Basic logic gates
Introduce the basic logic gates in terms of
a) their function,
b) their circuit symbol,
c) their truth table and
d) their equivalent in Boolean algebra (a mathematical method based on human reasoning which will be explained later).
The NOT gate or inverter.
The NOT gate is the simplest of all logic circuits. It has just one input and one output. If the input is a logic level 1 then the output is a logic level 0. Similarly if the input is 0 then the output is 1 so that the output is the inverse of the input. The circuit symbol is
The truth table for a NOT gate is
The Boolean algebra equivalent is
X-> ‾A
The OR gate.
The output of an OR gate is at logic level 1 when any of the inputs are high otherwise it is at logic level 0. There may be any number of inputs. The circuit symbol for a three input OR gate is
The Boolean algebra equivalent is
X = A + B + C
The truth table of a three input OR gate is
|
A
|
B
|
C
|
X
|
|
0
|
0
|
0
|
0
|
|
0
|
0
|
1
|
1
|
|
0
|
1
|
0
|
1
|
|
0
|
1
|
1
|
1
|
|
1
|
0
|
0
|
1
|
|
1
|
0
|
1
|
1
|
|
1
|
1
|
0
|
1
|
|
1
|
1
|
1
|
1
|
The AND gate.
The output of an AND gate is only high when all of the inputs are high, otherwise the output is low. There may be any number of inputs just like the OR gate. The circuit symbol for a three input AND gate is
The truth table for a three input AND gate is
|
A
|
B
|
C
|
X
|
|
0
|
0
|
0
|
0
|
|
0
|
0
|
1
|
0
|
|
0
|
1
|
0
|
0
|
|
0
|
1
|
1
|
0
|
|
1
|
0
|
0
|
0
|
|
1
|
0
|
1
|
0
|
|
1
|
1
|
0
|
0
|
|
1
|
1
|
1
|
1
|
The Boolean algebra equivalent is
X = A.B.C