Binary Clocks
A binary clock swaps digits for rows of lights that are either on or off. Once you know the trick, reading one takes a few seconds of simple addition.
What a binary clock is
A binary clock shows the time using the two-symbol number system that computers use. Each light, window or dot on its face stands for a power of two, and it is either lit, meaning 1, or dark, meaning 0. Adding up the values of the lit lights in a row gives you a number, and the rows together give you hours, minutes and sometimes seconds.
Many binary clocks are electronic desk novelties or hobby projects, but the idea has also been used for public clocks and works of art. The Saarland clock museum's guide describes both of the main ways of laying the time out.
Reading a BCD binary clock
The most common layout is binary-coded decimal, or BCD. Instead of converting the whole hour or minute into binary, it converts each ordinary decimal digit separately. A clock showing 10:37 therefore has one column for the 1, one for the 0, one for the 3 and one for the 7.
Each column is read from the bottom up. As the Saarland museum explains, the lowest light is worth 1, the next 2, then 4, then 8. To read a column, add the values of the lights that are on. A column with the 1 and 2 lights lit shows 3; one with the 1, 2 and 4 lights lit shows 7. Four lights are enough for any digit from 0 to 9, and the museum notes that early computing called such a group of four bits a nibble.
There is a small cost to this approach. A University of Maryland computer science lecture on number formats notes that BCD spends four bits on every decimal digit, and since four bits can make 16 patterns, six of them go unused for each digit. On a clock that waste is visible: some lights in a BCD column can never be lit, because no digit of the time needs them. The tens-of-hours digit, for example, never goes above 2, so that column needs only two lights at most.
In the museum's example photo, taken at 1:07 in the afternoon, the lit windows in each column add up to the digits of that time. BCD clocks are easy to learn because you only ever add up to four small numbers per column, and you read the time digit by digit, just as on an ordinary digital display.
See also: the ordinary digital readout a binary clock encodes on OnlineClock.app.
Reading a true binary clock
A true binary clock converts the whole number at once. The station clock that the artist Norbert Möslang designed for the facade of the main railway station in St. Gallen, Switzerland, is a good example. According to the Saarland museum, it has three lines: hours worth 16, 8, 4, 2 and 1, and minutes and seconds each worth 32, 16, 8, 4, 2 and 1.
Five lights can count to 31, enough for every hour of a 24-hour day, and six can count to 63, enough for 59 minutes or seconds. To read it, add the lit values in each line. Hours showing the 8 and 1 lights mean 9 o'clock; minutes showing 16, 8 and 1 mean 25 past. The museum's example photo of the St. Gallen clock reads 9:25:50 in the morning.
True binary is more compact, but most people find it slower to read, because the numbers being added are bigger.
See also: how the 24-hour clock numbers the hours of the day on OnlineClock.app.
Early binary clocks
The Computer History Museum in California holds an early example: an IC clock made in 1975 by Dr. Gregory Duckworth, hand-built from medium-scale integration circuit boards. Its lights show the time in binary-coded decimal, and it is set with a knob on the back.
That same year Berlin got a public clock built on a related idea. The Mengenlehreuhr, or set theory clock, was developed in 1975 by the inventor Dieter Binninger on behalf of the Berlin Senate, according to the Saarland museum. Atlas Obscura describes its 24 lights: some stand for five-hour units, some for single hours and others for minutes and seconds, and the time is found by adding the lit blocks. Strictly it counts largely in fives rather than twos, but it works on the same principle of adding lit units.
Accounts of the clock's later life differ in the details. The Berlin newspaper taz says it first stood on the Kurfürstendamm, was switched off by the city in 1995, and was put up again in 1996 by a group of local business people behind the Europa-Center, beside the Berlin tourist center. Atlas Obscura describes it as moved in 1995 to a spot in front of a Berlin high-rise, where it still lights up with the time. Binninger himself died in a plane crash in 1991.
How to recognize one
A binary clock has no hands and no numerals on its main display, just a grid or rows of lights, sometimes with small labels such as 1, 2, 4 and 8 along one side. If the lights are arranged in four or six narrow columns of up to four lights each, it is almost certainly a BCD clock. If they run in three long rows of five or six lights, it is probably true binary, like the St. Gallen station clock.
A clock whose lights include blocks worth five hours each is more likely to be a copy of the Berlin set theory clock than a binary clock.
Questions people ask
What is the difference between BCD and true binary?
A BCD clock converts each decimal digit of the time separately, so 37 minutes is shown as a 3 and a 7. A true binary clock converts the whole number, so 37 minutes is shown as 32 + 4 + 1.
Is the Berlin set theory clock a binary clock?
Not strictly. Some of its lights stand for five-hour units and others for single hours, minutes and seconds, so it counts largely in fives, but like a binary clock it is read by adding up the lit units.
How long does it take to learn to read a binary clock?
Only a few minutes for a BCD clock: learn that the lights are worth 1, 2, 4 and 8 from the bottom up, and add the lit ones in each column.