# How to Read a Binary Clock Display

Binary clocks display the time digitally using the base-2 representation of numbers. In binary, only 1's and 0's are used to form numbers. A sleek binary clock display has 3 columns (or rows, depending on how the clock is oriented). The first column displays the current hour, the middle column displays the minutes, and the last column displays the seconds. The hour column has four lights, since 12 has four digits in binary and 12 is the largest hour number. The minutes and seconds columns each have six lights, since 59 has six digits in binary and 59 is the highest number of minutes or seconds.

When a light is on, it represents 1, and when a light is off, it represents 0. The bottom row of lights represents 2^{0} = 1, the next row represents 2^{1} = 2, and so on until the top row, which represents 2^{5} = 32. The image below shows how 10:25:46 is shown on a binary clock.

The binary representation of 10 is 1010, the binary form of 25 is 11001, and the binary form of 46 is 101110. One of the nice visual features of a binary clock is that the seconds column changes every second, so the clock blinks.

Another style of binary clock has six columns. The first two columns display the two digits of the hour, the middle columns display the two digits of the minutes, and the last two columns show the digits of the seconds. Use the table below as an aid when converting a decimal number to binary. Learning how to read a binary clock takes a little practice, but once you get comfortable with the number system, you will start to memorize the patterns.

0 | 0 | 15 | 1111 | 30 | 11110 | 45 | 101101 |

1 | 1 | 16 | 10000 | 31 | 11111 | 46 | 101110 |

2 | 10 | 17 | 10001 | 32 | 100000 | 47 | 101111 |

3 | 11 | 18 | 10010 | 33 | 100001 | 48 | 110000 |

4 | 100 | 19 | 10011 | 34 | 100010 | 49 | 110001 |

5 | 101 | 20 | 10100 | 35 | 100011 | 50 | 110010 |

6 | 110 | 21 | 10101 | 36 | 100100 | 51 | 110011 |

7 | 111 | 22 | 10110 | 37 | 100101 | 52 | 110100 |

8 | 1000 | 23 | 10111 | 38 | 100110 | 53 | 110101 |

9 | 1001 | 24 | 11000 | 39 | 100111 | 54 | 110110 |

10 | 1010 | 25 | 11001 | 40 | 101000 | 55 | 110111 |

11 | 1011 | 26 | 11010 | 41 | 101001 | 56 | 111000 |

12 | 1100 | 27 | 11011 | 42 | 101010 | 57 | 111001 |

13 | 1101 | 28 | 11100 | 43 | 101011 | 58 | 111010 |

14 | 1110 | 29 | 11101 | 44 | 101100 | 59 | 111011 |

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