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