Logic Circuits (5.5) PDF - Aviation Australia

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logic circuits boolean logic digital signals timing diagrams

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This document provides a comprehensive overview of logic circuits and their applications within the context of Aviation Australia's training materials. It covers key concepts like Boolean logic, digital signals, and timing diagrams, offering a detailed explanation of their principles and components.

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```markdown # Aviation Australia ## Logic Circuits (5.5) ### Learning Objectives 5.5.1.1 Identification of common logic gate symbols, tables and equivalent circuits (Level 2). 5.5.1.2 Describe the applications of logic circuits used in aircraft systems and schematic diagrams (Level 2). 5.5.1.3...

```markdown # Aviation Australia ## Logic Circuits (5.5) ### Learning Objectives 5.5.1.1 Identification of common logic gate symbols, tables and equivalent circuits (Level 2). 5.5.1.2 Describe the applications of logic circuits used in aircraft systems and schematic diagrams (Level 2). 5.5.1.3 Interpret and understand logic diagrams (S). 5.5.1.4 Describe the operation and use of latches and clocked flip-flop logic circuitry (S). ## Boolean Logic ### Representing Binary Quantities In digital systems, the information that is being processed is usually present in binary form. Binary quantities can be represented by any device that has only two operating states or possible conditions. For example, a switch has only two states: open or closed. We can arbitrarily let an open switch represent binary 0 and a closed switch represent binary 1. With this assignment, we can now represent any binary number as shown in the illustration on the left, where the states of the various switches represent $10010_2$. The image shows two diagrams that demonstrate representing binary quauntities: 1. Several switches are shown, some open and some closed. From left to right, they represent the binary number $10010$. 2. A punched card shows the binary code for $01100$, $10010$ and $01101$. Another example is shown in the diagram on the right, where holes punched in paper are used to represent binary numbers. A punched hole is a binary 1, and absence of a hole is a binary 0. Numerous other devices have only two operating states or can be operated in two extreme conditions. Among these are a light bulb (bright or dark), diode (conducting or non-conducting), relay (energised or de-energised), transistor (cut off or saturated), photocell (illuminated or dark), thermostat (open or closed), mechanical clutch (engaged or disengaged) and spot on a magnetic disc (magnetised or demagnetised). In electronic digital systems, binary information is represented by voltages (or currents) that are present at the inputs and outputs of the various circuits. Typically, the binary 0 and 1 are represented by two nominal voltage levels. For example, 0 V might represent binary 0, and +5 V might represent binary 1. In actuality, because of circuit variations, the O and 1 would be represented by voltage ranges. This is illustrated below, where any voltage between 0 and 0.8 V represents a 0 and any voltage between 2 and 5 V represents a 1. All input and output signals normally fall within one of these ranges, except during transitions from one level to another. Here is a description of a voltage level diagram | Voltage Level | Binary Representation | | --- | --- | | 5V to 2V | Binary 1 | | 2V to 0.8V | NOT USED | | 0.8V to 0V | Binary 0 | We can now see another significant difference between digital and analogue systems. In digital systems, the exact value of a voltage is not important; for example, for the voltage assignments in the diagram, a voltage of 3.6 V means the same as a voltage of 4.3 V. In analogue systems, the exact value of a voltage is important. For instance, if the analogue voltage is proportional to the temperature measured by a transducer, the 3.6 V represents a different temperature than does 4.3 V. In other words, the voltage value carries significant information. This characteristic means the design of accurate analogue circuitry is generally more difficult than that of digital circuitry because of the way exact voltage values are affected by variations in component values, temperature and noise (random voltage fluctuations). ## Digital Signals and Timing Diagrams The diagram below shows a typical digital signal and its variation over time. It is a graph of voltage versus time (t) and is called a timing