**Data** refers to the symbols that represent people, events, things, and ideas. Data can be a name, a number, the colors in a photograph, or the notes in a musical composition

**Data Representation** refers to the form in which data is stored, processed, and transmitted.Devices such as smartphones, ipodsand computer store data in digital formats that can be handled by electronic circuitry.

**Digitization** is the process of converting information, such as text, numbers, photo, or music, into digital data that can be manipulated by electronic devices.

**The Digital Revolution** has evolved through four phases, beginning with big, expensive, standalone computers, and progressing to today’s digital world in which small, inexpensive digital devices are everywhere.

### Introduction

Data stored in different kinds

- Numeric (0,1,2..9)
- Alphabetic (A, B, C…Z)
- Alphanumeric
- Special Characters

All of them is represented in terms of 0s and 1sAnd their unique combinations

Our discussion is focus on following number systems

- Decimal number
- Binary number system,
- Octal number system, and
- Hexadecimal number system

**Base or Radix**

Base / Radix |
Name |

2 | Binary system |

8 | Octal system |

10 | Decimal system |

16 | Hexadecimal system |

## NUMBER SYSTEM

**Face value**

Face value of a digit in a number is the value of the digit itself. Wherever it appears.

**Place value/Position Value**

Place value of a digit in a number is the value of the digit where it to appear.

**Eg**

1. 768534, find place value and face value of 5 in given no;

Face Value of 5 is ; 5

Place Value of 5 is; 5*100= 500

2. 0.03721; **find place value of 3.**

**Another way;**

The Place Value/Position value of a digit is 【Base^{Position}】

In 768534 Place Value/Position valueof 5 is = 10^{2}–>5*10^{2}

A number in a particular base is written as 【(number)_{base of number}】For example, (23)_{10} means that the number 23 is a decimal number(345)_{8} shows that 345 is an octal number.

### A. Decimal Number System

It consists of 10 digits number—0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.

probably the most commonly used number system

All number in this numbering system are combination of 0-9 digits

Represented by base or radix 10/ base 10 number system

Position |
3 | 2 | 1 | 0 | -1 | -2 | -3 |

Position Value |
10^{3} |
10^{2} |
10^{1} |
10^{0} |
10^{-1} |
10^{-2} |
10^{-3} |

Quantity |
1000 | 100 | 10 | 1 | 1/10 | 1/100 | 1/1000 |

### B. Binary Number System

The binary number system consists of two digits—0 and 1.

All binary numbers are formed using combination of 0 and 1.

All number in this numbering system are unique combination of 1s & 0s

Represented by base or radix 2

Position |
3 | 2 | 1 | 0 | -1 | -2 | -3 |

Position Value |
2^{3} |
2^{2} |
2^{1} |
2^{0} |
2^{-1} |
2^{-2} |
2^{-3} |

Quantity |
8 | 4 | 2 | 1 | 1/2 | 1/4 | 1/8 |

### C. Octal Number System

The octal number system consists of eight digits—0 to 7.

All octal numbers are represented using these eight digits

Also called“oct”in short, is the base-8 number system

Position |
3 | 2 | 1 | 0 | -1 | -2 | -3 |

Position Value |
8^{3} |
8^{2} |
8^{1} |
8^{0} |
8^{-1} |
8^{-2} |
8^{-3} |

Quantity |
512 | 64 | 8 | 1 | 1/8 | 1/64 | 1/512 |

### D. HexaDecimal Number System

The hexadecimal number system consists of sixteen digits—0 to 9, A, B, C, D, E, F, where (A is for 10, B is for 11, C-12, D-13, E-14, F-15).

All hexadecimal numbers are represented using these 16 digits.

In short “hex”

Base 16 Number System

Position |
3 | 2 | 1 | 0 | -1 | -2 | -3 |

Position Value |
16^{3} |
16^{2} |
16^{1} |
16^{0} |
16^{-1} |
16^{-2} |
16^{-3} |

Quantity |
4096 | 256 | 16 | 1 | 1/16 | 1/256 | 1/4096 |

Decimal | Binary | Octal | Hexadecial |

0 | 0000 | 0 | 0 |

1 | 0001 | 1 | 1 |

2 | 0010 | 2 | 2 |

3 | 0011 | 3 | 3 |

4 | 0100 | 4 | 4 |

5 | 0101 | 5 | 5 |

6 | 0110 | 6 | 6 |

7 | 0111 | 7 | 7 |

8 | 1000 | 10 | 8 |

9 | 1001 | 11 | 9 |

10 | 1010 | 12 | A |

11 | 1011 | 13 | B |

12 | 1100 | 14 | C |

13 | 1101 | 15 | D |

14 | 1110 | 16 | E |

15 | 1111 | 17 | F |

## Signed And Unsigned Number