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
Symbol | Truth Table |
|
B | A | Q |
0 | 0 | 0 |
0 | 1 | 0 |
1 | 0 | 0 |
1 | 1 | 1 |
Boolean Expression Q = A . B |
Read as A AND B gives Q |
The Logic OR Gate
Symbol | Truth Table |
|
B | A | Q |
0 | 0 | 0 |
0 | 1 | 1 |
1 | 0 | 1 |
1 | 1 | 1 |
Boolean Expression Q = A + B |
Read as A OR B gives Q |
Inverting Logic Gates
The Logic NAND Gate
Symbol | Truth Table |
|
B | A | Q |
0 | 0 | 1 |
0 | 1 | 1 |
1 | 0 | 1 |
1 | 1 | 0 |
Boolean Expression Q = A . B |
Read as A AND B gives NOT Q |
The Logic NOR Gate
Symbol | Truth Table |
|
B | A | Q |
0 | 0 | 1 |
0 | 1 | 0 |
1 | 0 | 0 |
1 | 1 | 0 |
Boolean Expression Q = A + B |
Read as A OR B gives NOT Q |
Exclusive Logic Gates
The Logic Exclusive-OR Gate (Ex-OR)
Symbol | Truth Table |
|
B | A | Q |
0 | 0 | 0 |
0 | 1 | 1 |
1 | 0 | 1 |
1 | 1 | 0 |
Boolean Expression Q = A B |
Read as A OR B but not BOTH gives Q |
The Logic Exclusive-NOR Gate (Ex-NOR)
Symbol | Truth Table |
|
B | A | Q |
0 | 0 | 1 |
0 | 1 | 0 |
1 | 0 | 0 |
1 | 1 | 1 |
Boolean Expression Q = A B |
Read if A AND B the SAME gives Q |
Single Input Logic Gates
The Buffer
Symbol | Truth Table |
|
A | Q |
0 | 0 |
1 | 1 |
Boolean Expression Q = A |
Read as A gives Q |
The NOT gate (Inverter)
Symbol | Truth Table |
|
A | Q |
0 | 1 |
1 | 0 |
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
Inputs | Truth Table Outputs for 2-input Logic Gates |
B | A | AND | NAND | OR | NOR | EX-OR | EX-NOR |
0 | 0 | 0 | 1 | 0 | 1 | 0 | 1 |
0 | 1 | 0 | 1 | 1 | 0 | 1 | 0 |
1 | 0 | 0 | 1 | 1 | 0 | 1 | 0 |
1 | 1 | 1 | 0 | 1 | 0 | 0 | 1 |
Truth Table Output for Single-input Gates |
A | NOT | Buffer |
0 | 1 | 0 |
1 | 0 | 1 |
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.
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