diagram. The horizontal time scale is marked off at regular intervals, beginning at $t_0$ and proceeding to $t_1$, $t_2$ and so on. For the example timing diagram shown here, the signal starts at 0 V (a binary 0) at time $t_0$ and remains there until time $t_1$. At $t_1$, the signal makes a rapid transition (jump) up to 4 V (a binary 1). At $t_2$, it jumps back down to 0 V. Similar transitions occur at $t_3$ and $t_5$. The below timing diagram shows a digital signal changing over discrete time increments. The VOLTS values are split between showing 4V or 0V over different timeslots. At time $t_0$ volts are read as 0V and at time $t_1$ volts are read as 4V. The change happens again at $t_2$, then at $t_3$ volts jump up to 4V, staying there through $t_4$ jumping back to 0V at $t5$ Note that the signal does not change at $t_4$ but stays at 4 V from $t_3$ to $t_5$. The transitions on this timing diagram are drawn as vertical lines, so they appear to be instantaneous when they are not. In many situations, however, the transition times are so short compared to the times between transitions that we can show them on the diagram as vertical lines. We will encounter situations later where it will be necessary to show the transitions more accurately on an expanded time scale. Timing diagrams are used extensively to show how digital signals change with time, and especially to show the relationship between two or more digital signals in the same circuit or system. By displaying one or more digital signals on an oscilloscope or logic analyser, we can compare the signals to their expected timing diagrams. This is an essential part of the testing and troubleshooting procedures used in digital systems. ## Boolean Constants and Variables Boolean algebra differs significantly from ordinary algebra in that Boolean constants and variables are allowed to have only two possible values: 0 or 1. A Boolean variable is a quantity that may, at different times, be equal to either 0 or 1. Boolean variables are often used to represent the voltage level present on a wire or at the I/O terminals of a circuit. For example, in a certain digital system, the Boolean value of O might be assigned to any voltage in the range from 0 to 0.8 V, while the Boolean value of 1 might be assigned to any voltage in the range 2 to 5 V. Thus, Boolean 0 and 1 do not represent actual numbers but the state of a voltage variable, or what is called its logic level. A voltage in a digital circuit is said to be at the logic 0 level or the logic 1 level, depending on its actual numerical value. In digital logic, several other terms are used synonymously with 0 and 1. Some of the more common ones are shown in the table. We will use the 0/1 and LOW/HIGH designations most of the time. | Logic 0 | Logic 1 | | ----------- | ----------- | | False | True | | Off | On | | Low | High | | No | Yes | | Open switch | Closed Switch | ## Boolean Values As we said in the introduction, boolean algebra is a means of expressing the relationship between a logic circuit's inputs and outputs. The inputs are considered logic variables whose logic levels at any time determine the output levels. In all our work to follow, we will use letter symbols to represent logic variables. For example, the letter A might represent a certain digital circuit input or output, and at any time we must have either A = 0 or A = 1; if not one, then the other. Because only two values are possible, Boolean algebra is relatively easy to work with as compared to ordinary algebra. In Boolean algebra there are no fractions, decimals, negative numbers, square roots, cube roots, logarithms, imaginary numbers and so on. In fact, in Boolean algebra there are only three basic operations: * AND * OR * NOT ## AND, OR and NOT These basic operations are called logic operations. Digital circuits called logic gates can be constructed from diodes, transistors and resistors connected in such a way that the circuit output is the result of a basic logic operation (OR, AND, NOT) performed on the inputs. We will be using Boolean algebra first to describe and analyse these basic logic gates, then later to analyse and design combinations of logic gates connected as logic circuits. The image shows three overlapping circles used to demonstrate boolean logic. * OR - A venn diagram depicts two circles with text reading ‘black OR white' over the entire surface. * AND - A venn diagram depicts two circles with text reading 'black AND white’ over the overlapping area. * NOT - A venn diagram depicts two circles with text ‘black AND NOT white' over a crescent shape of