Explaining the Value of Knowledge of Digital Logic I am a college teacher developing an introduction to digital logic for grades 8-12.  This is a special topic that will be presented in three 50-minute periods with in-class exercises.  It won't go beyond basic combinational logic.  Provisionally, module 1 starts with gates and truth tables and ends with a half-adder; module 2 extends to a four-bit ripple-carry adder, and module 3 extends the ripple-carry adder to make a two's complement adder/subtractor.  These are not set in stone, but will be rather soon.

I am struggling with how to explain the importance of a knowledge of digital logic to high school and upper middle school students.  I want something better than, "To help you understand that computers are not magic."  Ideally, the explanation would be only a short paragraph, and memorable.

So, how can I explain the importance of comprehension of simple digital logic to pre-college students?  That is, how do I explain why students should care about this topic?

Edit:  Well, I'm teaching this to eighth-graders beginning Wednesday!  Day one is about what I planned last fall.  Day 2 has a ripple-carry adder and something else.  I'm still dithering between adder-subtractor and S-R latch which becomes a D-latch.  (I'm not sure the kids have enough grounding in binary arithmetic for the adder-subtractor.)

Day 3 now introduces a little bit of Boolean algebra.  The kids are introduced to Kat, who is heading for Hogwarts, and must design Kat's cat checker.  There are five inputs and three possible "OK" results from among the combinations.

For the explanation that everything computers do comes from a few simple circuits, as suggested by Ben I. below, I'm going to show this video at the beginning of day 1: https://www.youtube.com/watch?v=ZoqMiFKspAA
Your best bet of how to answer why students should care is to stop and ask yourself what good reasons there are to care about it (or any topic). Do that before reading on?

OK, so my answer is: because science. The word means knowledge. If you want to know something instead of just have opinions (possibly wrong) or worse, then you will want to be finding out. But why bother to know anything, is really the question. Caring is your issue. Caring means that one can influence things, and not caring means that one will be pushed around helplessly by circumstances.

Is it effective to care, is the obvious question? Can we actually learn enough to have any effect? When things seem perplexing and obscenely complicated, then it appears hopeless. Science brings hope because it is able to render the complex simple enough to manage. When I found out that all matter is composed of just 3 elementary particles, and that there are basically only 2 forces that affect us, only one of which we have any control over, it was revolutionary. If more people knew these things, they might wish to learn more. When you ponder the 88 keys on a piano, able to make basically all (western) music, or the 92 naturally occurring elements making basically all things, it is astonishing. The organization of atoms (predicted 2500 years ago) in to the stunning wonder of the Periodic Table is a great story!

All computers are made of transistors, and built up in to a few simple circuits replicated millions of times, like the cells of the body or brain. If that is not inspiring and provoking of interest, I would release the students from school, as they are unreachable: they don't care to have an influence on their own future.