Logic gates and truth tables

Last time

Before we start: last time, in Circuits and truth tables from a logic statement, you learned these points. Here they are again on one card. Keep them in mind, because today builds on them.

Computers are made of switches

Inside every processor, millions of tiny switches decide yes or no. Each decision is made by a logic gate. A gate takes one or two inputs, each a one or a zero, and produces one output. In this lesson we learn six gates, and how to read them in a circuit.

Gates and truth tables

A logic gate is an electronic component that performs a logical operation on binary inputs. One means true, on or high. Zero means false, off or low. A truth table shows the output for every possible combination of inputs. A logic circuit joins gates together: the output of one becomes the input of the next.

The NOT gate

The NOT gate has one input, and it reverses it. If A is zero, the output is one. If A is one, the output is zero. The expression is X equals NOT A.

AND and OR

AND outputs one only when both inputs are one. OR outputs one when either input is one, or both. Look down the AND column: three zeros, then one. Look down the OR column: a zero, then three ones.

NAND, NOR and XOR

NAND is NOT AND: it outputs zero only when both inputs are one. NOR is NOT OR: it outputs one only when both inputs are zero. XOR, exclusive OR, outputs one when the inputs are different.

Remember them

AND means all ones. OR means any one. XOR means different. NAND and NOR are simply the opposite of AND and OR. The small circle on NOT, NAND and NOR means invert the output. In the exam, every gate except NOT has exactly two inputs.