So, hey guys today we are going to learn **“How to convert a binary number into a hexadecimal number”**.

Before starting this blog let’s take a recap about what are binary decimal and a hexadecimal numbers. So, let’s started…

**Binary Number**

Binary numbers are those number who uses only two-digit of a number system **0(Zero)** and **1(One)** and their base is **“2”**. Example is **101, 010, 1001, 01100111**, etc. These types of numbers are known as Binary Numbers.

**Hexadecimal Number**

A Hexadecimal Number is a number that uses 16-digits of a number system. In which the range of a hexadecimal number between **0 **to **9** (0,1,2,3,4,5,6,7,8,9) and** A** to **F** (A,B,C,D,E,F). A to F is equivalent to the number **10** to **16** (10, 11, 12, 13, 14, 15, and last 16). This number system is known as **Hexa-Decimal Number**. Example: **9, 12, 27, 2BC, 9DF, 6EA, 5AFE** etc.,

To get about more details about this topic go to this link “Computer Number System”

For better understanding let start directly with the example…

**Example 1:** Convert a binary number **(101) _{2} **into a Hexadecimal number?

**Sol:**

**Step 1: **Firstly we have to convert the given number into a decimal number. Let’s convert it…

= (101)_{2}= 1x2^{2}+ 0x2^{1}+ 1x2^{0}= 1x4 + 0x2 + 1x1 = 4 + 0 + 1 = 5 Hence, the decimal value is(5)_{10}

**Step 2: **Now, we have to divide the given number by **16 **until the quotients come to 0.

Decimal No.÷ by 16 | Quotient | Remainder | Remainder in hexadecimal |
---|---|---|---|

5 ÷ 16 | 0 | 5 | 5 |

Hence, our final answer is **(5) _{16}**.

**Example 2:** Convert the binary number **(10110) _{2}** into a Hexadecimal number?

**Sol:**

**Step 1: **Firstly we have to convert the given number into a decimal number. Let’s convert it…

= (10110)_{2}= 1x2^{4}+ 0x2^{3}+ 1x2^{2}+ 1x2^{1}+ 0x2^{0}= 1x16 + 0x8 + 1x4 + 1x2 + 0x1 = 16 + 0 + 4 + 2 + 0 = 22 Hence, the decimal value is(22)_{10}

**Step 2: **Now, we have to divide the given number by **16 **until the quotients come to 0.

Decimal No.÷ by 16 | Quotient | Remainder | Remainder in hexadecimal |
---|---|---|---|

22 ÷ 16 | 1 | 6 | 6 |

1÷ 16 | 0 | 1 | 1 |

Now, write all the remainder from downward to the upward manner like this = 16

Hence, our final answer is **(16) _{16}**.

**Example 3:** Convert the binary number **(11101101) _{2}** into a Hexadecimal number?

**Sol:**

**Step 1: **Firstly we have to convert the given number into a decimal number. Let’s convert it…

= (11101101)_{2}= 1x2^{7}+ 1x2^{6}+ 1x2^{5}+ 0x2^{4}+ 1x2^{3}+ 1x2^{2}+ 0x2^{1}+ 1x2^{0}= 1x128 + 1x64 + 1x32 + 0x16 + 1x8 + 1x4 + 0x2 + 1x1 = 128 + 64 + 32 + 0 + 8 + 4 + 0 + 1 = 237 Hence, the decimal value is(237)_{10}

**Step 2: **Now, we have to divide the given number by **16 **until the quotients come to 0.

Decimal No.÷ by 16 | Quotient | Remainder | Remainder in hexadecimal |
---|---|---|---|

237 ÷ 16 | 14 | 13 | D |

14 ÷ 16 | 0 | 14 | E |

Now, write the hexadecimal remainder from downward to the upward manner like this = ED

Hence, our final answer is **(ED) _{16}**.

**Example 4: **Convert the binary number **(1011001111) _{2}** into a Hexadecimal number?

**Sol:**

**Step 1: **Firstly we have to convert the given number into a decimal number. Let’s convert it…

= (1011001111)_{2}= 1x2^{9}+ 0x2^{8}+ 1x2^{7}+ 1x2^{6}+ 0x2^{5}+ 0x2^{4}+ 1x2^{3}+ 1x2^{2}+1x2^{1}+ 1x2^{0}= 1x512 + 0x256 + 1x128 + 1x64 + 0x32 + 0x16 + 1x8 + 1x4 + 1x2 + 1x1 = 512 + 0 + 128 + 64 + 0 + 0 + 8 + 4 + 2 + 1 = 719 Hence, the decimal value is(719)_{10}

**Step 2: **Now, we have to divide the given number by **16 **until the quotients come to 0.

Decimal No.÷ by 16 | Quotient | Remainder | Remainder in hexadecimal |
---|---|---|---|

719 ÷ 16 | 44 | 15 | F |

44 ÷ 16 | 2 | 12 | C |

2 ÷ 16 | 0 | 2 | 2 |

Now, write the hexadecimal remainder from downward to the upward manner like this = 2CF

Hence, our final answer is **(2CF) _{16}**.

**Example 5:** Convert the binary number **(10000000001) _{2}** into Hexadecimal number?

**Sol:**

**Step 1: **Firstly we have to convert the given number into a decimal number. Let’s convert it…

= (1000000001)_{2}= 1x2^{10}+ 0x2^{9}+ 0x2^{8}+ 0x2^{7}+ 0x2^{6}+ 0x2^{5}+ 0x2^{4}+ 0x2^{3}+0x2^{2}+ 0x2^{1}+ 1x2^{0}= 1x1024 + 0x512 + 1x256 + 1x128 + 0x64 + 0x32 + 1x16 + 1x8 + 1x4 + 1x2 + 1x1 = 1024 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 1 = 1025 Hence, the decimal value is(1025)_{10}

**Step 2: **Now, we have to divide the given number by **16 **until the quotients come to 0.

Decimal No.÷ by 16 | Quotient | Remainder | Remainder in hexadecimal |
---|---|---|---|

1025 ÷ 16 | 64 | 1 | 1 |

64 ÷ 16 | 4 | 0 | 0 |

4 ÷ 16 | 0 | 4 | 4 |

Now, write the hexadecimal remainder from downward to the upward manner like this = 401

Hence, our final answer is **(401) _{16}**.

**Example 6:** Convert the binary number **(11110000) _{2}** into a Hexadecimal number?

**Sol:**

**Step 1: **Firstly we have to convert the given number into a decimal number. Let’s convert it…

= (11110000)_{2}= 1x2^{7}+ 1x2^{6}+ 1x2^{5}+ 0x2^{4}+ 0x2^{3}+ 0x2^{2}+ 0x2^{1}+ 0x2^{0}= 1x128 + 1x64 + 1x32 + 1x16 + 0x8 + 0x4 + 0x2 + 0x1 = 128 + 64 + 32 + 16 + 0 + 0 + 0 + 0 = 240 Hence, the decimal value is(240)_{10}

**Step 2: **Now, we have to divide the given number by **16 **until the quotients come to 0.

Decimal No.÷ by 16 | Quotient | Remainder | Remainder in hexadecimal |
---|---|---|---|

240 ÷ 16 | 15 | 0 | 0 |

15 ÷ 16 | 0 | 15 | F |

Now, write the hexadecimal remainder from a downward to an upward manner like this = F0

Hence, our final answer is **(F0) _{16}**.