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} | {
"context": "3.2.1 The NOT Gate (Inverter)\nFigure 3.4 shows the simplest logic structure that exists in a computer. It is con-\nstructed from two MOS transistors, one P-type and one N-type. Figure 3.4a is the\nschematic representation of that circuit. Figure 3.4b shows the behavior of the\ncircuit if the input is supplied with 0 volts. Note that the P-type transistor acts\nlike a short circuit and the N-type transistor acts like an open circuit."
} |
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] | {
"indices": [
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],
"values": [
0.45021338715555703,
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]
} | {
"context": "4b shows the behavior of the\ncircuit if the input is supplied with 0 volts. Note that the P-type transistor acts\nlike a short circuit and the N-type transistor acts like an open circuit. The output\nis, therefore, connected to 1.2 volts. On the other hand, if the input is supplied\nwith 1.2 volts, the P-type transistor acts like an open circuit, but the N-type tran-\nsistor acts like a short circuit."
} |
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} | {
"context": " On the other hand, if the input is supplied\nwith 1.2 volts, the P-type transistor acts like an open circuit, but the N-type tran-\nsistor acts like a short circuit. The output in this case is connected to ground (i.e.,\n0 volts). The complete behavior of the circuit can be described by means of a\ntable, as shown in Figure 3.4c. If we replace 0 volts with the symbol 0 and 1.2"
} |
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} | {
"context": "1.2 volts\n. \n0 volts\n \n1 0\nFigure 3.4\nA CMOS inverter.\nvolts with the symbol 1, we have the truth table (Figure 3.4d) for the complement\nor NOT function, which we studied in Chapter 2.\nIn other words, we have just shown how to construct an electronic circuit that\nimplements the NOT logic function discussed in Chapter 2. We call this circuit\na NOT gate, or an inverter.\n3.2."
} |
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] | {
"indices": [
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"values": [
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]
} | {
"context": "3.2.2 OR and NOR Gates\nFigure 3.5 illustrates a NOR gate. Figure 3.5a is a schematic of a circuit that\nimplements a NOR gate. It contains two P-type and two N-type transistors.\nFigure 3.5b shows the behavior of the circuit if A is supplied with 0 volts\nand B is supplied with 1.2 volts. In this case, the lower of the two P-type transis-\ntors produces an open circuit, and the output C is disconnected from the 1."
} |
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} | {
"context": "2 volts. In this case, the lower of the two P-type transis-\ntors produces an open circuit, and the output C is disconnected from the 1.2-volt\npower supply. However, the leftmost N-type transistor acts like a piece of wire,\nconnecting the output C to 0 volts.\nNote that if both A and B are supplied with 0 volts, the two P-type transistors\nconduct, and the output C is connected to 1.2 volts."
} |
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] | {
"indices": [
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"values": [
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0.4633143131816905,
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]
} | {
"context": "Note that if both A and B are supplied with 0 volts, the two P-type transistors\nconduct, and the output C is connected to 1.2 volts. Note further that there is no\nambiguity here, since both N-type transistors act as open circuits, and so C is\ndisconnected from ground.\nIf either A or B is supplied with 1.2 volts, the corresponding P-type transistor\nresults in an open circuit. That is sucient to break the connection from C to\nthe 1."
} |
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"indices": [
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} | {
"context": "2 volts, the corresponding P-type transistor\nresults in an open circuit. That is sucient to break the connection from C to\nthe 1.2-volt source. However, 1.2 volts supplied to the gate of one of the N-type"
} |
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} | {
"context": "1\n1\n0\n1.2 volts\n0 volts\n1.2 volts\nA\nB\nFigure 3.5\nThe NOR gate.\ntransistors is sucient to cause that transistor to conduct, resulting in C being\nconnected to ground (i.e., 0 volts).\nFigure 3.5c summarizes the complete behavior of the circuit of Figure 3.5a.\nIt shows the behavior of the circuit for each of the four pairs of voltages that can\nbe supplied to A and B. That is,\nA = 0 volts,\nB = 0 volts\nA = 0 volts,\nB = 1."
