Boolean Algebra

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A light switch can only be in one of two states: on or off. There is no in between setting. Boolean algebra is a kind of math built entirely around that same idea, except instead of "on" and "off" it uses "true" and "false," and instead of adding and subtracting numbers, it combines true and false statements using a small set of simple rules.

An English mathematician named George Boole invented this system in 1854, in a book with the wonderful title "The Laws of Thought." He was just trying to turn ordinary logical reasoning into something you could calculate with, like arithmetic. Computers would not exist for almost a hundred more years, but when they finally were invented, engineers discovered that Boole's math was exactly what they needed.

The three basic moves

Boolean algebra mostly comes down to three simple operations:

• AND is true only when both things are true. A light wired so it only turns on when switch A and switch B are both flipped on is doing an AND.
• OR is true when at least one thing is true. A light wired so it turns on if switch A or switch B, or both, are flipped on is doing an OR.
• NOT flips a value to its opposite. A switch that turns a light off exactly when you flip it on is doing a NOT.

Everything else in Boolean algebra, no matter how complicated, is just these three moves combined and chained together in different patterns.

Why every computer depends on it

Modern computer chips are built from billions of tiny electronic switches called transistors, wired together to perform AND, OR, and NOT on tiny pulses of electricity that stand for true and false. A single piece of computer memory, called a bit, is always exactly one of those two values, usually written as 1 for true and 0 for false. Every single thing a computer does, showing a photo, playing a song, checking a password, is ultimately millions of these true and false switches flipping according to Boolean algebra's rules, just extremely fast.

Where else it shows up

• Searching "cats AND dogs" versus "cats OR dogs" on a search engine gives very different results, and that difference is pure Boolean algebra.
• Spreadsheet formulas with AND, OR, and IF let you combine several true or false conditions into one decision.
• Everyday reasoning like "I can go outside if my homework is done and it is not raining" is really a Boolean algebra statement, whether you write out the math or not.

Fun facts

• George Boole never saw a single computer built on his ideas. He died in 1864, more than 70 years before the first ones existed.
• The word "bit" is short for "binary digit," a fancy way of saying a single true or false value, exactly what Boolean algebra is built from.
• Boole's daughter, Ethel Lilian Voynich, grew up to become a successful novelist, best known for writing "The Gadfly."
• Nobody connected Boole's math to electrical circuits until 1937, when an American graduate student named Claude Shannon wrote a master's thesis showing that Boolean algebra could design and simplify switching circuits. It is often called one of the most important master's theses of the entire 20th century.