# Binary to Hexadecimal Converter

To use this **binary to hex conversion tool**, you must type a binary value like 11011011 into the left field below and hit the Convert button. The converter will give you the hexadecimal (base-16) equivalent of the given value.

## Binary System

The **binary numeral system** uses the number 2 as its base (radix). As a base-2 numeral system, it consists of only two numbers: 0 and 1.

While it has been applied in ancient Egypt, China and India for different purposes, the binary system has become the language of electronics and computers in the modern world. This is the most efficient system to detect an electric signal’s off (0) and on (1) state. It is also the basis for binary code that is used to compose data in computer-based machines. Even the digital text that you are reading right now consists of binary numbers.

Reading a binary number is easier than it looks: This is a positional system; therefore, every digit in a binary number is raised to the powers of 2, starting from the rightmost with 2^{0}. In the binary system, each binary digit refers to 1 bit.

## Hexadecimal System (Hex System)

The **hexadecimal system (shortly hex)**, uses the number 16 as its base (radix). As a base-16 numeral system, it uses 16 symbols. These are the 10 decimal digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) and the first six letters of the English alphabet (A, B, C, D, E, F). The letters are used because of the need to represent the values 10, 11, 12, 13, 14 and 15 each in one single symbol.

Hex is used in mathematics and information technologies as a more friendly way to represent binary numbers. Each hex digit represents four binary digits; therefore, hex is a language to write binary in an abbreviated form.

Four binary digits (also called nibbles) make up half a byte. This means one byte can carry binary values from 0000 0000 to 1111 1111. In hex, these can be represented in a friendlier fashion, ranging from 00 to FF.

In html programming, colors can be represented by a 6-digit hexadecimal number: FFFFFF represents white whereas 000000 represents black.

### How to Convert Binary to Hex

**Converting from binary to hex** is easy since hexadecimal numbers are simplified versions of binary strings. You just need to remember that each hex digit represents four binary digits. It follows that four binary digits will be equal to one hex digit. The method is easier than it sounds but it’s always useful to use a binary to hex conversion chart to save time.

**Step 1:** Write down the binary number and group the digits (0’s and 1’s) in sets of four. Start doing this from the right. If the leftmost group doesn’t have enough digits to make up a set of four, add extra 0’s to make a group.

**Step 2:** Write 8, 4, 2 and 1 below each group. These are the weights of the positions or place holders in the number (2^{3}, 2^{2}, 2^{1} and 2^{0}).

**Step 3:** Every group of four in binary will give you one digit in hexadecimal. Multiply the 8, 4, 2 and 1’s by the digit above.

**Step 4:** Add the products within each set of four. Write the sums below the groups they belong to.

**Step 5:** The digits you get from the sums in each group will give you the hexadecimal number, from left to right.

Now, let’s apply these steps to, for example, the binary number (10101010)_{2}

**Step 1:** 10101010 has eight digits and therefore can be grouped in sets of four without adding 0’s.

Think of the number as (1010)(1010)

**Step 2:** Write 8, 4, 2 and 1 below each group.

1010 1010

8421 8421

**Step 3: **Multiply the 8, 4, 2 and 1’s with the digit above.

1010 1010

8421 8421

8020 8020

**Step 4:** Add the products within each set of four.

In the first group, 8 + 2 = 10

In the second group, 8 + 2 = 10

Write these digits below the groups they belong to.

1010 1010

8421 8421

8020 8020

10 10

**Step 5:** Notice that, in order to represent values above 9, letters will be used. 10 is represented as the letter A in the hexadecimal system. Therefore, (10101010)_{2} = (AA)_{16}

#### Binary to Hex Conversion Examples

**Example 1**: (10001110)_{2} = (8E)_{16}

1000 1110

8421 8421

8000 8420

8 15

8 E

**Example 2**: (111011.111)_{2} = (3B.E)_{16}

(Notice that this binary number has a decimal point and cannot be automatically grouped in sets of four. You need to add 0’s both the leftmost and the rightmost parts.)

0011 1011. 1110

8421 8421 8421

0021 8021 8420

3 11. 14

3 B. E

#### Binary to Hexadecimal Conversion Chart

The following binary to hexadecimal conversion chart shows which four binary digits are equivalent to which hex symbol:

