## Hex to Binary Converter

In this post, we will learn the basic steps to convert a hexadecimal to binary number.

There are two methods to convert hexadecimal to binary, one is the short method and another is long method or the traditional method of hex to binary conversion. Here we will discuss only the steps relating to the short method and the long method of conversion will be covered in later post.

## How to Convert Hex to Binary

- The Hexadecimal number system has 16 digits starting from 0 to F, where the largest hexadecimal digit is (F)
_{16}. - Referring to the hexadecimal to binary conversion table, we see that the binary equivalent of the largest hexadecimal digit (F)
_{16}is (1111)_{2}and minimum of four binary digits(bits) are required to represent the largest hexadecimal digit in the binary system. - In order to convert the given hexadecimal number to binary number, we convert each hexadecimal digit into four-bit binary number beginning from the right most hexadecimal digit towards the leftmost digit (MSD).
- At the end, the four-bit binary numbers are combined to form the single binary number equivalent to the given hexadecimal number.

The above steps are explained with an example for better understanding with steps in converting from hexadecimal to binary:

## Hex to Binary Examples

**Example 1 : Convert (FA98)**_{16} Hexadecimal to binary number (?)_{2}

_{16}Hexadecimal to binary number (?)

_{2}

**Step 1 :** Each digit from the given hexadecimal number is written down leaving small space between each digit as shown below

**Hexadecimal Number → F A 9 8**

**Step 2 :** Referring to the conversion table to find the binary equivalents of each hexadecimal digit.

The binary equivalents are:

F-1111

A-1010

9-1001

8-1000

**Step 3:** Write down the four-bit binary numbers below each hexadecimal digit as shown below:

** Hexadecimal Number -> F A 9 8
** ↓ ↓ ↓ ↓
** Binary Number -> 1111 1010 1001 1000**

**Hence, the binary equivalent of the given hexadecimal number is (1111101010011000) _{2}**

**Example 2 : Convert (3FDA)**_{16} Hex to binary number (?)_{2}

_{16}Hex to binary number (?)

_{2}

**Step 1**: We first write down each hexadecimal digit from the given Hexadecimal number separating each each digit as shown below:

**Hexadecimal Number → 3 F D A**

**Step 2:** In order to convert the entire hexadecimal number to binary. We have to individually convert each hexadecimal digit to 4 bit binary number, starting from the right most digit (A) to left most digit (3).

Referring the Hex to Binary table to find the binary equivalents of each hexadecimal digit.

3 – 0011

F – 1111

D – 1101

A – 1010

**Step 3:** We combine and write down each 4 bit binary equivalents of each hexadecimal digit as shown below:

** Hexadecimal Number -> 3 F D A
↓ ↓ ↓ ↓
Binary Number -> 0011 1111 1101 1010**

**Now, if we combine the converted binary digits. We get the final Hex to binary Equivalent which is (0011111111011010) _{2}**

## How to Convert Fractional Hex to Binary

The process of converting fractional hexadecimal number to Binary is similar to what we have already discussed in converting the integer Hexadecimal number to Binary. We will find the four bit binary equivalent of each hexadecimal digit and then combine them.

- First we take all the hexadecimal digits after the decimal point starting from left to right. Write down each hexadecimal digit just the same way we did in the examples above.
- We will now have to find the binary equivalent of each digit of the fractional hexadecimal number using the Hex to Binary table.
- Write down the 4 bit binary equivalent below each hexadecimal digit, from right to left after the decimal point.
- Grouping and combining the binary equivalents of each hexadecimal digit will give the final Fractional Hexadecimal to binary conversion value. This will become more clear with some illustrated examples of fractional hex to binary conversion below:

## Examples of Fractional Hex to Binary

**Example 1: Convert (A9.5B4) fractional hex to fractional binary**

Step 1: In this example, we have the a hexadecimal number which has both the integer part(A9) and the fractional part(5B4). Just like the previous examples we write down both the integer part and the fractional part as shown below:

**Hexadecimal Number → A 9 . 5 B** **4**

Step 2: Now we convert each hexadecimal digit to its 4 bit binary equivalent on either side of the decimal point using the Hex to binary table.

From the table, We know:

A – 1010

9 – 1001

5 – 0101

B – 1011

4 – 0100

Step 3: Next we write down the converted binary values below each hexadecimal digit on either side of the decimal point, as shown below:

** Hexadecimal Number -> A 9 . 5 B 4
↓ ↓ ↓ ↓ ↓
Binary Number -> 1010 1001 . 0101 1011 0100**

New we combine all the binary digits together from right to left for the integer part and from left to right for the fractional part to get the **final binary equivalent of the fractional hexadecimal number -> (10101001.010110110100) _{2}**

## Hex to Binary Table

Hexadecimal | Binary |

0 | 0000 |

1 | 0001 |

2 | 0010 |

3 | 0011 |

4 | 0100 |

5 | 0101 |

6 | 0110 |

7 | 0111 |

8 | 1000 |

9 | 1001 |

A | 1010 |

B | 1011 |

C | 1100 |

D | 1101 |

E | 1110 |

F | 1111 |

Tools to use to verify hex to binary conversion: Hex to binary Converter