Only Yes and No

What this book is about

In the HSC ICT book, binary is taught as a conversion rule — divide by two, write the remainder, read it upwards. Logic gates are taught by memorising truth tables. So students can perform the steps and still have no idea why those are the rules, or what any of it has to do with a computer.

This book goes the other way. First we see what can be done with switches; then we find out why those operations are called AND, OR and XOR; and at the end we build a machine that adds two numbers together, out of nothing but gates. What you need to know beforehand is: how to add, what "place value" means — that the 2 in 205 means two hundred — and roughly how the switch in a torch works. Nothing else.

Stop at page 37. Across those two pages 1011 and 0110 are added by two completely separate routes: once by detouring through decimal, once staying in binary with the carry rule. Both give 10001. The two methods share nothing, so if the carry rule were wrong they would disagree. That page is the spine of the book. Keep paper and pen to hand — in at least ten places you are asked to stop and fill in a row yourself.

What is inside

• Two is enough: lit or not lit, the shopkeeper's box of weights, why ten and why two
• Deciding with yes and no — two switches in a row is AND, side by side is OR, NOT, the

staircase light that is a real XOR, truth tables and NAND

• Adding with gates: one bit, the full adder, four of them joined, and why subtraction is

addition in disguise

• The switch itself — the relay, the transistor, how many fit on a chip, and why it gets hot
• Beyond numbers: letters as numbers, pictures and colour, memory, the clock, and base sixteen
• Who built it — Piṅgala's light and heavy syllables, Leibniz in 1703, George Boole, Claude

Shannon and the bridge between them, and the long road of two symbols

• Two experiments, everything on one sheet, worked exercises, a bilingual glossary and a quiz