} |
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"indices": [
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"values": [
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]
} | {
"context": "It shows the behavior of the circuit for each of the four pairs of voltages that can\nbe supplied to A and B. That is,\nA = 0 volts,\nB = 0 volts\nA = 0 volts,\nB = 1.2 volts\nA = 1.2 volts,\nB = 0 volts\nA = 1.2 volts,\nB = 1.2 volts\nIf we replace the voltages with their logical equivalents, we have the truth\ntable of Figure 3.5d. Note that the output C is exactly the opposite of the logical\nOR function that we studied in Chapter 2."
} |
505148 | [
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"context": "5d. Note that the output C is exactly the opposite of the logical\nOR function that we studied in Chapter 2. In fact, it is the NOT-OR function,\nmore typically abbreviated as NOR. We refer to the circuit that implements the\nNOR function as a NOR gate.\nIf we augment the circuit of Figure 3.5a by adding an inverter at its output, as\nshown in Figure 3.6a, we have at the output D the logical function OR."
} |
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} | {
"context": "5a by adding an inverter at its output, as\nshown in Figure 3.6a, we have at the output D the logical function OR. Figure 3.6a\nis the circuit for an OR gate. Figure 3.6b describes the behavior of this circuit if\nthe input variable A is set to 0 and the input variable B is set to 1. Figure 3.6c\nshows the circuits truth table."
} |
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} | {
"context": "64\nA\nB\n1 0 0 1\n1 1 0 1\nFigure 3.6\nThe OR gate.\n3.2.3 Why We Cant Simply Connect P-Type to Ground\nSome bright students have looked at our implementation of the OR gate (a NOR-\ngate followed by an inverter) and asked the question, why cant we simply connect\nthe transistors as shown in Figure 3.7a?\nLogically, it looks very tempting. Four transistors instead of six."
} |
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0.46785238308125726,
0.46785238308125726,
0.46785238308125726,
0.46785238308125726,
0.46785238308125726
]
} | {
"context": "7a?\nLogically, it looks very tempting. Four transistors instead of six. Unfortu-\nnately, the electrical properties of transistors make this problematic. When we\nconnect a P-type transistor to 1.2 volts or an N-type transistor to ground, there is\nno voltage across the transistor, resulting in outputs as shown in Figure 3.5, for\nexample, of 0 volts or 1.2 volts, depending on the input voltages to A and B."
} |
878196 | [
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} | {
"context": "5, for\nexample, of 0 volts or 1.2 volts, depending on the input voltages to A and B. How-\never, when we connect a P-type transistor to ground or an N-type transistor to 1.2\nvolts, because of the electrical characteristics of the transistors, we get what is\nusually referred to as a transmission voltage of approximately 0.5 volts across the\ntransistor. This results in the output of the transistor circuit of Figure 3."
} |
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} | {
"context": "5 volts across the\ntransistor. This results in the output of the transistor circuit of Figure 3.7 being\n0.5 volts + 0.5 volts, or 1.0 volt if A and B are both 0, and 0.7 volts (1.2 volts\nminus 0.5 volts) otherwise. Figure 3.7b shows the actual voltages in the resulting\ntruth table, rather than 0s and 1s. That is, even though the transistor circuit looks\nlike it would work, the transmission voltages across the transistors would yield\nan output voltage of 1 volt for a logical 0 and 0."
} |
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} | {
"context": "7b shows the actual voltages in the resulting\ntruth table, rather than 0s and 1s. That is, even though the transistor circuit looks\nlike it would work, the transmission voltages across the transistors would yield\nan output voltage of 1 volt for a logical 0 and 0.7 volts for a logical 1. Not what\nwe would like for an OR gate!"
} |
734031 | [
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] | {
"indices": [
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"values": [
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} | {
"context": "Figure 3.7\nAn OR gate (not really!).\n3.2.4 AND and NAND Gates\nFigure 3.8 shows an AND gate. Note that if either A or B is supplied with 0 volts,\nthere is a direct connection from C to the 1.2-volt power supply. The fact that C\nFigure 3.8\nThe AND gate."
