# NUMBER SYSTEM IN DIGITAL ELECTRONICS

**NUMBER SYSTEM IN DIGITAL ELECTRONICS**

** **A number system is simply a way of representing numeric values. **It** uses symbols called numerals to represent numeric quantities.

- It relates quantities and symbols. In number system there is an ordered set of symbols known as digits with rules for defined for performing arithmetic operations like addition, substraction,multiplication,division. The base of a system represents number digit in that particular number system.
- The table below describes four number system, their base and their distinct symbols:

Number System | Base / Radix | Distinct Symbols |

Binary | 2 | 0, 1 |

Octal | 8 | 0 – 7 |

Decimal | 10 | 0 – 9 |

Hexadecimal | 16 | 0 – 9, A, B, C, D, E, F |

- In hexadecimal format, A=>10,B=>11,C=>12,D=>13,E=>14,F=>15.

**Explanation **

**1.Binary**

- The number system with base two is known as binary.
- Only two symbols are used to represent numbers in this system i.e.,0 and 1,which are known as bits.
- A binary number consists of a sequence of bits,each bit of which is either 0 or 1.

**2. ****Octal**

- The number system with base eight is known as octal.
- In this system,eight symbols i.e.,0,1,2,…..7 are used to represent the number.
- Since its base is, 8=2
^{3 }every 3-bit group of binary can be represented by an octal digit. - An octal number is thus,1/3rd the length of the corresponding binary number.

**3.** **Decimal **

- It uses base 10.It includes digits from 0 to 9.
- It is a positional weighted system.
- In this system any number of any magnitude can be represented by the use of this ten symbols.
- Each symbol in the number is called digit.

**4.** **Hexadecimal **

- This system is very popular in computer cases.
- The base for hexadecimal number system is 16 which requires 16 distinct symbols to represent the number.
- There are numerals 0 to 9 and alphabets A to F.
- This is a alphanumeric number system because it uses both alphabets and numerical to represent a hexadecimal number.

**Related questions and answers:**

**Q1.What is a number systems?**

**Ans.** It is simply a way of representing numeric values. It uses symbols called numerals to represent numeric quantities . It relates quantities and symbols. In number system there is an ordered set of symbols known as digits with rules for defined for performing arithmetic operations like addition, subtraction,multiplication,division.

**Q2. Write the number system with their base and distinct symbols**.

**Ans**.

Number System | Base / Radix | Distinct Symbols |

Binary | 2 | 0, 1 |

Octal | 8 | 0 – 7 |

Decimal | 10 | 0 – 9 |

Hexadecimal | 16 | 0 – 9, A, B, C, D, E, F |

**Q3. Explain the binary number system .**

Ans. The number system with base two is known as binary number system.Only two symbols are used to represent numbers in this system i.e.,0 and 1,which are known as bits.

**Q4. What is octal and hexadecimal number system?**

**Ans**.Octal number system:The number system with base eight is known as octal number system.In this system,eight symbols i.e.,0,1,2,…..7 are used to represent the number.

Hexadecimal number system: This system is very popular in computer cases.The base for hexadecimal number system is 16 which requires 16 distinct symbols to represent the number. There are numerals 0 to 9 and alphabets A to F.

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