one of the circles. ## Truth Tables A truth table is a means of describing how a logic circuit's output depends on the logic levels present at the circuit's inputs. The illustration depicts a truth table for one type of two-input logic circuit. The table lists all possible combinations of logic levels present at inputs A and B along with the corresponding output level X. The first entry in the table shows that when A and B are both at the 0 level, the output x is at the O level. The second entry shows that when input B is changed to the 1 state, so that A = 0 and B = 1, the output X becomes a 1. In a similar way, the table shows what happens to the output state for any set of input conditions. The image depicts the truth table for a simple circuit | A | B | X | |---|---|---| | 0 | 0 | 0 | | 0 | 1 | 0 | | 1 | 0 | 0 | | 1 | 1 | 1 | The next table shows samples of truth tables for three- and four-input logic circuits. Again, each table lists all possible combinations of input logic levels on the left, with the resultant logic level for output x on the right. Of course, the actual values for x will depend on the type of logic circuit. Note that there are four table entries for the two-input truth table, eight entries for the three-input truth table and 16 entries for the four-input truth table. The number of input combinations will equal $2^N$ for an N input truth table. Also note that the list of all possible input combinations follows the binary counting sequence, so it is an easy matter to write down all the combinations without missing any. |A|B|C|D|X| |---|---|---|---|---| |0|0|0|0|0| |0|0|0|1|0| |0|0|1|0|0| |0|0|1|1|1| |0|1|0|0|1| |0|1|0|1|0| |0|1|1|0|0| |0|1|1|1|0| |1|0|0|0|0| |1|0|0|1|0| |1|0|1|0|1| |1|0|1|1|1| |1|1|0|0|1| |1|1|0|1|0| |1|1|1|0|0| |1|1|1|1|1| The truth table for a three-input circuit is represented by: |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|1| |1|1|1|1| ## Simple Logic Gates ### Logic Gates A logic gate is an ideal representation of a physical electronic device that implements boolean logic. A combination of logic gates creates a logic circuit. Logic circuits are used in electronic devices, creating integrated circuits and microprocessors. Logic circuits are formed by combining many logic gates. More complex logic circuits are assembled from simpler ones, which in turn are assembled from gates. The building block of all logic circuits is the logic gate. All logic actions, however complicated, can be analyzed and simplified into basic actions that are called OR gates, AND gates and NOT gates. The image shows integrated circuit components over a green circuit board. ## OR Gates The OR operation is the first of the three basic Boolean operations to be learned. The truth table below shows what happens when two logic inputs, A and B, are combined using the OR operation to produce an output, X. The table shows that the output is a logic 1 for every combination of input levels where one or more inputs are 1. The only case where X is a 0 is when both inputs are 0. Below is a truth table represented for an Or gate | A | B | X | |---|---|---| | 0 | 0 | 0 | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 1 | The boolean expression for the OR operation is: $X = A + B$ In this expression, the + sign does not stand for ordinary addition; it stands for the OR operation. The OR operation is like ordinary addition except for the case where A and B are both 1; the OR operation produces 1 + 1 = 1, not 1 + 1 = 2. In boolean algebra, 1 is as high as we go, so we can never have a result greater than 1. The same holds true for combining three inputs using the OR operation. Here we have X = A + B + C. If we consider the case where all three inputs are 1, we have X = 1+1+1 = 1. The expression x = A + B is read as 'X equals A OR B', which means X will be 1 when A or B or both are 1. Likewise, the expression X = A + B + C is read as 'X equals A OR B OR C', which means X will be 1 when A or B or C or any combination of them are 1. | 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 following illustration shows alternate equivalent OR logic gates and circuits. There are 3 diagrams that demonstrate an OR gate and how it functions. From left to right: 1. An open circuit and a closed circuit linked through an OR gate to complete a circuit. if either wire is connected, the circuit is complete 2. Shows the equation A OR B (where A is an input and B is an input). 