} |
946469 | [
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"indices": [
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"values": [
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} | {
"context": "(e) NOR gate \n(d) NAND gate \nFigure 3.9\nBasic logic gates.\nAgain, we note that there is no ambiguity. The fact that at least one of the two\ninputs A or B is supplied with 0 volts means that at least one of the two N-type\ntransistors whose gates are connected to A or B is open, and that consequently, C\nis disconnected from ground. Furthermore, the fact that C is at 1.2 volts means\nthe P-type transistor whose gate is connected to C is open-circuited."
} |
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] | {
"indices": [
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"values": [
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]
} | {
"context": "Furthermore, the fact that C is at 1.2 volts means\nthe P-type transistor whose gate is connected to C is open-circuited. Therefore,\nD is not connected to 1.2 volts.\nOn the other hand, if both A and B are supplied with 1.2 volts, then both\nof their corresponding P-type transistors are open. However, their corresponding\nN-type transistors act like pieces of wire, providing a direct connection from C\nto ground."
} |
774440 | [
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} | {
"context": "2 volts, then both\nof their corresponding P-type transistors are open. However, their corresponding\nN-type transistors act like pieces of wire, providing a direct connection from C\nto ground. Because C is at ground, the rightmost P-type transistor acts like a\nclosed circuit, forcing D to 1.2 volts.\nFigure 3.8b is a truth table that summarizes the behavior of the circuit of\nFigure 3.8a."
} |
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] | {
"indices": [
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],
"values": [
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0.7849979036300037,
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]
} | {
"context": "8b is a truth table that summarizes the behavior of the circuit of\nFigure 3.8a. Note that the circuit is an AND gate. The circuit shown within the\ndashed lines (i.e., having output C) is a NOT-AND gate, which we generally\nabbreviate as NAND.\nThe gates just discussed are very common in digital logic circuits and in\ndigital computers. There are billions of inverters (NOT gates) in Intels Skylake\nmicroprocessor."
} |
824910 | [
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} | {
"context": "The gates just discussed are very common in digital logic circuits and in\ndigital computers. There are billions of inverters (NOT gates) in Intels Skylake\nmicroprocessor. As a convenience, we can represent each of these gates by stan-\ndard symbols, as shown in Figure 3.9. The bubble shown in the inverter, NAND,\nand NOR gates signies the complement (i.e., NOT) function. From now on, we\nwill not draw circuits showing the individual transistors."
} |
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} | {
"context": ", NOT) function. From now on, we\nwill not draw circuits showing the individual transistors. Instead, we will raise\nour level of abstraction and use the symbols shown in Figure 3.9.\n3.2.5 Gates with More Than Two Inputs\nBefore we leave the topic of logic gates, we should note that the notion of AND,\nOR, NAND, and NOR gates extends to larger numbers of inputs. One could build\na three-input AND gate or a four-input OR gate, for example."
} |
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} | {
"context": "5 Gates with More Than Two Inputs\nBefore we leave the topic of logic gates, we should note that the notion of AND,\nOR, NAND, and NOR gates extends to larger numbers of inputs. One could build\na three-input AND gate or a four-input OR gate, for example. An n-input AND\ngate has an output value of 1 only if ALL n input variables have values of 1. If\nany of the n inputs has a value of 0, the output of the n-input AND gate is 0."
} |
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] | {
"indices": [
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],
"values": [
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]
} | {
"context": " An n-input AND\ngate has an output value of 1 only if ALL n input variables have values of 1. If\nany of the n inputs has a value of 0, the output of the n-input AND gate is 0. An\nn-input OR gate has an output value of 1 if ANY of the n input variables has a\nvalue of 1. That is, an n-input OR gate has an output value of 0 only if ALL n\ninput variables have values of 0."
