Symbol
Truth Table
2-input AND Digital Logic Gate
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
Digital Logic Gates
There are three basic types of digital logic gates, 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 in digital electronics 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 based 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.
Symbol | Truth Table | ||
2-input AND Digital Logic Gate | 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 | ||
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 | ||
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 | ||
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 | ||
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 (odd) | ||
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 (even) | ||
Symbol | Truth Table | |
| A | Q |
0 | 0 | |
1 | 1 | |
Boolean Expression Q = A | Read as A gives Q | |
Symbol | Truth Table | |
| A | Q |
0 | 1 | |
1 | 0 | |
Boolean Expression Q = not A or A | Read as inverse of | |
The operation of the above Digital Logic Gates and their Boolean expressions can be summarised 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.
The following logic gates truth table compares the logical functions of the 2-input logic gates detailed above.
Inputs | Truth Table Outputs For Each Gate | ||||||
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 |
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.
As well as using pull-up or pull-down resistors to prevent unused logic gates from floating about, spare inputs to gates and latches can also be connected together or connected to left-over or spare gates within a single IC package as shown.
