Gates:The
building blocks of digital electronics... (LESSON 2)
The 7
types of gates
If
you are going through this tutorial in order you should already
understand basically what a gate is. Each type of gate turns on to a
special set of conditions. In lesson 1 the focus was centered around
the AND gate, but that is only one type of gate. There are several more
that are used frequently in almost all digital devices (computers,
calculators, digital clocks...)
Want to try a simulation for one of these gates? Just click on
the symbol above...
**COLOR NOT PART OF
STANDARDIZED LOGIC GATE SYMBOL**
These are the symbols and names for the 8 common logical gates. Each
gate has a compliment, meaning it has an anti-gate, or a gate that does
the exact opposite. The compliment for the AND gate is the NAND gate
(pronounced like it's spelled). Here is a comparison between the AND
GATE and the NAND GATE to demonstarte what I mean by opposite.
Notice that based on the given inputs, the NAND GATE responds with the
opposite of what an AND GATE would do. The NAND gate only turns on if
both input A AND
B are NOT
high. The NAND GATE symbol differs from that of the AND GATE because of
the circle on the output. Any time you see this circle just think of
inversion. Whatever goes through this circle gets changed to its
compliment. One becomes a zero and a zero becomes a one.
A truth table for the NAND gate compared to one for an AND GATE:
NAND GATE TRUTH TABLE
AND GATE TRUTH TABLE
A
B
OUT
0
0
1
0
1
1
1
0
1
1
1
0
A
B
OUT
0
0
0
0
1
0
1
0
0
1
1
1
Since the only difference between the AND
GATE and the NAND GATE is the inverted output the equation for the NAND
gate is almost almost the same. The NAND GATES equation is: A*B = . The line above the "OUT"
represents the compliment. If out equalled a 1 before, it now equals a
0. The line compliments the output (inverts it).
So with the case of lighting LEDs, the LED would only turn off if both
inputs were 1, the opposite of the AND GATE.
The truth tables for all of the 8 gates (including the ones already
discussed) are below:
A
B
OUT
0
0
0
0
1
0
1
0
0
1
1
1
A
B
OUT
0
0
1
0
1
1
1
0
1
1
1
0
A
B
OUT
0
0
0
0
1
1
1
0
1
1
1
1
A
B
OUT
0
0
1
0
1
0
1
0
0
1
1
0
A
B
OUT
0
0
0
0
1
1
1
0
1
1
1
0
A
B
OUT
0
0
1
0
1
0
1
0
0
1
1
1
IN
OUT
0
0
1
1
IN
OUT
0
1
1
0
Here is a trick to help memorize the truth
tables:
First, the Inverter and Buffer are pretty simple,
since they are only 1 input logic gates. The buffer logically does
nothing, it just passes the state of its input to the output.
Electrically, however, the buffer is important. It can help lower the
loads of individual gates. To know more about the electrical workings
of gates CLICK HERE.
For the remaining six gates, pair them with their
compliments. If you remember one, the other is simply the opposite. The
OR GATE turns on if A OR B OR Both is
high. The NOR GATE is the oppoiste (see truth table). The XOR GATE
(Exclusive OR GATE) is similar to the OR gate but excludes the
condition of BOTH. It turns on only if A OR B is high,
but not both. And, once again, the XNOR GATE is the opposite.
You should know understand what the gates do. Don't
worry if you have no idea why any of this matters. In the following
lessons we will build simple circuits using combinations of these
gates. Then, using those simple circuits, build complex digital devices.