} |
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"context": "1 1 0 0\n1 1 1 1\nFigure 3.10\nA three-input AND gate.\nFigure 3.10 illustrates a three-input AND gate. Figure 3.10a shows its truth\ntable. Figure 3.10b shows the symbol for a three-input AND gate.\nQuestion: Can you draw a transistor-level circuit for a three-input AND gate?\nHow about a four-input AND gate? How about a four-input OR gate?\n3.3 Combinational Logic Circuits\nNow that we understand the workings of the basic logic gates, the next step\nis to build some of the logic structures that are important components of the\nmicroarchitecture of a computer."
} |
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} | {
"context": "Question: Can you draw a transistor-level circuit for a three-input AND gate?\nHow about a four-input AND gate? How about a four-input OR gate?\n3.3 Combinational Logic Circuits\nNow that we understand the workings of the basic logic gates, the next step\nis to build some of the logic structures that are important components of the\nmicroarchitecture of a computer.\nThere are fundamentally two kinds of logic structures, those that include the\nstorage of information and those that do not."
} |
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} | {
"context": "3 Combinational Logic Circuits\nNow that we understand the workings of the basic logic gates, the next step\nis to build some of the logic structures that are important components of the\nmicroarchitecture of a computer.\nThere are fundamentally two kinds of logic structures, those that include the\nstorage of information and those that do not. In Sections 3.4, 3.5, and 3.6, we\nwill deal with structures that store information."
} |
106516 | [
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} | {
"context": "5, and 3.6, we\nwill deal with structures that store information. In this section, we will deal with\nstructures that do not store information. These structures are sometimes referred\nto as decision elements. Usually, they are referred to as combinational logic struc-\ntures because their outputs are strictly dependent on the combination of input\nvalues that are being applied to the structure right now."
} |
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} | {
"context": "These structures are sometimes referred\nto as decision elements. Usually, they are referred to as combinational logic struc-\ntures because their outputs are strictly dependent on the combination of input\nvalues that are being applied to the structure right now. Their outputs are not at\nall dependent on any past history of information that is stored internally, since no\ninformation can be stored internally in a combinational logic circuit."
} |
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} | {
"context": "Usually, they are referred to as combinational logic struc-\ntures because their outputs are strictly dependent on the combination of input\nvalues that are being applied to the structure right now. Their outputs are not at\nall dependent on any past history of information that is stored internally, since no\ninformation can be stored internally in a combinational logic circuit.\nWe will next examine three useful combinational logic circuits: a decoder, a\nmux, and a one-bit adder."
} |
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} | {
"context": "Their outputs are not at\nall dependent on any past history of information that is stored internally, since no\ninformation can be stored internally in a combinational logic circuit.\nWe will next examine three useful combinational logic circuits: a decoder, a\nmux, and a one-bit adder.\n3.3.1 Decoder\nFigure 3.11 shows a logic gate implementation of a two-input decoder. A decoder\nhas the property that exactly one of its outputs is 1 and all the rest are 0s."
} |
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} | {
"context": "11 shows a logic gate implementation of a two-input decoder. A decoder\nhas the property that exactly one of its outputs is 1 and all the rest are 0s. The one\noutput that is logically 1 is the output corresponding to the input pattern that it is\nexpected to detect. In general, decoders have n inputs and 2n outputs. We say the\noutput line that detects the input pattern is asserted. That is, that output line has\nthe value 1, rather than 0 as is the case for all the other output lines."
} |
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} | {
"context": "We say the\noutput line that detects the input pattern is asserted. That is, that output line has\nthe value 1, rather than 0 as is the case for all the other output lines. In Figure 3.11,\nnote that for each of the four possible combinations of inputs A and B, exactly one\noutput has the value 1 at any one time. In Figure 3.11b, the input to the decoder\nis 10, resulting in the third output line being asserted."
} |
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] | {
"indices": [
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],
"values": [
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]
} | {
"context": " In Figure 3.11b, the input to the decoder\nis 10, resulting in the third output line being asserted."
