Hexadecimal and binary are two widely used number systems in computer science and digital electronics. Understanding how to convert between these systems is essential for anyone working in fields related to computing, data representation, or digital circuitry.

**Hexadecimal (Base 16)**: This system uses 16 symbols: 0-9 to represent values zero to nine and A-F (or a-f) to represent values ten to fifteen.**Binary (Base 2)**: This system uses only two symbols: 0 and 1.

In this article, we’ll explore how to convert a hexadecimal number to its binary equivalent. We’ll break down the conversion process step by step and provide examples to ensure a clear understanding.

### Why Convert Hexadecimal to Binary?

Hexadecimal numbers are often used in programming and digital systems because they provide a more compact representation of binary data. For example, a single hexadecimal digit represents four binary digits (bits). This makes it easier to read and write long binary sequences.

### Hexadecimal to Binary Conversion Process

Converting a hexadecimal number to binary is straightforward. Each hexadecimal digit is directly mapped to a four-bit binary equivalent. Below is the conversion table:

Hexadecimal | Binary |
---|---|

0 | 0000 |

1 | 0001 |

2 | 0010 |

3 | 0011 |

4 | 0100 |

5 | 0101 |

6 | 0110 |

7 | 0111 |

8 | 1000 |

9 | 1001 |

A (10) | 1010 |

B (11) | 1011 |

C (12) | 1100 |

D (13) | 1101 |

E (14) | 1110 |

F (15) | 1111 |

### Step-by-Step Conversion Example

Let’s take the hexadecimal number `2F3`

and convert it to binary.

**Step 1: Break Down the Hexadecimal Number**

Start by writing down the hexadecimal number and break it down into individual digits:

- 2
- F
- 3

**Step 2: Convert Each Hexadecimal Digit to Binary**

Using the conversion table, convert each digit to its corresponding binary value:

**2**in binary is`0010`

.**F**(which represents 15 in decimal) in binary is`1111`

.**3**in binary is`0011`

.

**Step 3: Combine the Binary Values**

Now, concatenate all the binary values obtained:

- 2 →
`0010`

- F →
`1111`

- 3 →
`0011`

So, the binary equivalent of hexadecimal `2F3`

is `0010 1111 0011`

.

### Another Example

Let’s convert the hexadecimal number `A9C`

to binary.

**Step 1: Break Down the Hexadecimal Number**

- A
- 9
- C

**Step 2: Convert Each Hexadecimal Digit to Binary**

**A**(which represents 10 in decimal) in binary is`1010`

.**9**in binary is`1001`

.**C**(which represents 12 in decimal) in binary is`1100`

.

**Step 3: Combine the Binary Values**

- A →
`1010`

- 9 →
`1001`

- C →
`1100`

The binary equivalent of hexadecimal `A9C`

is `1010 1001 1100`

.

### Practice Problem

Try converting the hexadecimal number `3B7`

to binary using the steps provided above.

**Solution:**

**3**in binary is`0011`

.**B**(which represents 11 in decimal) in binary is`1011`

.**7**in binary is`0111`

.

The binary equivalent of `3B7`

is `0011 1011 0111`

.

### Conclusion

Converting from hexadecimal to binary is a crucial skill in various fields related to computing and electronics. By following the simple steps outlined in this guide, you can easily convert any hexadecimal number into its binary equivalent. This process, once practiced, becomes second nature and is fundamental for tasks such as programming, debugging, and understanding digital circuit designs.