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

00000001 | 1 |

00000010 | 2 |

00000011 | 3 |

00000100 | 4 |

00000101 | 5 |

00000110 | 6 |

00000111 | 7 |

00001000 | 8 |

00001001 | 9 |

00001010 | A |

00001011 | B |

00001100 | C |

00001101 | D |

00001110 | E |

00001111 | F |

00010000 | 10 |

00010001 | 11 |

00010010 | 12 |

00010011 | 13 |

00010100 | 14 |

00010101 | 15 |

00010110 | 16 |

00010111 | 17 |

00011000 | 18 |

00011001 | 19 |

00011010 | 1A |

00011011 | 1B |

00011100 | 1C |

00011101 | 1D |

00011110 | 1E |

00011111 | 1F |

00100000 | 20 |

00100001 | 21 |

00100010 | 22 |

00100011 | 23 |

00100100 | 24 |

00100101 | 25 |

00100110 | 26 |

00100111 | 27 |

00101000 | 28 |

00101001 | 29 |

00101010 | 2A |

00101011 | 2B |

00101100 | 2C |

00101101 | 2D |

00101110 | 2E |

00101111 | 2F |

00110000 | 30 |

00110001 | 31 |

00110010 | 32 |

00110011 | 33 |

00110100 | 34 |

00110101 | 35 |

00110110 | 36 |

00110111 | 37 |

00111000 | 38 |

00111001 | 39 |

00111010 | 3A |

00111011 | 3B |

00111100 | 3C |

00111101 | 3D |

00111110 | 3E |

00111111 | 3F |

01000000 | 40 |

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

01000001 | 41 |

01000010 | 42 |

01000011 | 43 |

01000100 | 44 |

01000101 | 45 |

01000110 | 46 |

01000111 | 47 |

01001000 | 48 |

01001001 | 49 |

01001010 | 4A |

01001011 | 4B |

01001100 | 4C |

01001101 | 4D |

01001110 | 4E |

01001111 | 4F |

01010000 | 50 |

01010001 | 51 |

01010010 | 52 |

01010011 | 53 |

01010100 | 54 |

01010101 | 55 |

01010110 | 56 |

01010111 | 57 |

01011000 | 58 |

01011001 | 59 |

01011010 | 5A |

01011011 | 5B |

01011100 | 5C |

01011101 | 5D |

01011110 | 5E |

01011111 | 5F |

01100000 | 60 |

01100001 | 61 |

01100010 | 62 |

01100011 | 63 |

01100100 | 64 |

01100101 | 65 |

01100110 | 66 |

01100111 | 67 |

01101000 | 68 |

01101001 | 69 |

01101010 | 6A |

01101011 | 6B |

01101100 | 6C |

01101101 | 6D |

01101110 | 6E |

01101111 | 6F |

01110000 | 70 |

01110001 | 71 |

01110010 | 72 |

01110011 | 73 |

01110100 | 74 |

01110101 | 75 |

01110110 | 76 |

01110111 | 77 |

01111000 | 78 |

01111001 | 79 |

01111010 | 7A |

01111011 | 7B |

01111100 | 7C |

01111101 | 7D |

01111110 | 7E |

01111111 | 7F |

10000000 | 80 |

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

10000001 | 81 |

10000010 | 82 |

10000011 | 83 |

10000100 | 84 |

10000101 | 85 |

10000110 | 86 |

10000111 | 87 |

10001000 | 88 |

10001001 | 89 |

10001010 | 8A |

10001011 | 8B |

10001100 | 8C |

10001101 | 8D |

10001110 | 8E |

10001111 | 8F |

10010000 | 90 |

10010001 | 91 |

10010010 | 92 |

10010011 | 93 |

10010100 | 94 |

10010101 | 95 |

10010110 | 96 |

10010111 | 97 |

10011000 | 98 |

10011001 | 99 |

10011010 | 9A |

10011011 | 9B |

10011100 | 9C |

10011101 | 9D |

10011110 | 9E |

10011111 | 9F |

10100000 | A0 |

10100001 | A1 |

10100010 | A2 |

10100011 | A3 |

10100100 | A4 |

10100101 | A5 |

10100110 | A6 |

10100111 | A7 |

10101000 | A8 |

10101001 | A9 |

10101010 | AA |

10101011 | AB |

10101100 | AC |

10101101 | AD |

10101110 | AE |

10101111 | AF |

10110000 | B0 |

10110001 | B1 |

10110010 | B2 |

10110011 | B3 |

10110100 | B4 |

10110101 | B5 |

10110110 | B6 |

10110111 | B7 |

10111000 | B8 |

10111001 | B9 |

10111010 | BA |

10111011 | BB |

10111100 | BC |

10111101 | BD |

10111110 | BE |

10111111 | BF |

11000000 | C0 |

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

11000001 | C1 |

11000010 | C2 |

11000011 | C3 |

11000100 | C4 |

11000101 | C5 |

11000110 | C6 |

11000111 | C7 |

11001000 | C8 |

11001001 | C9 |

11001010 | CA |

11001011 | CB |

11001100 | CC |

11001101 | CD |

11001110 | CE |

11001111 | CF |

11010000 | D0 |

11010001 | D1 |

11010010 | D2 |

11010011 | D3 |

11010100 | D4 |

11010101 | D5 |

11010110 | D6 |

11010111 | D7 |

11011000 | D8 |

11011001 | D9 |

11011010 | DA |

11011011 | DB |

11011100 | DC |

11011101 | DD |

11011110 | DE |

11011111 | DF |

11100000 | E0 |

11100001 | E1 |

11100010 | E2 |

11100011 | E3 |

11100100 | E4 |

11100101 | E5 |

11100110 | E6 |

11100111 | E7 |

11101000 | E8 |

11101001 | E9 |

11101010 | EA |

11101011 | EB |

11101100 | EC |

11101101 | ED |

11101110 | EE |

11101111 | EF |

11110000 | F0 |

11110001 | F1 |

11110010 | F2 |

11110011 | F3 |

11110100 | F4 |

11110101 | F5 |

11110110 | F6 |

11110111 | F7 |

11111000 | F8 |

11111001 | F9 |

11111010 | FA |

11111011 | FB |

11111100 | FC |

11111101 | FD |

11111110 | FE |

11111111 | FF |

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No need to multiply by 0 or 1 you can simply add the digits to get the correct answer

1010 1010

8421 = 10 8421 = 10

= AA

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Example 1 is correct. The arithmetic related to 8420 indeed equals 14, but the way you are counting may be fooling you. Recall that counting starts at zero, so the tenth digit is actually the number 9. When you reach ten in hex, you start using letters. Thus 10=A, 11=B, 12=C, 13=D, 14=E, and 15=F.

As other said befores there is a error in example 1, 8420 is equal to 14 not 15

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