## What is Number System? Definition and Types

**What is Number System? Definition and Type**s – The number system is technique to represent or express the numbers. **Decimal number** system is the most common number system. Other popular number systems include **binary number system, octal number system, hexadecimal number system**, etc.

Lets discus in detail-

### Number System Chart

**Decimal**

**Base –**10

**Symbols –**0,1,2,3,4,5,6,7,8,9

**Example –**(2756)

_{10}

**Binary **

**Base –**2

**Symbols –**0,1

**Example –**(100110)

_{2}

**Octal **

**Base –**8

**Symbols –**0,1,2,3,4,5,6,7

**Example –**(1576)

_{8}

**Hexadecimal**

**Base –**16

**Symbols –**0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F

**Example –**(3DB)

_{16}

## Decimal Number System (Base 10)

In this number system, the digits 0 to 9 represents numbers. As it uses 10 digits to represent a number, it is also called the base 10 number system. Each digit has a value based on its position called place value. The value of the position increases by 10 times as we move from right to left in the number.

For example, the value of 456 is

= 4 x 10^{2} + 5 x 10^{1} + 6 x 10^{0}

= 400 + 50 + 6

## Binary Number System (Base 2)

A computer can understand only the “on” and “off” state of a switch. These two states are represented by 1 and 0. The combination of 1 and 0 form binary numbers. These numbers represent various data. As two digits are used to represent numbers, it is called a binary or base 2 number system.

Each binary digit is also called a bit. Binary number system is also positional value system, where each digit has a value expressed in powers of 2.

For example, (101101)2 in decimal is

= 1 x 25 + 0 x 24 + 1 x 23 + 1 x 22 + 0 x 21 + 1 x 20

= 1 x 32 + 0 x 16 + 1 x 8 + 1 x 4 + 0 x 2 + 1 x 1

= 32 + 8 + 4 + 1

= (45)10

In any binary number, the rightmost digit is called **least significant bit (LSB)** and leftmost digit is called **most significant bit (MSB)**.

**Also read this : What is a Hardware?**

### Octal Number System (Base 8)

_{8}in decimal is

^{1}+4×8

^{0}

_{10}

### Hexadecimal Number System (Base 16)

Computer memory is measured in terms of how many bits it can store. Here is a chart for memory capacity conversion.

- 1 byte (B) = 8 bits
- 1 Kilobytes (KB) = 1024 bytes
- 1 Megabyte (MB) = 1024 KB
- 1 Gigabyte (GB) = 1024 MB
- 1 Terabyte (TB) = 1024 GB
- 1 Exabyte (EB) = 1024 PB
- 1 Zettabyte = 1024 EB
- 1 Yottabyte (YB) = 1024 ZB

## Number System Relationship

The following table depicts the relationship between decimal, binary, octal and hexadecimal number systems.Hexa decimal |
Decimal | Octal | Binary |
---|---|---|---|

0 | 0 | 0 | 0000 |

1 | 1 | 1 | 0001 |

2 | 2 | 2 | 0010 |

3 | 3 | 3 | 0011 |

4 | 4 | 4 | 0100 |

5 | 5 | 5 | 0101 |

6 | 6 | 6 | 0110 |

7 | 7 | 7 | 0111 |

8 | 8 | 10 | 1000 |

9 | 9 | 11 | 1001 |

A | 10 | 12 | 1010 |

B | 11 | 13 | 1011 |

C | 12 | 14 | 1100 |

D | 13 | 15 | 1101 |

E | 14 | 16 | 1110 |

F | 15 | 17 | 1111 |

## Practice Questions

Q 1: How would you represent 10111 in the decimal number system?

A) 23

B) 24

C) 25

D) 22

Ans: A) 23

Q 2: The LSB and MSB in the following number are: 1220

A) 1 & 0

B) 0 & 1

C) 10

D) 01

Ans: A) 0 & 1