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Note that logic gates are not always required because simple logic functions can be performed with switches or diodes:
Logic gate symbolsThere are two series of symbols for logic gates:
Inputs and outputsGates have two or more inputs, except a NOT gate which has only one input. All gates have only one output. Usually the letters A, B, C and so on are used to label inputs, and Q is used to label the output. On this page the inputs are shown on the left and the output on the right.
The inverting circle (o)Some gate symbols have a circle on their output which means that their function includes inverting of the output. It is equivalent to feeding the output through a NOT gate. For example the NAND (Not AND) gate symbol shown on the right is the same as an AND gate symbol but with the addition of an inverting circle on the output.
There are summary truth tables below showing the output states for
all types of 2-input and 3-input gates. These can be helpful if you are trying to select
a suitable gate.
Logic ICsLogic gates are available on special ICs (chips) which usually contain several gates of the same type, for example the 4001 IC contains four 2-input NOR gates. There are several families of logic ICs and they can be split into two groups:
The 4000 and 74HC families are the best for battery powered projects because they will work with a good range of supply voltages and they use very little power. However, if you are using them to design circuits and investigate logic gates please remember that all unused inputs MUST be connected to the power supply (either +Vs or 0V), this applies even if that part of the IC is not being used in the circuit!
NOT gate (inverter)The output Q is true when the input A is NOT true, the output is the inverse of the input: Q = NOT A
A NOT gate can only have one input. A NOT gate is also called an inverter.
AND gateThe output Q is true if input A AND input B are both true: Q = A AND B
An AND gate can have two or more inputs, its output is true if all inputs are true.
NAND gate (NAND = Not AND)This is an AND gate with the output inverted, as shown by the 'o' on the output.
The output is true if input A AND input B are NOT both true: Q = NOT (A AND B)
A NAND gate can have two or more inputs, its output is true if NOT all inputs are true.
OR gateThe output Q is true if input A OR input B is true (or both of them are true): Q = A OR B
An OR gate can have two or more inputs, its output is true if at least one input is true.
NOR gate (NOR = Not OR)This is an OR gate with the output inverted, as shown by the 'o' on the output.
The output Q is true if NOT inputs A OR B are true: Q = NOT (A OR B)
A NOR gate can have two or more inputs, its output is true if no inputs are true.
EX-OR (EXclusive-OR) gateThe output Q is true if either input A is true OR input B is true, but not when both of them are true: Q = (A AND NOT B) OR (B AND NOT A)
This is like an OR gate but excluding both inputs being true.
The output is true if inputs A and B are DIFFERENT.
EX-OR gates can only have 2 inputs.
EX-NOR (EXclusive-NOR) gateThis is an EX-OR gate with the output inverted, as shown by the 'o' on the output.
The output Q is true if inputs A and B are the SAME (both true or both false): Q = (A AND B) OR (NOT A AND NOT B)
EX-NOR gates can only have 2 inputs.
Summary truth tablesThe summary truth tables below show the output states for all types of 2-input and 3-input gates.
Combinations of logic gatesLogic gates can be combined to produce more complex functions. They can also be combined to substitute one type of gate for another.
Q = A AND NOT B
Working out the function of a combination of gatesTruth tables can be used to work out the function of a combination of gates.
D = NOT (A OR B)
Substituting one type of gate for anotherLogic gates are available on ICs which usually contain several gates of the same type, for example four 2-input NAND gates or three 3-input NAND gates. This can be wasteful if only a few gates are required unless they are all the same type. To avoid using too many ICs you can reduce the number of gate inputs or substitute one type of gate for another.
Reducing the number of inputsThe number of inputs to a gate can be reduced by connecting two (or more) inputs together. The diagram shows a 3-input AND gate operating as a 2-input AND gate.
Making a NOT gate from a NAND or NOR gateReducing a NAND or NOR gate to just one input creates a NOT gate. The diagram shows this for a 2-input NAND gate.
Any gate can be built from NAND or NOR gatesAs well as making a NOT gate, NAND or NOR gates can be combined to create any type of gate! This enables a circuit to be built from just one type of gate, either NAND or NOR. For example an AND gate is a NAND gate then a NOT gate (to undo the inverting function). Note that AND and OR gates cannot be used to create other gates because they lack the inverting (NOT) function.
To change the type of gate, such as changing OR to AND, you must do three things:
NAND gate equivalentsThe table below shows the NAND gate equivalents of NOT, AND, OR and NOR gates:
Substituting gates in an example logic systemThe original system has 3 different gates: NOR, AND and OR. This requires three ICs (one for each type of gate).
To re-design this system using NAND gates only begin by replacing each gate with its NAND gate equivalent, as shown in the diagram below.
Then simplify the system by deleting adjacent pairs of NOT gates (marked X above). This can be done because the second NOT gate cancels the action of the first.
The final system is shown on the right. It has five NAND gates and requires two ICs (with four gates on each IC). This is better than the original system which required three ICs (one for each type of gate).
Substituting NAND (or NOR) gates does not always increase the number of gates,
but when it does (as in this example) the increase is usually only one or two gates.
The real benefit is reducing the number of ICs required by using just one type of gate.
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