Binary numbers are in base-2 (using only 0 and 1), while hexadecimal numbers are in base-16 (using digits 0-9 and letters A-F). The beauty of this conversion lies in the fact that four binary digits perfectly map to one hexadecimal digit, making the process straightforward.

### Why Convert Binary to Hexadecimal?

Binary numbers can get very lengthy, especially in computer memory. Hexadecimal provides a shorter way to represent these numbers. For example, the binary `1010 1100`

can be compactly written as `AC`

in hexadecimal. Hexadecimal numbers are easier to read and use for humans, particularly when dealing with large binary values like those in programming or digital electronics.

## Step-by-Step Conversion Process

### 1. Group Binary Digits into Sets of Four

Start from the rightmost digit of the binary number and break it into groups of four. If the number of digits isn’t a multiple of four, add zeros to the left to complete the last group.

Example: To convert `101101`

to hexadecimal:

- Group into sets of four:
`10 1101`

- Add leading zeros to complete the leftmost group:
`0010 1101`

### 2. Convert Each Group to a Hexadecimal Digit

Each 4-bit binary group can be treated as a separate number. Convert each group to its hexadecimal equivalent. Use this quick reference table:

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

0000 | 0 |

0001 | 1 |

0010 | 2 |

0011 | 3 |

0100 | 4 |

0101 | 5 |

0110 | 6 |

0111 | 7 |

1000 | 8 |

1001 | 9 |

1010 | A |

1011 | B |

1100 | C |

1101 | D |

1110 | E |

1111 | F |

- For our example (
`0010 1101`

):`0010`

= 2`1101`

= D

### 3. Combine the Hexadecimal Digits

Combine the hexadecimal digits you obtained from each group to form the final hexadecimal number.

Example: The binary `101101`

converts to hexadecimal as **2D**.

## Worked-Out Examples

### Example 1: Convert `11011100`

to Hexadecimal

**Step 1:** Group into sets of four: `1101 1100`

**Step 2:** Convert each group to hexadecimal using the table:

`1101`

= D`1100`

= C

**Step 3:** Combine the hexadecimal digits: **DC**

### Example 2: Convert `101010011`

to Hexadecimal

**Step 1:** Group into sets of four: `101 0100 011`

- Add leading zeros:
`0001 0100 011`

**Step 2:** Convert each group:

`0001`

= 1`0100`

= 4`0011`

= 3

**Step 3:** Combine the digits: **143**

### Example 3: Convert `100111011011`

to Hexadecimal

**Step 1:** Group into sets of four: `1001 1101 1011`

**Step 2:** Convert each group:

`1001`

= 9`1101`

= D`1011`

= B

**Step 3:** Combine the digits: **9DB**

## Quick Tips for Conversion

**Always Group in Fours:**To convert binary to hexadecimal, split the binary number into groups of four. If the leftmost group has fewer than four digits, add zeros to its left to make it a full group of four.**Memorize the Basic Table:**Having the binary-to-hexadecimal table handy or memorized makes the process faster. Each 4-bit binary group directly translates to a single hexadecimal digit.**Cross-Check Your Work:**After converting, the hexadecimal number should only contain digits (0-9) and letters (A-F). If it doesn’t, double-check your grouping and conversion steps.

## Practice Table: Binary to Hexadecimal

Here’s a practice table with a few binary numbers to try converting on your own:

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

101011 | 0001 0101 | 15 |

110101011010 | 1101 0101 1010 | D5A |

100101 | 0001 0010 1 | 92 |

111010101111 | 1110 1010 011 | EA7 |

Binary to hexadecimal conversion is an essential skill in computing, and with practice, you’ll find it becomes second nature.