} |
287250 | [
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} | {
"context": "A\nB\n1, if A, B is 11\n0\nFigure 3.11\nA two-input decoder.\nThe decoder is useful in determining how to interpret a bit pattern. We will\nsee in Chapter 5 that the work to be carried out by each instruction in the LC-\n3 computer is determined by a four-bit pattern that is the part of the instruction\ncalled the opcode, A 4-to-16 decoder is a simple combinational logic structure\nfor identifying what work is to be performed by each instruction."
} |
277049 | [
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"indices": [
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"values": [
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} | {
"context": "The decoder is useful in determining how to interpret a bit pattern. We will\nsee in Chapter 5 that the work to be carried out by each instruction in the LC-\n3 computer is determined by a four-bit pattern that is the part of the instruction\ncalled the opcode, A 4-to-16 decoder is a simple combinational logic structure\nfor identifying what work is to be performed by each instruction.\n3."
} |
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"indices": [
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} | {
"context": "We will\nsee in Chapter 5 that the work to be carried out by each instruction in the LC-\n3 computer is determined by a four-bit pattern that is the part of the instruction\ncalled the opcode, A 4-to-16 decoder is a simple combinational logic structure\nfor identifying what work is to be performed by each instruction.\n3.3.2 Mux\nFigure 3.12a shows a logic gate implementation of a two-input multiplexer, more\nFigure 3."
} |
155417 | [
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] | {
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} | {
"context": "2 Mux\nFigure 3.12a shows a logic gate implementation of a two-input multiplexer, more\nFigure 3.12\nA 2-to-1 mux."
} |
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] | {
"indices": [
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"values": [
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} | {
"context": "OUT\nFigure 3.13\nA four-input mux.\nThe mux of Figure 3.12 works as follows: Suppose S = 0, as shown in\nFigure 3.12b. Since the output of an AND gate is 0 unless all inputs are 1, the out-\nput of the rightmost AND gate is 0. Also, the output of the leftmost AND gate is\nwhatever the input A is. That is, if A = 0, then the output of the leftmost AND gate\nis 0, and if A = 1, then the output of the leftmost AND gate is 1."
} |
293900 | [
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"indices": [
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"values": [
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} | {
"context": "Also, the output of the leftmost AND gate is\nwhatever the input A is. That is, if A = 0, then the output of the leftmost AND gate\nis 0, and if A = 1, then the output of the leftmost AND gate is 1. Since the output\nof the rightmost AND gate is 0, it has no eect on the OR gate. Consequently,\nthe output at C is exactly the same as the output of the leftmost AND gate. The\nnet result of all this is that if S = 0, the output C is identical to the input A."
} |
397281 | [
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"indices": [
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"values": [
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} | {
"context": "Consequently,\nthe output at C is exactly the same as the output of the leftmost AND gate. The\nnet result of all this is that if S = 0, the output C is identical to the input A.\nOn the other hand, if S = 1, it is B that is ANDed with 1, resulting in the\noutput of the OR gate having the value of B.\nIn summary, the output C is always connected to either the input A or the\ninput Bwhich one depends on the value of the select line S."
} |
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] | {
"indices": [
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} | {
"context": "On the other hand, if S = 1, it is B that is ANDed with 1, resulting in the\noutput of the OR gate having the value of B.\nIn summary, the output C is always connected to either the input A or the\ninput Bwhich one depends on the value of the select line S. We say S selects the\nsource of the mux (either A or B) to be routed through to the output C. Figure 3.12c\nshows the standard representation for a mux."
} |
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} | {
"context": "Figure 3.12c\nshows the standard representation for a mux.\nIn general, a mux consists of 2n inputs and n select lines. Figure 3.13a\nshows a gate-level description of a four-input mux. It requires two select lines.\nFigure 3.13b shows the standard representation for a four-input mux.\nQuestion: Can you construct the gate-level representation for an eight-input\nmux? How many select lines must you have?\n3."
