 4 in units of space, 3 in the ten position, 2 in the hundreds, and 1 in the thousands, and its value as written

(1x1000) + (2x100) + (3x10) + (4xl) (1x10^{3}) + (2x10

^{2}) + (3x10

^{1}) + (4xl0

^{0}) 1000 + 200 + 30 + 4 1234

As a computer programmer or IT professional, you should understand the following number systems that are commonly used in computers.

S.N. | Number system and description |
---|---|

1 |
Base 2nd digit used: 0, 1 |

2 |
Base 8th digit used: 0 to 7 |

3 |
Base 16. Digit Used: 0 to 9, Letters Used: A- F |

### Binary number system

### Characteristic of binary number system are as follows:

Uses two digits, 0 and 1.

Also as a base 2 number system

Each position in a binary number has a 0 base (2) power. Example 2

^{0}Last position in a binary number represents an x power of base (2). Example 2

^{x}where x represents the last position - 1.

### example

Binary number: 10101_{2}

Calculation of the decimal equivalent:

step | Binary number | Decimal number |
---|---|---|

Step 1 | 10101_{2} | ((1 x 2^{4}) + (0x2^{3}) + (1 x 2^{2}) + (0x2^{1}) + (1 x 2^{0}))_{10} |

step 2 | 10101_{2} | (16 + 0 + 4 + 0 + 1)_{10} |

step 3 | 10101_{2} | 21_{10} |

** Note :** 10101_{2} is usually written as 10101.

### Octal number system

### Characteristic of octal number system are as follows:

Uses eight digits, 0,1,2,3,4,5,6,7.

Also as a base 8 number system

Each position in octal number represents a 0 power of the base (8). Example 8

^{0}Last position in an octal number represents ax performance of the base (8). Example 8

^{x}where x represents the last position -1.

### example

Octal number: 12570_{8}

Calculation of the decimal equivalent:

step | Octal number | Decimal number |
---|---|---|

Step 1 | 12570_{8} | ((1 x 8^{4}) + (2 x 8^{3}) + (5 x 8^{2}) + (7 x 8^{1}) + (0x8^{0}))_{10} |

step 2 | 12570_{8} | (4096 + 1024 + 320 + 56 + 0)_{10} |

step 3 | 12570_{8} | 5496_{10} |

**Note :** 12570_{8} is usually written as 12570.

### Hexadecimal number system

### Characteristic of hexadecimal number system are as follows:

Uses 10 digits and 6 letters, 0,1,2,3,4,5,6,7,8,9, A, B, C, D, E, F.

Letters represent a number starting from 10. A = 10. B = 11, C = 12, D = 13, E = 14, F = 15.

Also as a base 16 number system

Each position in a hexadecimal number represents a 0 power from the base (16). Example 16

^{0}Last position in a hexadecimal number represents an x base 16 (16) power. Example 16

^{x}where x represents the last position -1.

### example

Hexadecimal number: 19FDE_{16}

Calculation of the decimal equivalent:

step | Binary number | Decimal number |
---|---|---|

Step 1 | 19FDE_{16} | ((1 x 16^{4}) + (9 x 16^{3}) + (F x 16^{2}) + (D x 16^{1}) + (E x 16^{0}))_{10} |

step 2 | 19FDE_{16} | ((1 x 16^{4}) + (9 x 16^{3}) + (15 x 16^{2}) + (13 x 16^{1}) + (14 x 16^{0}))_{10} |

step 3 | 19FDE_{16} | (65536+ 36864 + 3840 + 208 + 14)_{10} |

Step 4 | 19FDE_{16} | 106462_{10} |

**Note :** 19FDE_{16} is usually written as 19FDE.

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