Binary | Decimal |
---|---|

0 | 0 |

1 | 1 |

10 | 2 |

11 | 3 |

100 | 4 |

101 | 5 |

110 | 6 |

111 | 7 |

1000 | 8 |

1001 | 9 |

1010 | 10 |

1011 | 11 |

1100 | 12 |

1101 | 13 |

1110 | 14 |

1111 | 15 |

10000 | 16 |

10001 | 17 |

10010 | 18 |

10011 | 19 |

10100 | 20 |

10101 | 21 |

10110 | 22 |

10111 | 23 |

11000 | 24 |

11001 | 25 |

11010 | 26 |

11011 | 27 |

11100 | 28 |

11101 | 29 |

11110 | 30 |

11111 | 31 |

100000 | 32 |

100001 | 33 |

100010 | 34 |

100011 | 35 |

100100 | 36 |

100101 | 37 |

100110 | 38 |

100111 | 39 |

101000 | 40 |

101001 | 41 |

101010 | 42 |

101011 | 43 |

101100 | 44 |

101101 | 45 |

101110 | 46 |

101111 | 47 |

110000 | 48 |

110001 | 49 |

110010 | 50 |

110011 | 51 |

110100 | 52 |

110101 | 53 |

110110 | 54 |

110111 | 55 |

111000 | 56 |

111001 | 57 |

111010 | 58 |

111011 | 59 |

111100 | 60 |

111101 | 61 |

111110 | 62 |

111111 | 63 |

Binary | Decimal |
---|---|

1000000 | 64 |

1000001 | 65 |

1000010 | 66 |

1000011 | 67 |

1000100 | 68 |

1000101 | 69 |

1000110 | 70 |

1000111 | 71 |

1001000 | 72 |

1001001 | 73 |

1001010 | 74 |

1001011 | 75 |

1001100 | 76 |

1001101 | 77 |

1001110 | 78 |

1001111 | 79 |

1010000 | 80 |

1010001 | 81 |

1010010 | 82 |

1010011 | 83 |

1010100 | 84 |

1010101 | 85 |

1010110 | 86 |

1010111 | 87 |

1011000 | 88 |

1011001 | 89 |

1011010 | 90 |

1011011 | 91 |

1011100 | 92 |

1011101 | 93 |

1011110 | 94 |

1011111 | 95 |

1100000 | 96 |

1100001 | 97 |

1100010 | 98 |

1100011 | 99 |

1100100 | 100 |

1100101 | 101 |

1100110 | 102 |

1100111 | 103 |

1101000 | 104 |

1101001 | 105 |

1101010 | 106 |

1101011 | 107 |

1101100 | 108 |

1101101 | 109 |

1101110 | 110 |

1101111 | 111 |

1110000 | 112 |

1110001 | 113 |

1110010 | 114 |

1110011 | 115 |

1110100 | 116 |

1110101 | 117 |

1110110 | 118 |

1110111 | 119 |

1111000 | 120 |

1111001 | 121 |

1111010 | 122 |

1111011 | 123 |

1111100 | 124 |

1111101 | 125 |

1111110 | 126 |

1111111 | 127 |

Binary is a base 2 number system. The word binary is derived from the word “binarius,” which means “consisting of two.” Like the latin translation of the word suggests this is a counting system that consists of only two digits, 0 and 1. These two digits are used to represent all numbers.

In the binary system each digit’s value is based on the power of two. This means that every digit you move to the left in a binary number string represents a higher power of 2. This is different from a number system like decimal, which most of us use every day which instead uses a base-10 system and therefore each digit as you move to the left represents a higher power of 10.

Because binary is a base 2 number system with only two digits it very quickly becomes tiresome to count in binary. For example in binary is we were to count to ten:

1, 10, 11, 100, 101, 110, 111, 1000, 1001, 1010

This is a lot more complicated than counting in our base-10 decimal number system. Computers however use binary to process and store data as it is efficient for them because it aligns perfectly with their internal electronic circuits. Circuits can represent this data in two states: on (1) and off (0).

The core difference between the decimal number system and the binary number system is that the decimal system uses 10 digits (0 to 9), while the binary system uses 2 digits (0 and 1).

In the decimal system place value increases by a power of ten every digit to the left.

However, in the binary number system place values increase by a power of two every digit to the left. .

Other number systems such as hexadecimal and octal, place values increase by a power of sixteen and eight respectively every digit to the left.

Once you understand the fundamentals of binary it is quite easy to start counting in binary numbers. Like in decimal binary numbers begin at 0. The number one is then represented as 1 in binary (again just like decimal). Here is where it starts to get tricky. The number two is represented as 10. In binary this means 2 power of 1 (2) plus 1 power of zero (0). If we move to the number three we get 11 (two to the power of 1 (2) plus 1 power of one (0)).

Now if we want to move to four we need to add a new place value to the left. We therefore get 100. Breaking this down we get (four to the power of 1 (4) plus two to the power of 0 (2) plus 1 power of one (0)). From this we can see a pattern emerging. The next four numbers repeat the pattern, where we get. 101 (five), 110 (six), 111 (seven) and then 1000 (eight) where we need to increase the place value to a new power of two.