3. A circuit displays diodes A and B, going through a resistor to an output. ## AND Gates The AND operation is the second basic boolean operation. The truth table below shows what happens when two logic inputs, A and B, are combined using the AND operation to produce output X. The table shows that X is a logic 1 only when both A and B are at the logic 1 level. For any case when one of the inputs is 0, the output is 0. The boolean expression for the AND operation is: $X = A \cdot B$ In this expression the "." sign stands for the boolean AND operation and not the multiplication operation. However, the AND operation on boolean variables operates the same as in ordinary multiplication, as examination of the truth table shows, so we can think of them as being the same. This characteristic can be helpful when evaluating logic expressions that contain AND operations. The expression X = A. B is read as 'X equals A AND B', which means that X will be 1 only when A and B are both 1. The sign is usually omitted so that the expression simply becomes X = AB. | A | B | X | |---|---|---| | 0 | 0 | 0 | | 0 | 1 | 0 | | 1 | 0 | 0 | | 1 | 1 | 1 | For the case when there are three AND inputs, we have $X = A \cdot B \cdot C = ABC$ This is read as "X equals A AND B AND C", which means X will be 1 only when A, B and C are all 1. | 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 following illustration shows alternate equivalent AND logic gates and circuits. There are three circuit diagrams: 1. Shows an electrical circuit with an AND gate. 2. Shows the equation AND with inputs A and B, resulting in output X. 3. A circuit with voltages going through didoes A and B, and a 4.7k resistor for the Out value, and labeled +6Y over the circuit. ## NOT Gate (Inverter) The NOT operation is unlike the OR and AND operations in that it can be performed on a single input variable. For example, if the variable A is subjected to the NOT operation, the result X can be expressed as follows. $X = \overline{A}$ It is often referred to as an inverter and throughout this lesson the terms 'NOT gate' and 'inverter' are used interchangeably. Truth table: | A | X | |---|---| | 0 | 1 | | 1 | 0 | The image shows an input A, an output A', with an inverter used to convert and change between states. Where the over-bar represents the NOT operation. This expression is read as 'X equals NOT A' or 'X equals the inverse of A' or 'x equals the complement of A'. Each of these is in common usage, and all indicate that the logic value of $X = \overline{A}$ is opposite to the logic value of A. The truth table clarifies this for the two cases A = 0 and A = 1. ## Combining Gates Multiple input gates can be constructed by placing gates in special configurations. A three-input AND gate may be constructed using two AND gates connected as shown. A three-input OR gate may be constructed using two OR gates connected as shown. The images show an OR and an AND gate attached to separate OR and AND gates, as another input to the secondary gate. ## Logic Circuits ### Simple AND and OR Circuits Any logic circuit, no matter how complex, can be completely described using the three basic boolean operations because the OR gate, AND gate and NOT circuit are the basic building blocks of digital systems. For example, consider the circuit in the illustration. This circuit has three inputs, A, B and C, and a single output, X. Using the boolean expression for each gate, we can easily determine the expression for the output. The image shows a simple AND and OR gate implementation. * A and B are inputs in an AND gate * C is an input in an OR gate * The result x = AB+C. The expression for the AND gate output is written A.B. This AND output is connected as an input to the OR gate along with C, another input. The OR gate operates on its inputs so that its output is the OR sum of the inputs. Thus, we can express the OR output as: $X = A \cdot B + C$ This final expression could also be written as X = C + A.B since it does not matter which term of the OR sum is written first. Occasionally, there may be confusion as to which operation in an expression is performed first. Thus, the expression A.B + C can be interpreted in two different ways: 1. A.B is ORed with C, or 2. A is ANDed with the term B + C. To avoid this confusion, it will be understood that if an expression contains both AND and OR operations, the AND operations are performed first unless there are parentheses in the expression, in which case the operation inside the parentheses is to be performed first. This is the same rule used in ordinary algebra to determine the order of operations. In the previous circuit, the output X = 1 when the following conditions are met: * C is 1 * C is 0 and A and B are both 1 When C is 