Binary clock

Most binary clocks use six columns, one for each digit of the time. The first two columns are the hours, the middle two the minutes and the last two the seconds. In each column the bottom dot is worth 1, and every dot above it is worth twice the one below, so 2, then 4, then 8. Add up the lit dots in a column and you have that digit.

Take 21:47:03. The first hours column has one dot lit, the 2. The second has just the 1, so the hour is 21. For the minutes, the tens column shows the 4 and the ones column lights 4 with 2 and 1, which add up to 7. The seconds have nothing lit in the tens and the 2 and 1 in the ones, so 03.

This way of writing each decimal digit in its own four bits is called binary-coded decimal, or BCD. The tens columns need fewer dots than the others, since the tens of minutes and seconds never go past 5 and the tens of hours never past 2. That's why the clock above has short columns. With the numbers turned on, each column's digit is shown underneath so you can check yourself.

The second layout skips the digits and writes each part of the time as one binary number. Hours take five places on a 24-hour clock, enough for 0 to 23. Minutes and seconds each take six, enough for 0 to 59, which makes 17 dots in all. The places are worth 32 at the left, halving each step to 1 at the right, just as in any binary number.

A big public clock of this kind is on St. Gallen railway station in Switzerland. Made by the artist Norbert Möslang, it shows the time on three lines of lights, one each for the hours, the minutes and the seconds across the front of the station.

The third layout throws out hours and minutes altogether. Its first dot says whether it's past noon, which is half the day. The second splits that half again, into quarters of a day, and each dot after that halves the one before. After sixteen dots the smallest step is 1/65536 of a day, which comes to about 1.32 seconds.

Sixteen bits make exactly four hex digits, so true binary time is easy to write down. Noon is 8000 in hex, six in the evening is C000, and the last moment before midnight is FFFF. Because 1.32 seconds isn't a whole second, the clock shows the start of each step rounded down to the second.

Quiz me sets the clock to a random time and hides the numbers. Type the time you read, press Check, and the answer appears. It works in any of the three layouts, and on the 12-hour clock either am or pm counts, because a 12-hour binary clock has no dot that tells them apart.

The practice sheet prints eight clocks in whichever layout is chosen, with a line under each for the answer and a short key at the top. The answers are in small print at the bottom of the page, so fold that strip under before handing it out. Every print gives a fresh set of times.