Basic Logic Circuits
Boolean logic is a symbolic system used in representing the truth value of statements. It is employed in the binary system used by digital computers primarily because the only truth values (true and false) can be represented by the binary digits 1 and 0. A circuit in computer memory can be open or closed, depending on the value assigned to it. The fundamental operations of Boolean logic, often called Boolean operators, are “and,” “or,” and “not;” combinations of these make up 13 other Boolean operators. Six of these operators are discussed.
The Inverter Logic
The inverter circuit performs a basic logic function called inversion. The purpose of the inverter is to convert one logic state into the opposite state. In terms of a binary digit, this would be like converting a 1 to a 0 or a 0 to a 1. When a high voltage is applied to the inverter input, low voltage is the output. When a low voltage is applied to the input, a high voltage is on the output. This operation can be put into what is known as a logic or truth table. The standard logic symbol is shown in Figure 12-253.
Figure 12-254 shows the possible logic states for this gate. This is the common symbol for an amplifier with a small circle on the output. This type of logic can also be considered a NOT gate.
The AND Gate
The AND gate is made up of two or more inputs and a single output. The logic symbol is shown in Figure 12-255.
Inputs are on the left and the output is on the right in each of the depictions. Gates with two, three, and four inputs are shown; however, any number of inputs can be used in the AND logic as long as the number is greater than one. The operation of the AND gate is such that the output is high only when all of the inputs are high. If any of the inputs are low, the output is also low. Therefore, the basic purpose of an AND gate is to determine when certain conditions have been met at the same time. A high level on all inputs produces a high level on the output. Figure 12-256 shows a simplified diagram of the AND logic with two switches and a light bulb.
Notice that both switches need to be closed in order for the light bulb to turn on. Any other combination of switch positions is an open circuit and the light does not turn on. An example of AND logic could possibly be engage logic found in an autopilot. In this case, the autopilot would not be allowed to be engaged unless certain conditions are first met. Such conditions could be: Vertical gyro is valid AND directional gyro is valid AND all autopilot control knobs are in detents AND servo circuits are operational. Only when these conditions are met does the autopilot engage. [Figure 12-257]
The OR Gate
The OR gate has two or more inputs and one output and is normally represented by the standard logic symbol and truth table. [Figure 12-258]
Note that the OR gate can have any number of inputs as long as it is greater than one. The operation of the OR gate is such that a high on any one of the inputs produces a high on the output. The only time that a low is produced on the output is if there are no high levels on any input. Figure 12-259 is a simplified circuit that illustrates the OR logic. The example used is a “DOOR UNSAFE” annunciator.
Let’s say in this case that the plane has one cabin door and a baggage door. In order for the annunciator light on the master warning panel to extinguish, both doors must be closed and locked. If any one of the doors is not secured properly, the baggage door OR the cabin door, then the “DOOR UNSAFE” annunciator illuminates. In this case, two switches are in parallel with each other. If either one of the two switches is closed, the light bulb lights up. The lamp is off only when both switches are open.
The NAND Gate
The term NAND is a combination of the NOT-AND gate and indicates an AND function with an inverted output. A standard logic symbol for a two input NAND gate is shown in Figure 12-260.
Notice that an equivalent AND gate with an inverter is also shown. The logical operation of the NAND gate is such that a low output occurs only if all inputs are high. If any of the inputs are low, the output is high. An example of a two input NAND gate and its corresponding truth table are shown in Figure 12-261.
The NOR Gate
The term NOR is a combination of the NOT and OR and indicates an OR function with an inverted output. The standard logic symbol for a two-inputs NOR gate is shown in Figure 12-263. Notice that an equivalent AND gate with an inverter is also shown. The logical operation of the NOR gate is such that a low output happens when any of its inputs are high. Only when all of its inputs are low is the output high. The logic of this gate produces resultant outputs that are the opposite of the OR gate.
In the NOR gate, the low output is the active output level. Figure 12-263 illustrates the logical operation of a two-input NOR gate for all of its possible combinations and the truth table.
Exclusive OR Gate
The exclusive OR gate is a modified OR gate that produces a 1 output when only one of the inputs is a 1. The abbreviation often used is X-OR. It is different from the standard OR gate in that when both inputs are a 1, then the output remains at a 0. The standard symbol and truth table for the X-OR gate are shown in Figure 12-264.
Exclusive NOR Gate The exclusive NOR (X-NOR) gate is nothing more than an X-OR gate with an inverted output. It produces a 1 output when all inputs are 1s and also when all inputs are 0s. The standard symbol is shown in Figure 12-265.
The Integrated Circuit
All of the logic functions so far discussed plus many other components are available in some form of an integrated circuit. The digital systems found in today’s aircraft owe their existence to a large extent to the design of the integrated circuit (IC). In most cases, the IC has an advantage over the use of discrete components in that they are smaller, consume less power, are very reliable, and are inexpensive. The most noticeable characteristic of the IC is its size and in comparison to the discrete semiconductor component, can easily be on the order of thousands of times smaller. [Figure 12-266]
A monolithic integrated circuit is an electronic circuit that is constructed entirely on a single chip or wafer of semiconductor material. All of the discrete components, such as resistors, transistors, diodes, and capacitors, can be constructed on these small pieces of semiconductor material and are an integral part of the chip. There are a number of levels of integration. Those levels are: small-scale integration, medium-scale integration, large-scale integration, and microprocessors. The small-scale integration is considered the least complex design of the digital ICs. These ICs contain the basic components, such as the AND, OR, NOT, NOR and NAND gates. [Figure 12-267]
The medium-scale integration can contain the same components as found in the small-scale design but in larger numbers ranging from 12 to 100. The medium-scale designs are house circuits that are more complex, such as encoders, decoders, registers, counters, multiplexers, smaller memories, and arithmetic circuits. [Figure 12-268] The large-scale integrated circuits contain even more logic gates, larger memories than the medium-scale circuits, and in some cases microprocessors.
The microprocessor is a device that can be programmed to perform arithmetic and logical operations and other functions in a preordered sequence. The microprocessor is usually used as the central processing unit (CPU) in today’s computer systems when it is connected to other components, such as memory chips and input/output circuits. The basic arrangement and design of the circuits residing in the microprocessor is called the architecture.