} |
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} | {
"context": "13b shows the standard representation for a four-input mux.\nQuestion: Can you construct the gate-level representation for an eight-input\nmux? How many select lines must you have?\n3.3.3 A One-Bit Adder (a.k.a. a Full Adder)\nRecall in Chapter 2, we discussed binary addition. A simple algorithm for binary\naddition is to proceed as you have always done in the case of decimal addition,\nfrom right to left, one column at a time, adding the two digits from the two values\nplus the carry in, and generating a sum digit and a carry to the next column."
} |
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"values": [
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} | {
"context": "a Full Adder)\nRecall in Chapter 2, we discussed binary addition. A simple algorithm for binary\naddition is to proceed as you have always done in the case of decimal addition,\nfrom right to left, one column at a time, adding the two digits from the two values\nplus the carry in, and generating a sum digit and a carry to the next column. The\nonly dierence here (with binary addition) is you get a carry after 1, rather than\nafter 9."
} |
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} | {
"context": "A simple algorithm for binary\naddition is to proceed as you have always done in the case of decimal addition,\nfrom right to left, one column at a time, adding the two digits from the two values\nplus the carry in, and generating a sum digit and a carry to the next column. The\nonly dierence here (with binary addition) is you get a carry after 1, rather than\nafter 9.\nFigure 3.14 is a truth table that describes the result of binary addition on one\ncolumn of bits within two n-bit operands."
} |
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]
] | {
"indices": [
818459139,
3554024053,
75456649,
245221680,
2099560782,
442064690,
2774602186,
1034183227,
2257684172,
699539807,
1960040400,
2339220210,
358389376,
3511121922,
3881767927,
1296924235,
3005552705
],
"values": [
0.5963591629875121,
0.5963591629875121,
0.5963591629875121,
0.5963591629875121,
0.5963591629875121,
0.5963591629875121,
0.5963591629875121,
0.5963591629875121,
0.5963591629875121,
0.7471491088151536,
0.5963591629875121,
0.5963591629875121,
0.5963591629875121,
0.5963591629875121,
0.5963591629875121,
0.5963591629875121,
0.5963591629875121
]
} | {
"context": "\nFigure 3.14 is a truth table that describes the result of binary addition on one\ncolumn of bits within two n-bit operands. At each column, there are three values"
} |
287004 | [
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] | {
"indices": [
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"values": [
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0.7570057190292556,
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]
} | {
"context": "1\n1\n1\n1\n1\nFigure 3.14\nThe truth table for a one-bit adder.\nthat must be added: one bit from each of the two operands A and B and the carry\nfrom the previous column. We designate these three bits as Ai, Bi, and Ci. There\nare two results, the sum bit (Si) and the carry over to the next column, Ci+1. Note\nthat if only one of the three bits equals 1, we get a sum of 1, and no carry (i.e."
} |
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} | {
"context": "Note\nthat if only one of the three bits equals 1, we get a sum of 1, and no carry (i.e.,\nCi+1 = 0). If two of the three bits equal 1, we get a sum of 0, and a carry of 1. If\nall three bits equal 1, the sum is 3, which in binary corresponds to a sum of 1 and\na carry of 1.\nFigure 3.15 shows a logic gate implementation of a one-bit adder. Note that\neach AND gate in Figure 3.15 produces an output 1 for exactly one of the eight\ninput combinations of Ai, Bi, and Ci."
} |
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] | {
"indices": [
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"values": [
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} | {
"context": " Note that\neach AND gate in Figure 3.15 produces an output 1 for exactly one of the eight\ninput combinations of Ai, Bi, and Ci. The output of the OR gate for Ci+1 must be 1\nin e\npro\nFigure 3.15\nGate-level description of a one-bit adder."
} |
522071 | [
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]
} | {
"context": "S0\nS1\nS2\nS3\nFigure 3.16\nA circuit for adding two 4-bit binary numbers.\nare the outputs of the AND gates corresponding to those input combinations.\nSimilarly, the inputs to the OR gate that generates Si are the outputs of the AND\ngates corresponding to the input combinations that require an output 1 for Si in\nthe truth table of Figure 3.14.\nNote that since the input combination 000 does not result in an output 1 for\neither Ci+1 or Si, its corresponding AND gate is not an input to either of the two\nOR gates."
