Avionics News February 2020 - 65

Figure 3: The symbol and truth table for an OR gate

Figure 5: The symbol and truth table for a NOT gate

curved at the input side and is pointed on the output side. I
like to think of an OR gate as an "ANY" gate. A one at any
input will produce a one on the output. Like the AND gate,
the OR gate can have more than two inputs. Imagine this
gate in a smoke detector system with multiple sensors. If any
of the sensors detects smoke, or if all of the sensors detect
smoke, then an output, or one, will be produced.
Our logical readers can guess what is next and that is
the NOR gate in Figure 4. The NOR gate is "NOT OR."
Take note of the negation bubble on the pointed output.
The rule here is that a one on any input will produce a
zero on the output.
Sometimes, an engineer will want to negate, or invert, a
logic input. He or she could wire a NAND gate with both
inputs tied together, but that is not necessary because NOT
gates exist. As shown in Figure 5, the NOT gate is simply a
triangle, like those used to symbolize amplifiers, with a single
input and a single output. The negation bubble on the output
makes this a NOT gate. Without the negation symbol, this
would be a simple amplifier or buffer. The truth table for the
NOT gate is simple. Whatever the input is, the output isn't.
Therefore, a one changes to zero, and a zero changes to one.
The last two gates discussed here will both be covered in
Figure 6. The first is the exclusive OR or XOR gate. This
symbol looks like an OR gate with an extra curved line at
the input. Exclusive OR means the output will be a one, only
when one of the inputs is a one. If both inputs are zero, then
the output will be zero. If both outputs are a one, then the
output will be zero. With my students, I like to describe the
XOR gate in terms of dating. Joe won't go to the dance alone.
He can take Alice to the dance, or he can take Becky to the
dance, but he can't take both to the dance. Becky and Alice
don't like each other. The date must be exclusive or not at all.
As you have already guessed, there exists an XNOR, or
exclusive NOR gate, where you need to have both inputs at
zero, or both inputs at one to get a one on the output. Think
back to poor Joe. This time, Becky and Alice are best friends
forever, and they give Joe an ultimatum: "Take us both to the

dance or stay home; neither of us will leave the other behind."
These gates are the building blocks of digital circuits
and are considered combinational logic. By arranging the
combinational elements discussed here and adding a clock,
we can form sequential logic circuits, which is the basis for
digital computing.
Engineers will use combinations of logic gates to get a
desired output from the available inputs. Of course, engineers
will not want to use any more logic gates than is absolutely
necessary, so they will use math to simplify the circuit. This
math is known as Boolean algebra, which is named for
George Boole, a 19th century mathematician. In Boolean
logic, all values are either true or false. Thus, Boolean logic
lends itself well to digital circuits. Those using advanced
search functions in Google will be familiar with Boolean
expressions.
The gates discussed above can all be described as Boolean
expressions. For example, for a two-input AND gate, the
expression would be: A * B = X.
For a two-input NAND gate, the expression would be:
A * B = X.
For a two input OR gate, the expression would be:
A + B = X.
For a two input NOR gate, the expression would be:
A + B = X.
For a two input XOR gate, the expression would be:
A Ꚛ B = X.
For a two input XNOR gate, the expression would be:
A Ꚛ B = X.
Of course, there is much more to Boolean algebra, but it's
worth studying. It all starts with these simple logic gates. At
another time, we will explore sequential logic. q

Figure 4: The symbol and truth table for a NOR gate

Figure 6: The symbols and a truth table for XOR and XNOR gates
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Avionics News February 2020

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