## Seven Segment Displays

You probably haven’t thought much about them. However, they are everywhere! You might know seven segment displays from the digital watches that we all had in the 80s, making up each digit of the time, as well as from many other electronic clocks, thermometers, radios, CD players, VCRs/DVDs, calculators and even in lifts.

In fact, seven segment displays premiered in the 1968 film 2001: A Space Odyssey and were later to appear in the first digital watch – the Pulsar – which came out in 1972 and cost \$2,100. It’s ironic that by the time 2001 came, the digital watch had already gone out of fashion.

Anyway, in the early hours of the morning recently, I was staring at the clock and started wondering about the fact that although seven segments are used, only 10 different patterns are displayed. There are 128 (i.e. 2 to the power of 7) different patterns that can be displayed on a seven segment display, which is a few more than are really needed. In fact, you should only need four segments to display 10 patterns, so three of the segments are, in a sense, redundant.

I wrote a quick and dirty computer program to see which segments could be removed, or burn-out, and you would still be able to tell the difference between the different digits. It turns out that the bottom and bottom-right segments could be removed, and the standard patterns that make up the digits one through zero are still unique. This is shown in following the diagram:

However, we can do better. There are a number of variations on the patterns used for some of the digits. There are alternatives for one, six, seven, nine and zero, as shown here:

I remember my Dad’s precious digital calculator from the late 70s used the variant for zero shown here. Although, I admit I don’t recall having seen it anywhere since.

Using the software I developed, I looked for whether by using any of these alternative versions of the digital numbers, if there was a way of removing three segments from the display but still being able to tell the difference between the numbers. In fact, there was a way to remove another segment, if we use the variants for zero and six (and also nine, since we might as well have them match, although it’s not necessary). This special set of digits is shown here:

From this set of digits, we can remove both right segments and the middle segment, and the remaining patterns for the digits can still be distinguished. Although, to be honest, it is a bit strange.

It does show that we don’t need the full seven segments, and only need four. But, clearly, it’s not possible to go any fewer.

I can’t think of any applications for this four segment display, but it makes me happy to know that it’s possible to make one that is also compatible with existing patterns for the ten digits. And if the special set of digits is used, then up to three segments can fail on a display while it remains (somewhat) useful.