# A CDE Definition

AND-OR-NOT

The fundamental operations of Boolean logic. To learn how they function and how they are wired together to build circuits, see Boolean logic.

**The Mathematics of Logic**

Boolean logic

The "mathematics of logic," developed by English mathematician George Boole in the mid-19th century. Its rules govern logical functions (true/false) and are the foundation of all electronic circuits in the computer. As add, subtract, multiply and divide are the primary operations of arithmetic, AND, OR and NOT are the primary operations of Boolean logic. Boolean logic is turned into logic gates on the chip, and the logic gates make up logic circuits that perform functions such as how to add two numbers together.

Various permutations of AND, OR and NOT are used, including NAND, NOR, XOR and XNOR. The rules, or truth tables, for AND, OR and NOT follow. See Boolean search, binary, logic gate and Bebop to the Boolean Boogie.

Curious About the Chip?

Wired in patterns of Boolean logic and in less space than a postage stamp, transistors in one of today's high-speed chips collectively open and close quadrillions of times every second. If you are curious about how it really works down deep in the layers of the silicon, read the rest of "Boolean logic," then "chip" and, finally, "transistor." It is a fascinating venture into a microscopic world.The following AND, OR and NOT examples use mechanical switches to show open and closed transistors. The switching part of an actual transistor is solid state (see transistor).

**An AND Gate (Wired in Series)**

**An OR Gate (Wired in Parallel)**

**A NOT Gate (Input Is Reversed)**

**The Hierarchy**

**Adding Two Bits Together**

**The Half-Adder Circuit**

**Try It Yourself**

**Before/After Your Search Term**

**Terms By Topic**

Click any of the following categories for a list of fundamental terms.