1, A and B don't matter to the output due to the OR gate. However, if C is 0, then A and B produce a 1 from the AND gate and therefore a 1 from the OR gate. Any other conditions result in X = 0. ### Alternate AND OR Circuit To illustrate further, consider the circuit shown below. The expression for the OR gate output is simply A + B. This output serves as an input to the AND gate along with another input, C. Thus, we express the output of the AND gate as X = (A + B).C. Note the use of parentheses here to indicate that A and B are ORed first, before their OR sum is ANDed with C. Without the parentheses, it would be interpreted incorrectly since A + B.C means A is ORed with the product B.C. Shows two inputs A and B, that go into an OR gate where A+B, also joins with another input C to create x = (A+B).C ### Inverters in Circuits Whenever an inverter is present in a logic-circuit diagram (NOT gate), its output expression is simply equal to the input expression with a bar over it. In the case where an inverted value needs to be expressed in plain text, if the variable is A, it will be referred to as 'A_bar'. Where possible however, a physical bar will be drawn over the variable. The following diagram below shows two examples of circuits using inverters. 1. Has two inputs A and B. Input A has a Not, then combines with B to result x = A' + B 2. Shows an OR gate over inputs A and B, and that results as an input to a NOT gate with results x = (A' +B)' On the left, input A is fed through an inverter, whose output is therefore A_bar. The inverter output is then fed to an OR gate together with B. The equation (for the circuit on the left) is A\_bar + B. Note that the bar is over the A alone, indicating that A is first inverted and then ORed with B. On the right, the output of the OR gate is equal to A + B and is fed through an inverter. The inverter output is therefore equal to the complete input expression negated. X equals the inverse of (A OR B). $(left) \rightarrow X = \overline{A} + B$ $(right) \rightarrow X = \overline{A + B}$ Note that in the right circuit, the bar covers the entire expression (A + B). This is important because, as will be shown later, the following expressions are NOT equal. $\overline{A + B} \neq \overline{A} + \overline{B}$ $e. g. A = 1, B = 0$ $\overline{A+B} = \overline{1 + 0} = \overline{1} = 0$ $\overline{A} + \overline{B} = \overline{1} + \overline{0} = 0$ The first expression indicates that A is inverted and B is inverted, and the results are then ORed, whereas the second expression indicates that A is ORed with B and then their OR sum is inverted. ### Logic Circuit Worked Examples #### Example 1 Find the outputs of each logic gate and the total output of the logic circuit below. Write each answer using the correct logic syntax. The circuit diagram is shown with inputs of A, B, C and D. There are gates and inverters, and it ends with one output and an up-facing arrow. #### Example 2 Find the outputs of each logic gate and the total output of the logic circuit below. Write each answer using the correct logic syntax. There are inputs from A to E ending in an upward facing arrow. Many AND, NOT and OR gates function in sequence to produce the final result. ## Compound Logic Gates ### NOR Gate The symbol for a two-input NOR gate is shown below. It is the same as the OR gate symbol except that it has a small circle on the output. The small circle represents the inversion operation. Thus, the NOR gate operates like an OR gate followed by an inverter. | A | B | X | |---|---|---| | 0 | 0 | 1 | | 0 | 1 | 0 | | 1 | 0 | 0 | | 1 | 1 | 0 | The truth table shows that the NOR gate output is the exact inverse of the OR gate output for all possible input conditions. An OR gate output goes HIGH when any input is HIGH, and the NOR gate output goes LOW when any input is HIGH. This same operation can be extended to NOR gates with more than two inputs. Image showing the NOR gate where X = (A+B)' ### NOR gate and NOR gate timing diagram This image shows two waveforms inverted, showing OR in comparison to NOR gates. The NOR gate symbol also displays A = (A'+B)' ### NOR gate circuit equivalents 2 separate NAND gates are shown over two circuit diagrams. The inputs are connected to transistors. ## NAND Gate The symbol for a two-input NAND gate is shown in the diagram. It is the same as the AND gate symbol except for the small circle on the output. Once again, this small circle denotes the inversion operation. The output is the same as an AND gate with a bar over all the inputs (shown below). | A | B | X | |---|---|---| | 0 | 0 | 1 | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 | Shows A AND B coming into a NOT gate with output labelled (A AND B)'. The NAND operates like an AND gate followed by an inverter (NOT), thus the circuits in the diagram below are equivalent. The images show that the equivalent to a NAND gate is an AND gate that then runs through an inverter. The truth table in the diagram shows that the NAND gate output is the exact inverse of the AND gate for all possible input conditions. The AND output goes HIGH only when all inputs are HIGH, while the NAND output goes LOW only when all inputs are HIGH. This same characteristic is true of NAND gates having more than two inputs. ## Exclusive-OR (XOR) An exclusive-OR (XOR), in the case of a two input circuit, means that if the input is either A or B it returns 1. If the input is both A and B it returns O, and if the input is neither A or B it returns O. Consider the logic circuit in the diagram below. The image displays inputs from A and B ending in an XOR table. It goes through gates that invert each before being input into an AND gate and combined. The Truth table is shown with a symbol being A (+) B. $X= \overline{A}B+A\overline{B}$ | A | B | X | |---|---|---| | 0 | 0 | 0 | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 | To reiterate the explanation above, the accompanying truth table shows that X = 1 for only the following two cases: * A = 0 and B = 1 * A = 1 and B = 0 Thus, the output of an XOR produces a HIGH whenever the two inputs are at opposite levels. This exclusive-OR circuit will hereafter be abbreviated to XOR. $X = \overline{A}B+A\overline{B}$ or alternatively $(\overline{A} \cdot B) + (A \cdot \overline{B}) = 1$ ## XOR Gate | A | B | X | |---|---|---| | 0 | 0 | 0 | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 | The IEEE/ANSI symbol for an XOR gate is shown below as well as the shorthand logic equation for an XOR. The dependency notation (= 1) inside the block indicates that the output will be active-HIGH only when a single input is HIGH. where $\oplus$ = XOR The images show the XOR gates in both traditional and new notation. ## Exclusive-NOR (XNOR) The $\oplus$ symbol represents XOR. The exclusive-NOR circuit (abbreviated XNOR) operates completely opposite to the XOR circuit. The following diagram shows an XNOR circuit and its accompanying truth table. | A | B | X | |---|---|---| | 0 | 0 | 1 | | 0 | 1 | 0 | | 1 | 0 | 0 | | 1 | 1 | 1 | The image contains a circuit diagram with both the equations and the diagram. The output expression of an XNOR circuit is as follows. $X = \overline{A}B+A\overline{B}$ This indicates along with the truth table that X will be 1 for two cases: * A = B = 1 (the AB term) * A = B = 0 (the not AB term). The XNOR produces a HIGH output whenever the two inputs are at the same level. It should be apparent that the output of the XNOR circuit is the exact inverse of the output of the XOR circuit. The traditional symbol for an XNOR gate is obtained by simply adding a small circle at the output of the XOR symbol. Show the XNOR gate in both tradional and new notation, resulting in $X = A \oplus B$ The IEEE/ANSI symbol adds the small triangle on the output of the XOR symbol. Both symbols indicate an output that goes to its active-LOW state when only one input is HIGH. ## The Universal Gates The NOR gate and the NAND gate can be said to be universal gates since combinations of them can be used to accomplish any of the basic operations and can thus produce an inverter, an OR gate or an AND gate. The non-inverting gates do not have this versatility since they cannot produce an invert. The image demonstrates gates. ANAND (AB)', (NOR A+B). Multiple configurations with AND, NAND and NOR gates are used to form circuits. ## Buffers If two inverter gates were to be connected together so that the output of one fed into the input of the other, the inverters would cancel each other out. This is a buffer. While this may seem like a pointless thing to do in a theoretical logic circuit, in a real electric logic circuit, it has many practical benefits. It is useful as an impedance-matching device (and operates slightly different depending on the type - voltage buffer or current buffer). In logic circuits, the buffer is a single-input device which has a gain of 1, mirroring the input at the output. The basic emitter follower can be used as a buffer for a voltage source. The common collector amplifier (BJT) is often called an emitter follower since its output is taken from an emitter resistor. The input and output table is represented | In | Out | |---|---| | 0 | 