Boolean algebra

So let's connect the dots here.

If a relay is an automated switch, and in our pet shop example, we proved that physical switches can perform complex Boolean logic.

Therefore, relays can perform automated Boolean logic.

Exactly.

Which brings us to our final act.

But to actually build it, Petzold tells us we have to put down our soldering irons, defer our hardware project, and go all the way back to elementary school to relearn how to count.

We have to learn binary.

But you now have the foundational physics and the Boolean logic to understand exactly why a computer physically requires binary to operate.

Both variations produced lower scores for all tested models, but Astra was still the clear outlier, outperforming all the other models by roughly a factor of three.

Heading Boolean circuits At some point I thought that Astra's internal calculations might work somewhat like an analog computer, which accumulates error with each operation, such that long chains of calculation become unreliable due to accumulating error.

In an attempt to avoid that issue, I created a benchmark task based on Boolean circuits, which should be less sensitive to accumulated error.

The boolean tasks look like this.

There's a details box here with the title full prompt.

Each step depends directly on the result of the previous step.

The destination of the previous step is one of the inputs of the AND OR operator of the next step.

Each step contains two sequential Boolean operations, so an end step task requires two end sequential Boolean operations.