The "mathematics of logic," developed by English mathematician George Boole in the mid-19th century. Just as add, subtract, multiply and divide are the primary operations of arithmetic, AND, OR and NOT are the primary operations of Boolean logic and building blocks of every digital circuit. Other common variations are derived from these three logical operators (see NAND
). See Boolean search
, logic gate
and Bebop to the Boolean Boogie
AND, OR and NOT Gates
Transistors wired in series and parallel patterns make up these "gates," which accept inputs of 0 (no pulse) or 1 (a pulse) and generate outputs of 0 or 1. While AND requires that both inputs are 1 to generate an output of 1, OR only needs one input to be 1. NOT reverses the input. For a conceptual diagram of these actions, see Boolean gates
Decimal Vs. Binary
Decimal arithmetic holds 10 values (0 to 9) in each digit position. In binary, there are only two (0 and 1). Note below the four possible result and carry bits when adding two binary digits (bits) together.
Add a One and Zero
Trace the red 1 (pulse, current) and white 0 (no pulse, no current) through the gates and notice their outputs. This half-adder circuit is in every CPU.
Trace the Flow Yourself
Choose any two binary digits as input and trace them through this half-adder circuit (0 is no current; 1 is current). Watch how the output is generated.
Patterns of Boolean Logic
Transistors, which are depicted here as mechanical switches, make up gates. Gates make up circuits, and circuits make up every digital device. There are billions of transistors in modern chips, and they fit in an area the size of a postage stamp. For more details on this mechanical conceptualization, see Boolean gates
. See transistor