7 lessons
What is a computer, really?
Before registers and pipelines mean anything, start with the one idea underneath all of them - a machine built from switches that only ever does exactly what it's told.
Binary, decimal and hexadecimal - counting with different amounts of fingers
Why computers count in binary, how place value math actually works, and how to freely convert between binary, decimal and hex by hand.
How does binary represent negative numbers?
There are no minus signs inside a computer. Here's how two's complement lets addition hardware handle negative numbers for free.
How does binary store 3.14? Floating point, BCD and character codes
Two's complement only handles whole numbers. Here's how computers represent fractions using scientific notation in binary, plus the smaller codes worth knowing - BCD, ASCII and parity bits.
Logic gates - teaching switches to make decisions
How a handful of transistors combine into AND, OR and NOT gates, and how Boolean algebra lets you calculate with true/false the same way you calculate with numbers.
Building an adder - combinational circuits from gates
Wire a handful of gates together and you get a circuit that adds numbers, or chooses between inputs. Here's how the half adder, full adder, and multiplexer actually work.
Giving circuits a memory - flip-flops, registers and the clock
Combinational circuits forget everything instantly. Here's how a tiny feedback loop lets a circuit remember one bit, and how a clock signal keeps millions of them in sync.