} |
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} | {
"context": "14.\nNote that since the input combination 000 does not result in an output 1 for\neither Ci+1 or Si, its corresponding AND gate is not an input to either of the two\nOR gates.\nFigure 3.16 shows a circuit for adding two 4-bit binary numbers, using four\nof the one-bit adder circuits of Figure 3.15. Note that the carry out of column i is\nan input to the addition performed in column i + 1."
} |
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} | {
"context": "15. Note that the carry out of column i is\nan input to the addition performed in column i + 1.\nIf we wish to implement a logic circuit that adds two 16-bit numbers, we can\ndo so with a circuit of 16 one-bit adders.\nWe should point out that historically the logic circuit of Figure 3.15 that\nprovides three inputs (Ai, Bi, and Ci) and two outputs (the sum bit Si and the\ncarry over to the next column Ci+1) has generally been referred to as a full adder\nto dierentiate it from another structure, which is called a half adder."
} |
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]
} | {
"context": "We should point out that historically the logic circuit of Figure 3.15 that\nprovides three inputs (Ai, Bi, and Ci) and two outputs (the sum bit Si and the\ncarry over to the next column Ci+1) has generally been referred to as a full adder\nto dierentiate it from another structure, which is called a half adder. The dis-\ntinction between the two is the carry bit. Note that the carry into the rightmost\ncolumn in Figure 3."
} |
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} | {
"context": "The dis-\ntinction between the two is the carry bit. Note that the carry into the rightmost\ncolumn in Figure 3.16 is 0. That is, in the rightmost circuit, S0 and C1 depend only\non two inputs, A0 and B0. Since that circuit depends on only two inputs, it has been\nreferred to as a half adder. Since the other circuits depend on all three inputs, they\nare referred to as full adders. We prefer the term one-bit adder as a simpler term\nfor describing what is happening in each column."
} |
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} | {
"context": "Since the other circuits depend on all three inputs, they\nare referred to as full adders. We prefer the term one-bit adder as a simpler term\nfor describing what is happening in each column.\n3.3.4 The Programmable Logic Array (PLA)\nFigure 3.17 illustrates a very common building block for implementing any col-\nlection of logic functions one wishes to implement. The building block is called\na programmable logic array (PLA)."
} |
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} | {
"context": "17 illustrates a very common building block for implementing any col-\nlection of logic functions one wishes to implement. The building block is called\na programmable logic array (PLA). It consists of an array of AND gates (called\nan AND array) followed by an array of OR gates (called an OR array). The num-\nber of AND gates corresponds to the number of input combinations (rows) in\nthe truth table."
} |
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"indices": [
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"values": [
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} | {
"context": " It consists of an array of AND gates (called\nan AND array) followed by an array of OR gates (called an OR array). The num-\nber of AND gates corresponds to the number of input combinations (rows) in\nthe truth table. For n-input logic functions, we need a PLA with 2n n-input AND"
} |
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} | {
"context": "72\nFigure 3.17\nA programmable logic array.\ngates. In Figure 3.17, we have 23 three-input AND gates, corresponding to three\nlogical input variables. The number of OR gates corresponds to the number of\nlogic functions we wish to implement, that is, the number of output columns in\nthe truth table. The implementation algorithm is simply to connect the output of\nan AND gate to the input of an OR gate if the corresponding row of the truth table\nproduces an output 1 for that output column."
} |
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} | {
"context": "The number of OR gates corresponds to the number of\nlogic functions we wish to implement, that is, the number of output columns in\nthe truth table. The implementation algorithm is simply to connect the output of\nan AND gate to the input of an OR gate if the corresponding row of the truth table\nproduces an output 1 for that output column. Hence the notion of programmable.\nThat is, we say we program the connections from AND gate outputs to OR gate\ninputs to implement our desired logic functions."
