In the previous posts, we have discussed the representation of numbers in different number systems. We have also solved example problems step by step and tried some shortcuts as well. Here we will briefly discuss number system conversion. In other words, we would see how we can represent a given number in another number system without any change in value.

In the following posts, we will discuss basic conversion techniques to convert any given number from one number system to another.

At this point, you would ask me, “Hey, why do we need to do this number conversion stuff? “.

This question is absolutely valid because, in electronics, the correct number system’s decision primarily depends on the type of application. To put it in a better way, let us take an example.

You are providing your mobile number to one of your classmates. For instance, this is your mobile number (123)-456-0123 in the decimal number system, and you decide to give it in the binary format as **(1111011)-111001000-1111011**.

However, when you give the same number in decimal format to your computer. The number will be converted to its binary equivalent, as shown above, and stored. (the computer understands only 0’s and 1’s).

From the above example, we can clearly distinguish when we require a decimal number system and a binary number system.

The octal number system and the hexadecimal number system were introduced mainly to make the machine codes more human friendly instead of the 0’s and 1’s.

The octal number system has fallen back, and rarely it finds any use in today’s applications. The hexadecimal number system is the most widely used number system today. Modern computers use hexadecimal format for memory addresses and make it a lot easier to debug whenever the computer throws out an error with a hexadecimal address instead of a long string of 0’s and 1’s.

We will start learning the conversion methods from the decimal number system as we are more familiar with the decimal number system. Under the decimal number system conversion, we will learn the following conversions

**Most common number system conversion used in every day:**

- Decimal number system to binary number system
- Decimal number system to octal number system
- Decimal number system to hexadecimal number system
- Binary number system to decimal number system
- Octal number system to decimal number system
- Hexadecimal number system to decimal number system

## Decimal, Binary, Octal & Hexadecimal Number System Conversion Table

The earlier posts covered the detailed procedure step by step for converting a given number from one number system to another with exams.

The below table gives the equivalent numbers in the four number systems that we will be using in basic electronics.

This conversion table is nothing but a simple cheat sheet for performing mathematical and logical operations on the various number systems that we came across earlier, similar to the multiplication tables (from 1 to 20) that we asked to memorize in lower grade math class to perform complex multiplication and division operations faster.

This table will act as a simple speed-up bonus to perform the mathematical operations among the number systems faster. We can also use this table to do number system conversion quickly.

Decimal Base 10 | Binary Base 2 | Octal Base 8 | Hexadecimal Base 16 |
---|---|---|---|

0 | 0 | 0 | 0 |

1 | 1 | 1 | 1 |

2 | 10 | 2 | 2 |

3 | 11 | 3 | 3 |

4 | 100 | 4 | 4 |

5 | 101 | 5 | 5 |

6 | 110 | 6 | 6 |

7 | 111 | 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 |

16 | 10000 | 20 | 10 |

Decimal Binary Octal & hexadecimal Conversion Table