To convert Binary to Hexadecimal, input binary value in the box below, and then click on the big blue button that says “CONVERT TO HEX” and Hex is generated, copy it or you can download output file.

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In Binary number system there are only two digits that are 0 and 1. In this number system every number (value) represents with 0 and. The base of binary number system is 2, because it has only two digits.

**Example: What is (110) _{2} in base 10?**

110_{2} = (1 x 2^{2}) + (1 x
2^{1}) + (0 x 1^{0}) = 6_{10}

In a Hexadecimal number system there are sixteen (16) alphanumeric values from 0 to 9 and A to F. In this number system every number (value) represents with 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E and F. The base of this number system is 16, because it has 16 alphanumeric values. Here A is 10, B is 11, C is 12, D is 14, E is 15 and F is 16.

**Example: What is 0xA5 in base 10?**

0xA5 = A5_{16} = (10 x 16^{1}) + (5 x
16^{0}) = 165_{10}

We know that the maximum digit in a hexadecimal system is 15, which can be represented by
1111_{2 }in a binary system. Hence, starting from the LSB, we group four digits at a
time and replace them with the hexadecimal equivalent of those groups and we get the final
hexadecimal number.

**Example 1: Convert 11010110 _{2 }into an equivalent hexadecimal number.**

* Solution. *The binary number given is 11010110 Starting with LSB and
grouping 4 bits 1101 0110 Hexadecimal equivalent D 6

Hence the hexadecimal equivalent number is (D6)_{16}.

**Example 2: Convert 110011110 _{2 }into an equivalent hexadecimal number.**

* Solution. *The binary number given is 110011110

Starting with LSB and grouping 4 bits 0001 1001 1110

Hexadecimal equivalent 1 9 E

Hence the hexadecimal equivalent number is (19E)_{16}.

Since at the time of grouping of four digits starting from the LSB, in Examples we find that the third group cannot be completed, since only one 1 is left out, so we complete the group by adding three 0s to the MSB side. Now if the number has a fractional part, as in the case of octal numbers, then there will be two different classes of groups—one for the integer part starting from the left of the decimal point and proceeding toward the left and the second one starting from the right of the decimal point and proceeding toward the right. If, for the second class, any uncompleted group is left out, we complete the group by adding 0s on the right side.

Hence the converted binary number is (0001011)_{2}

Hex |
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 |

Hexadecimal Numbers are commonly used in computer programming to simplify the binary
numbering system. As 16 is equivalent to 2^{4}, there is a linear relation between
binary and hexadecimal number system. This means four binary digits are equivalent to one
hexadecimal digit. But computers understand just 0 and 1 i.e. Binary number system so
computers use just binary number system while humans use hexadecimal number system to
shorten binary digits to make them understandable easily. Following are the fewer
applications of Hexadecimal Number system:

**To define colors on web pages:** To define a color on any web page we use RGB
where R stand for Red, G for Green ad B for Blue in the format of #RRGGBB.

**To allocate memory:** We can characterize every byte just as two hexadecimal
digits where as we have to use 8 digits while using binary.

**To represent MAC address:** Media Access control (MAC) addresses consist of 12 Hexadecimal digits in the format of MM:MM:MM:SS:SS or MMMM-MMSS-SSSS. Here, the first six digits shows the identity of the manufacturer while the last 6 shows the serial number.