0 | | 1 | 1 | The image contains two circuit diagrams and descriptions. An op-amp voltage follower can also serve as a voltage buffer. The voltage buffer, also known as a unity gain amplifier (an amplifier with a gain of 1) is one of the simplest possible op-amp circuits with closed-loop feedback. The voltage follower with an ideal op-amp gives simply $V_{out} = V_{in}$, but this turns out to be a very useful service because the input impedance of the op-amp is very high, giving effective isolation of the output from the signal source. You draw very little power from the signal source, thus avoiding 'loading' effects. The voltage follower is often used to construct buffers for logic circuits. ## Inverting Buffers (Inverter) The inverting buffer is a single-input device which produces the state opposite the input. If the input is high, the output is low, and vice versa. This device is commonly referred to as just an inverter. A transistor switch with a collector resistor can serve as an inverting buffer. When the switch is open, no current flows in the base, so the collector current is cut off. The resistor RC must be small enough to drive the transistor to saturation so that most of the voltage VCC appears across the load. The output is taken below the load resistor and can function as an inverting buffer in digital circuits. Input Out The input and output are represented in a table | In | Out | |---|---| | 0 | 1 | | 1 | 0 | An op-amp inverting amplifier with a gain of 1 serves as an inverting buffer. For an ideal op-amp, the inverting amplifier gain is given simply by: $\frac{V_{out}}{V_{in}} = \frac{-R_f}{R_1}$ For equal resistors, it has a gain of -1 and is used in digital circuits as an inverting buffer. The image also shows two circuits demonstrating what an inverting buffer looks and functions like ## Alternate Inverter Symbol The inverter symbol is utilised is not needed, but a more common method of indicating a signal is inverted is simply using an inversion symbol, O, on the leg of the device. Circuits are shown to demonstrate a variety of symbols and uses. The left has In Inverted A joining with B. B has the small circle to invert A and B. On the right shows a number of inverts. A, B and C are represented and A and B are inverted. A, B an C are added as the output, with all three showing invert. ## IEEE Gate Symbols Together with the American National Standards Institute (ANSI), the Institute of ANSI Electrical and Electronic Engineers (IEEE) has developed a standard set of logic IEEE symbols. The most recent revision of the standard is ANSI/IEEE Std 91-1984, IEEE Standard Graphic Symbols for Logic Functions. It is compatible with standard 617 of the International Electrotechnical Commission (IEC) and must be used in all logic diagrams drawn for the U.S. Department of Defense. These symbols are being used more and more as time progresses. | Symbol | Gate | |---|---| | \& | AND | | \& | NAND | | | BUFFER | | | INVERTER | | $\geq1$ | OR | | $\geq1$ | NOR | ## Fabrication of Gates Gates are fabricated as IC packs in dual, triple or quadruple circuit arrangements. The diagram illustrates a typical presentation of manufacturer's operating data, which in this example relates to a quadruple two-input NAND circuit arrangement contained within a Dual-In-Line (DIL) pack monolithic IC. The numbered squares represent the connecting pins. The images displays electrical components as used on a circuit board and functions Image showing where gates connect to, as well as circuit component placements ## Worked Logic Circuit Examples ### Logic Circuit Example Problems The following section provides some examples that may be worked through to demonstrate and understanding of logic gates, logic circuits and timing diagrams. The following section contains the answers for each example, however it is recommended that the questions are attempted prior to viewing the solutions. * Determine the logic operation performed by the following circuits. Each circuit can be simplified into a single logic operation (a single logic gate). Diagram A: Input Gate A is input through the NOT Gate B is input through the NOT Gate The results combines into one NOT Gate output X is presented Diagram B: Input Gate A is input through the NOT Gate B is input through the NOT Gate The results combines into one NOT Gate output X is presented ### Logic Circuit Example Solutions The truth table and single combined gate solutions for the previous section. A Write out thruth table |A | B | X | |--|--|--| |0 | 0 | 0 | |

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