Digital Circuits/Gates

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Logic gates are one of the fundamental units of a digital circuit. They can be made from only a handful of transitors each, and they can implement any logical function, and therefore build any digital device. At the most basic level, all digital circuits are combination of logic gates.

Logic Gates[edit]

AND, OR and NOT gates are the fundamental functions, out of which the other functions are built. The other functions available are

  • NAND: an inversion of AND's output.
  • NOR: an inversion of OR's output.
  • XOR (exclusive-OR): outputs high only if just one input is high.
  • XNOR: inversion of the output of XOR.

In total then, we have seven basic gates. Although there are sixteen possible outputs from two input logic gates, the other functions not represented here are usually made up of these seven. This idea can even be extended further - NOR or NAND are each capable of producing all the other functions and are sometimes called the "universal gates" (see NOR Logic and NAND Logic for more information). At the transistor level, many devices consist only of one of these gates. That said, by using the other gates, we make conceptualising and designing digital circuits much easier, and loses no generality, as the conversion to the relevant type of gate will be done by automatic tools if needed.

Only the NOT gate and the buffer (which just copies the input to the output) have one input. The other basic gates have two inputs, although we will later look at how to extend the concept to more inputs.

Name Function Symbol
ANSI IEC
Buffer Q=A Buffer ANSI Labelled.svg Buffer IEC Labelled.svg
NOT gate (Inverter) Q=\overline{A} NOT ANSI Labelled.svg NOT IEC Labelled.svg
AND gate Q = A \cdot B AND ANSI Labelled.svg AND IEC Labelled.svg
NAND gate (NOT−AND) Q = \overline{A \cdot B} NAND ANSI Labelled.svg NAND IEC Labelled.svg
OR gate Q = A + B OR ANSI Labelled.svg OR IEC Labelled.svg
NOR gate (NOT−OR) Q = \overline{A + B} NOR ANSI Labelled.svg NOR IEC Labelled.svg
XOR gate (Exclusive-OR) Q = A \oplus B XOR ANSI Labelled.svg XOR IEC Labelled.svg
XNOR gate (NOT−exclusive−OR) Q = \overline{A \oplus B} XNOR ANSI Labelled.svg XNOR IEC Labelled.svg

Truth Tables[edit]

The truth tables for the seven common logic gates are given below:

A B Logic Gate Output
NOT A A AND B A NAND B A OR B A NOR B A XOR B A XNOR B
0 0 1 0 1 0 1 0 1
0 1 1 0 1 1 0 1 0
1 0 0 0 1 1 0 1 0
1 1 0 1 0 1 0 0 1

Logic gates with more than 2 inputs[edit]

We can seperate and make a group of 2 and work on it. for eg:

Y=A+B+C then Y is also equal to X+C where X=A+B.

For further reading[edit]

  • The Apollo Guidance Computer, the first computer ever to use integrated circuits, was built from 4,100 ICs, each containing a single 3-input NOR logic gate.

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