# Hexadecimal to Binary Converter

To use this **hex to binary converter** tool, just type a hex value like 1E into the left field below, and then hit the Convert button.
Therefore, you can convert up to 16 hex characters (max. value of 7fffffffffffffff).

## 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.

## 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.

### How to Convert Hex to Binary

Converting from hex to binary is straightforward since hexadecimal numbers are simplified versions of binary strings. You just need to remember that each hex value will produce four binary digits.

**Step 1**: Write down the hex number. If there are any, change the hex values represented by letters to their decimal equivalents.**Step 2**: Each hex digit represents four binary digits and therefore is equal to a power of 2. The rightmost digit equals to 2^{0}(1), the next one equals to 2^{1}(2), the next one equals to 2^{2}(4) and the leftmost one equals to 2^{3}(8). Write these numbers (8, 4, 2 and 1) below the hex values.**Step 3**: Determine which powers of two (8, 4, 2 or 1) sum up to your hex digits. For example, if one of your hex values is 10, this means 8 and 2 sum up to 10 (4 and 1 are not used). If your hex number is 2, only 2 is used; 8, 4 and 1 are not.**Step 4**: Write down 1 below those 8, 4, 2 and 1’s that are used. Write down 0 below those that are not used.**Step 5**: Read the 1’s and 0’s from left to right to get the binary equivalent of the given hex number.

Let's apply these steps to the hex number (4FA)_{16}

Step 1: 4 F A 4 15 10 Step 2: 4 F A 4 15 10 8421 8421 8421 Step 3: 4 F A 4 5 10 8421 8421 8421 (Notice the bold digits sum up to the hex value above. So the bold digits are 1 and the others are 0.) Step 4: 4 F A 4 15 10 8421 8421 8421 0100 1111 1010 Step 5: (4FA)_{16}= (10011111010)_{2}

#### Hex to binary conversion examples

Example 1: (2C1)_{16}= (1011000001)_{2}2 C 1 2 12 1 8421 8421 8421 0010 1100 0001 Example 2: (9DB2)_{16}= (1001110110110010)_{2}9 D B 2 9 13 11 2 8421 8421 8421 8421 1001 1101 1011 0010

