From Logic to Circuits — Boole and Shannon
On this page 5 headings
Start here “If it’s raining and I have an umbrella, I’ll go out.” “If it’s Sunday or a holiday, there’s no school.” You use logic every day. About 90 years ago, a young student showed that this everyday logic could be built with electric switches. That idea made every computer possible.
In 1854, George Boole showed that logic is a kind of maths, not just philosophy. He worked with values that are only true or false.
This is now called Boolean algebra: the maths of binary values (1 = true, 0 = false).
For many years, people built machines from relays and vacuum tubes (the vacuum tube “triode” came in 1906), but nobody linked them to Boole’s logic.
In 1937, Claude Shannon, a master’s student at MIT, noticed that:
- switches in series (one after another) behave like AND: current flows only if switch A and switch B are closed;
- switches in parallel (side by side) behave like OR: current flows if switch A or switch B is closed.
His thesis showed that any Boolean logic can be built with switches. This started binary digital electronics.
A logic gate is a small circuit that does one logic job. You’ll study these properly next week.
| Gate | Output is 1 when… | Everyday version |
|---|---|---|
| AND | all inputs are 1 | Rain and umbrella → go out |
| OR | at least one input is 1 | Sunday or holiday → no school |
| NOT | the input is 0 (it flips it) | “Not raining” |
Digital logic design means taking a job (“light the lamp when both buttons are pressed”) and building it from gates. That’s exactly what the next weeks teach, step by step:
- Describe the job in a truth table (every input → output).
- Write it as a Boolean equation.
- Turn the equation into a circuit of gates.
In one line: Boole (1854) turned logic into maths with true/false values, and Shannon (1937) showed switches can build that logic. Together they gave us digital circuits made of gates like AND, OR and NOT. Exam words: Boolean algebra, George Boole, Claude Shannon, relays, vacuum tubes, series = AND, parallel = OR, logic gate, AND, OR, NOT, digital logic design, truth table.