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Digital Logic Gates Summary

In this section about Digital Logic Gates, we have seen that there are three main basic types of digital logic gate, the AND Gate , the OR Gate and the NOT Gate. We have also seen that each gate has an opposite or complementary form of itself in the form of the NAND Gate, the NOR Gate and the Buffer respectively, and that any of these individual gates can be connected together to form more complex Combinational Logic circuits.
We have also seen, that both the NAND gate and the NOR gate can both be classed as "Universal" gates as they can be used to construct any other gate type. In fact, any combinational circuit can be constructed using only two or three input NAND or NOR gates. We also saw that NOT gates and Buffers are single input devices that can also have a Tri-state High-impedance output which can be used to control the flow of data onto a common data bus wire.
Digital Logic Gates can be made from discrete components such as Resistors, Transistors and Diodes to form RTL (resistor-transistor logic) or DTL (diode-transistor logic) circuits, but today's modern digital 74xxx series integrated circuits are manufactured using TTL (transistor-transistor logic) based on NPN bipolar transistor technology or the much faster and low power CMOS MOSFET transistor logic used in the 74Cxxx, 74HCxxx, 74ACxxx and the 4000 series logic chips.
The eight most "standard" individual Digital Logic Gates are summarised below along with their corresponding truth tables.

Standard Logic Gates

The Logic AND Gate

SymbolTruth Table
2-input AND gate BAQ
000
010
100
111
Boolean Expression Q = A . B Read as A AND B gives Q


The Logic OR Gate

SymbolTruth Table
2-input OR gate BAQ
000
011
101
111
Boolean Expression Q = A + B Read as A OR B gives Q


Inverting Logic Gates

The Logic NAND Gate

SymbolTruth Table
2-input NAND gate BAQ
001
011
101
110
Boolean Expression Q = A . B Read as A AND B gives NOT Q


The Logic NOR Gate

SymbolTruth Table
2-input NOR gate BAQ
001
010
100
110
Boolean Expression Q = A + B Read as A OR B gives NOT Q


Exclusive Logic Gates

The Logic Exclusive-OR Gate (Ex-OR)

SymbolTruth Table
2-input Exclusive-Or Gate BAQ
000
011
101
110
Boolean Expression Q = A     B Read as A OR B but not BOTH gives Q


The Logic Exclusive-NOR Gate (Ex-NOR)

SymbolTruth Table
2-input Exclusive-Nor Gate BAQ
001
010
100
111
Boolean Expression Q =     B Read if A AND B the SAME gives Q


Single Input Logic Gates

The Buffer

SymbolTruth Table
Digital Buffer AQ
00
11
Boolean Expression Q = A Read as A gives Q


The NOT gate (Inverter)

SymbolTruth Table
The NOT gate AQ
01
10
Boolean Expression Q = not A or A Read as inverse of A gives Q

The operation of the above Digital Logic Gates and their Boolean expressions can be summerised into a single truth table as shown below. This truth table shows the relationship between each output of the main digital logic gates for each possible input combination.


Truth Table Summary

InputsTruth Table Outputs for 2-input Logic Gates
BAANDNANDORNOREX-OREX-NOR
00010101
01011010
10011010
11101001

Truth Table Output for Single-input Gates
ANOTBuffer
010
101

Pull-up and Pull-down Resistors

One final point to remember, when connecting together digital logic gates to produce logic circuits, any "unused" inputs to the gates must be connected directly to either a logic level "1" or a logic level "0" by means of a suitable "Pull-up" or "Pull-down" resistor ( for example 1kΩ resistor ) to produce a fixed logic signal. This will prevent the unused input to the gate from "floating" about and producing false switching of the gate and circuit.
Pull-up and Pull-down Resistors

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