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This is probably a very easy question to answer, but I am a visual artist and math is not my strong suit. Thanks in advance for your patience and replies.

I have a 16-segment LED alphanumeric display. I would like to light up every possible combination of those 16 segments, starting with "all off", moving through the many thousands of permutations (not just letters and numbers) to end up at "all on". Each combination flashed on the display will be unique.

How many unique combinations would this amount to? My hazy math skills jumped immediately to "16 to the power of 16" but that doesn't seem right somehow.

Can anyone please help me with this? Thank you. this image depicts the sort of display I'm referring to.

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    wow that was fast, thanks very much! – 2017-01-12
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    It's $2^{16}$, or $65536$. – 2017-01-12
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    When you get an answer you like you should accept it (the check mark). You can upvote it too (the up arrow) and can even upvote more than one answer. – 2017-01-12

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Here a fundamental combinatorial principle is at work that even an artist should be aware of.

If a pullover comes in $4$ colors, $3$ different necks, and $5$ sizes you have $4\cdot3\cdot5=60$ possibilities to choose the pullover that is right for you.

If you have $16$ lights that you can put to OFF or to ON independently then you have $2$ choices for each of these lights, making a total of $$2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2=65\,536$$ possibilities.

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The number of ways 16 settings can be switched on or off is $2^{16} = 65536$. In general if you have a binary system with $n$ bits the number of possible states is $2^n$.