Related converters: Binary To Hex Converter

#### Hexadecimal to Binary Conversion Chart

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

1 | 00000001 |

2 | 00000010 |

3 | 00000011 |

4 | 00000100 |

5 | 00000101 |

6 | 00000110 |

7 | 00000111 |

8 | 00001000 |

9 | 00001001 |

A | 00001010 |

B | 00001011 |

C | 00001100 |

D | 00001101 |

E | 00001110 |

F | 00001111 |

10 | 00010000 |

11 | 00010001 |

12 | 00010010 |

13 | 00010011 |

14 | 00010100 |

15 | 00010101 |

16 | 00010110 |

17 | 00010111 |

18 | 00011000 |

19 | 00011001 |

1A | 00011010 |

1B | 00011011 |

1C | 00011100 |

1D | 00011101 |

1E | 00011110 |

1F | 00011111 |

20 | 00100000 |

21 | 00100001 |

22 | 00100010 |

23 | 00100011 |

24 | 00100100 |

25 | 00100101 |

26 | 00100110 |

27 | 00100111 |

28 | 00101000 |

29 | 00101001 |

2A | 00101010 |

2B | 00101011 |

2C | 00101100 |

2D | 00101101 |

2E | 00101110 |

2F | 00101111 |

30 | 00110000 |

31 | 00110001 |

32 | 00110010 |

33 | 00110011 |

34 | 00110100 |

35 | 00110101 |

36 | 00110110 |

37 | 00110111 |

38 | 00111000 |

39 | 00111001 |

3A | 00111010 |

3B | 00111011 |

3C | 00111100 |

3D | 00111101 |

3E | 00111110 |

3F | 00111111 |

40 | 01000000 |

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

41 | 01000001 |

42 | 01000010 |

43 | 01000011 |

44 | 01000100 |

45 | 01000101 |

46 | 01000110 |

47 | 01000111 |

48 | 01001000 |

49 | 01001001 |

4A | 01001010 |

4B | 01001011 |

4C | 01001100 |

4D | 01001101 |

4E | 01001110 |

4F | 01001111 |

50 | 01010000 |

51 | 01010001 |

52 | 01010010 |

53 | 01010011 |

54 | 01010100 |

55 | 01010101 |

56 | 01010110 |

57 | 01010111 |

58 | 01011000 |

59 | 01011001 |

5A | 01011010 |

5B | 01011011 |

5C | 01011100 |

5D | 01011101 |

5E | 01011110 |

5F | 01011111 |

60 | 01100000 |

61 | 01100001 |

62 | 01100010 |

63 | 01100011 |

64 | 01100100 |

65 | 01100101 |

66 | 01100110 |

67 | 01100111 |

68 | 01101000 |

69 | 01101001 |

6A | 01101010 |

6B | 01101011 |

6C | 01101100 |

6D | 01101101 |

6E | 01101110 |

6F | 01101111 |

70 | 01110000 |

71 | 01110001 |

72 | 01110010 |

73 | 01110011 |

74 | 01110100 |

75 | 01110101 |

76 | 01110110 |

77 | 01110111 |

78 | 01111000 |

79 | 01111001 |

7A | 01111010 |

7B | 01111011 |

7C | 01111100 |

7D | 01111101 |

7E | 01111110 |

7F | 01111111 |

80 | 10000000 |

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

81 | 10000001 |

82 | 10000010 |

83 | 10000011 |

84 | 10000100 |

85 | 10000101 |

86 | 10000110 |

87 | 10000111 |

88 | 10001000 |

89 | 10001001 |

8A | 10001010 |

8B | 10001011 |

8C | 10001100 |

8D | 10001101 |

8E | 10001110 |

8F | 10001111 |

90 | 10010000 |

91 | 10010001 |

92 | 10010010 |

93 | 10010011 |

94 | 10010100 |

95 | 10010101 |

96 | 10010110 |

97 | 10010111 |

98 | 10011000 |

99 | 10011001 |

9A | 10011010 |

9B | 10011011 |

9C | 10011100 |

9D | 10011101 |

9E | 10011110 |

9F | 10011111 |

A0 | 10100000 |

A1 | 10100001 |

A2 | 10100010 |

A3 | 10100011 |

A4 | 10100100 |

A5 | 10100101 |

A6 | 10100110 |

A7 | 10100111 |

A8 | 10101000 |

A9 | 10101001 |

AA | 10101010 |

AB | 10101011 |

AC | 10101100 |

AD | 10101101 |

AE | 10101110 |

AF | 10101111 |

B0 | 10110000 |

B1 | 10110001 |

B2 | 10110010 |

B3 | 10110011 |

B4 | 10110100 |

B5 | 10110101 |

B6 | 10110110 |

B7 | 10110111 |

B8 | 10111000 |

B9 | 10111001 |

BA | 10111010 |

BB | 10111011 |

BC | 10111100 |

BD | 10111101 |

BE | 10111110 |

BF | 10111111 |

C0 | 11000000 |

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

C1 | 11000001 |

C2 | 11000010 |

C3 | 11000011 |

C4 | 11000100 |

C5 | 11000101 |

C6 | 11000110 |

C7 | 11000111 |

C8 | 11001000 |

C9 | 11001001 |

CA | 11001010 |

CB | 11001011 |

CC | 11001100 |

CD | 11001101 |

CE | 11001110 |

CF | 11001111 |

D0 | 11010000 |

D1 | 11010001 |

D2 | 11010010 |

D3 | 11010011 |

D4 | 11010100 |

D5 | 11010101 |

D6 | 11010110 |

D7 | 11010111 |

D8 | 11011000 |

D9 | 11011001 |

DA | 11011010 |

DB | 11011011 |

DC | 11011100 |

DD | 11011101 |

DE | 11011110 |

DF | 11011111 |

E0 | 11100000 |

E1 | 11100001 |

E2 | 11100010 |

E3 | 11100011 |

E4 | 11100100 |

E5 | 11100101 |

E6 | 11100110 |

E7 | 11100111 |

E8 | 11101000 |

E9 | 11101001 |

EA | 11101010 |

EB | 11101011 |

EC | 11101100 |

ED | 11101101 |

EE | 11101110 |

EF | 11101111 |

F0 | 11110000 |

F1 | 11110001 |

F2 | 11110010 |

F3 | 11110011 |

F4 | 11110100 |

F5 | 11110101 |

F6 | 11110110 |

F7 | 11110111 |

F8 | 11111000 |

F9 | 11111001 |

FA | 11111010 |

FB | 11111011 |

FC | 11111100 |

FD | 11111101 |

FE | 11111110 |

FF | 11111111 |

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