52 Project 2012: Foundational Electronic Components #8 – Logic Gates

This is entry #8 of my 52 Project 2012: Foundational Electronic Components Crash Course series.

What is a logic gate?

A logic gate is a simple semiconductor device that allows for specific conditional behavior control—namely, that the behavior of an output signal is dependent on the status of one or more input signals.

How does a logic gate work?

There are a few different basic types of logic gates (NOT, AND, OR, and XOR), all of which are built simply by connecting transistors together in unique ways. By combining NOT gates with AND, OR, and XOR gates, these basic devices can be extended to a few more useful logic gates as well (NAND, NOR, and XNOR).

All of these devices work with electrical representations of logical TRUE/FALSE values, where TRUE is typically indicated by a positive voltage differential (e.g. +3v or +5v), and FALSE is typically indicated by zero voltage differential. The behavior of any logic gate can be clearly described by a truth table: a simple table which shows all possible input values with corresponding output values.

Diodes alone may be used to construct AND and OR gates, but that is all. Without the addition of a NOT gate, other types of Boolean logic are not possible using only diodes, and complex combinations of multiple diode-logic gates are impractical because of the rapid voltage drop that comes of using many diodes in a series.

Instead, the most current technological implementation of Boolean logic circuitry relies on transistors, or specifically what is known as Transistor-Transistor Logic (or TTL). By using transistors as the fundamental logic unit, extremely complex logical circuits can be created without loss, since transistors can also function as amplifiers. For a schematic of a TTL-based NAND gate (for a simple example), go here.

At a foundational level, a logic gate circuit has at least one input terminal, at least one output terminal, a FALSE (GND) reference terminal, and a TRUE (+V) reference terminal.

NOT gates

The NOT gate is the simplest of all of these, as it has only a single input terminal and a single output terminal. Its function is to output the logical opposite of whatever is applied to the input terminal. The truth table for a NOT gate is therefore as follows:

AND gates

The AND gate requires both inputs A and B to be TRUE to make the output TRUE. In all other cases, the output will be FALSE. The truth table for an AND gate is as follows:

OR gates

The OR gate requires either of the inputs A or B to be TRUE to make the output TRUE. In both are FALSE, then the output will be FALSE. The truth table for an OR gate is as follows:

XOR gates

The XOR (eXclusive-OR) gate requires that only one of the inputs A or B may be TRUE to make the output TRUE. If neither of them are TRUE, or both of them are TRUE, then the output will be FALSE. The truth table for an XOR gate is as follows:

NAND gates

The NAND gate is the negated AND gate—the output is identical to an AND gate, but inverted. It produces a TRUE output unless both inputs are TRUE. Electrically, a NAND gate is merely an AND gate with a NOT gate on the output. The truth table for an AND gate is as follows:

NOR gates

The NOR gate is the negated OR gate. It produces a TRUE output unless either input is TRUE. Electrically, a NOR gate is an OR gate with a NOT gate on the output. The truth table for a NOR gate is as follows:

XNOR gates

The XNOR gate (eXclusive Not OR) is the negated XOR gate. It produces a TRUE output whenever both inputs are the same. Electrically, an XNOR gate is an XOR gate with a NOT gate on the output. The truth table for a NOR gate is as follows:

By combining these gates, literally any logical decision tree may be represented by an electrical circuit. It is also possible to use one single type of gate (usually either NAND or NOR) to mimic the behavior of any other gate. Doing this is usually less electrically efficient by some tiny amount, but often more financially efficient since one single gate may be purchased and implemented in bulk.

If you’re interested, read more information on logic gates at Wikipedia, or at The Electronics Club.

For a description of this 52 Project series and links to the all existing entries, go to the 52 Project 2012: Foundational Electronic Components Crash Course page.