nature The of logic circuits
A logic circuit is an electronic device used to mimic the operations of symbolic logic. Symbolic logic consists of expressions which contain variables and operations, and which may assume values of "true" or"false." In the same way, a logic circuit accepts input from one or more sources and produces a result of "on" or "off." The existence of such deceptively simple circuits creates a surprising number of technical possibilities, since these logic circuits turn out to be the basis of modern digital computers. In this experiment, you will deal with some of the more elementary logic circuits to see how some of the more complicated devices can be constructed from them.
Design considerations
The primary design consideration of a logic circuit is reliability: you need to be sure that the logical operation gives you the same answer every time you pose the question. To this end, The input must be tolerant to a reasonable range of "yes" or "no" voltages. The output should follow a predictable logical operation on the inputs. The output must be constant over a reasonable load. In particular, the output of one logic circuit should be usable as the input for another logic circuit with reliable and predictable results.
Example: the "AND" gate
As an example, consider the AND gate. This is a simple device with two inputs and one output. The circuit is depicted with the following symbol: The two leads on the left are input leads, and the one on the right is output. Additional connections which provide power to the circuit are not shown. The behavior of the output in response to the various input conditions may be tabulated as follows: Input A on on off off Output B on off on off on off off off
Logic table for the "AND" gate
The input/output table of a logic circuit is directly related to the "truth table" of the corresponding logical operator. In the case of the AND gate, the logical equivalent is the statement "C=AB" whose truth table looks like this: A True True False False B True False True False C True False False False + Notice the similarity to the electronic behavior of the circuit. Input A on on off off Output B on off on off on off off off
The one-to-one correspondence between "on" in the previous table and "true" in the table above is, of course, the reason an AND gate is constructed the way it is. Frequently, both tables are summarized using binary notation: 1 for "on" or "true," and 0 for "off" or "false."
A simple logic gate
So how do you make a logic circuit? In this lab, you won't need to; all of the logic circuits you will need are already available as integrated circuits. To help you understand how a logic circuit works, however, consider the following circuit: What happens at the output "C" when the inputs "A" and "B" are both grounded?
A simple logic gate
What happens at the output "C" when the inputs "A" and "B" are both grounded? If A and B are grounded, C will also be held at ground. Any current provided by the +10V power supply will drain away to ground through A and B. +What if A is held at ground and B is held at 10V?
A simple logic gate
What if A is held at ground and B is held at 10V? Again, terminal C will be held at ground. The 10V bias on terminal B keeps any current from flowing through the lower diode, but current can still flow through the upper diode to terminal A. + What if the voltages on A and B are reversed?
A simple logic gate
One combination remains: what if A and B are both held at +10V? This time terminal C rises to +10 volts. Current cannot flow through either diode, so terminal C rises to the voltage of the power supply.
A simple logic gate
The connection between the output of this circuit and the truth table of the AND gate should be obvious. If you substitute "T" for "10V" and "F" for"0," the table below is identical to the truth table for the AND operation. What if you make the reverse substitution, however?
A simple logic gate
If you make the reverse substitution, it turns out that you would get the truth table for the logical "OR" operator. Electronic devices which use "ground" for "false" are known as positive logic devices. Those using "ground" to represent "true" are known as negative logic devices.
Now that you know in general how a logic circuit works, there are some specific things you need to know about how the work together.
More criteria
Is design the output we designate as TRUE positive or negative? Is it hot or ground? What voltage ranges may be tolerated by the input? What happens to inputs which are not connected? How much current can the output provide in its "high" state? How much current can the "low" state drain away?
A set of circuits which meets these criteria consistently is referred to as a family of logic circuits. The family of logic circuits you will be working with are TTL (transistor-transistor logic) circuits.
TTL circuits
TTL circuits are among the most popular and widely used logic circuits. They are characterized by the following properties: They are positive logic devices. Logical "0" (False) is defined to be ground, and logical "1" (True) is defined as +5 volts. In fact, "0" can be anywhere in the range between 0 and 0.4V and the chip is still considered to be working within its tolerances. Similarly, "1" can be anywhere in the range from 2.4 to 5 volts, and a TTL chip will still recognize the input. Input in the range between 0.4 and 2.4 volts is not defined.
TTL circuits
Disconnected inputs rise to "1." To see how this can happen, return for a moment to the AND gate whose circuit we examined earlier. If neither A nor B is connected to anything (not even a ground) then all three terminals (A, B, and C) will rise to whatever voltage the power supply provides and stay there.
TTL circuits
The output of a TTL chip will provide 0.4 milliamperes when the output is "high" and will drain away about 16 ma when the output is low. Notice the factor of 40 difference between the current provided by a high state and a low state. If you need the chip to provide any useful current, such as to light an LED, you should plan to do so in a "low" state. The input of a TTL chip requires 0.04 ma to reach a high state and about 1.6 ma to reach a low state. Since there is a factor of 10 difference between what the input requires and what the output provides, each TTL chip can drive up to ten other chips simultaneously.
The NAND gate
One of the most useful circuits is the NAND gate. It has the following circuit symbol:
Its output is the inverse of the AND gate; its logically equivalent function is C=~(A B) (read: C equals not A and B). The truth table of the logical function is:
The NAND gate
It is not obvious at a glance why the NAND gate is so much more useful than a simple AND gate. The most important reason is that other logical components can be constructed using a NAND gate. For instance, you can make an inverter simply by wiring the two inputs of the NAND gate together: Tying the two inputs together like this forces them to have the same input polarity. The logic table of this device...