} |
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} | {
"context": "Hence the notion of programmable.\nThat is, we say we program the connections from AND gate outputs to OR gate\ninputs to implement our desired logic functions.\nFigure 3.15 shows seven AND gates connected to two OR gates since our\nrequirement was to implement two functions (sum and carry) of three input vari-\nables. Figure 3.17 shows a PLA that can implement any four functions of three\nvariables by appropriately connecting AND gate outputs to OR gate inputs."
} |
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} | {
"context": "Figure 3.17 shows a PLA that can implement any four functions of three\nvariables by appropriately connecting AND gate outputs to OR gate inputs. That\nis, any function of three variables can be implemented by connecting the outputs\nof all AND gates corresponding to input combinations for which the output is 1\nto inputs of one of the OR gates. Thus, we could implement the one-bit adder by\nprogramming the two OR gates in Figure 3."
} |
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} | {
"context": "That\nis, any function of three variables can be implemented by connecting the outputs\nof all AND gates corresponding to input combinations for which the output is 1\nto inputs of one of the OR gates. Thus, we could implement the one-bit adder by\nprogramming the two OR gates in Figure 3.17 whose outputs are W and X by\nconnecting or not connecting the outputs of the AND gates to the inputs of those\ntwo OR gates as specied by the two output columns of Figure 3."
} |
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} | {
"context": "Thus, we could implement the one-bit adder by\nprogramming the two OR gates in Figure 3.17 whose outputs are W and X by\nconnecting or not connecting the outputs of the AND gates to the inputs of those\ntwo OR gates as specied by the two output columns of Figure 3.14.\n3.3.5 Logical Completeness\nBefore we leave the topic of combinational logic circuits, it is worth noting an\nimportant property of building blocks for logic circuits: logical completeness."
} |
212931 | [
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} | {
"context": "3.5 Logical Completeness\nBefore we leave the topic of combinational logic circuits, it is worth noting an\nimportant property of building blocks for logic circuits: logical completeness. We\nshowed in Section 3.3.4 that any logic function we wished to implement could\nbe accomplished with a PLA. We saw that the PLA consists of only AND gates,\nOR gates, and inverters. That means that any logic function can be implemented,\nprovided that enough AND, OR, and NOT gates are available."
} |
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"values": [
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} | {
"context": " We saw that the PLA consists of only AND gates,\nOR gates, and inverters. That means that any logic function can be implemented,\nprovided that enough AND, OR, and NOT gates are available. We say that the set\nof gates {AND, OR, NOT} is logically complete because we can build a circuit\nto carry out the specication of any truth table we wish without using any other"
} |
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} | {
"context": "kind of gate. That is, the set of gates {AND, OR, and NOT} is logically complete\nbecause a barrel of AND gates, a barrel of OR gates, and a barrel of NOT gates are\nsucient to build a logic circuit that carries out the specication of any desired\ntruth table. The barrels may have to be big, but the point is, we do not need any\nother kind of gate to do the job.\nQuestion: Is there any single two-input logic gate that is logically complete?\nFor example, is the NAND gate logically complete? Hint: Can I implement a\nNOT gate with a NAND gate? If yes, can I then implement an AND gate using a\nNAND gate followed by a NOT gate? If yes, can I implement an OR gate using\njust AND gates and NOT gates?\nIf all of the above is true, then the NAND gate is logically complete, and I\ncan implement any desired logic function as described by its truth table with a\nbarrel of NAND gates."
} |
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"values": [
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]
} | {
"context": "The barrels may have to be big, but the point is, we do not need any\nother kind of gate to do the job.\nQuestion: Is there any single two-input logic gate that is logically complete?\nFor example, is the NAND gate logically complete? Hint: Can I implement a\nNOT gate with a NAND gate? If yes, can I then implement an AND gate using a\nNAND gate followed by a NOT gate? If yes, can I implement an OR gate using\njust AND gates and NOT gates?\nIf all of the above is true, then the NAND gate is logically complete, and I\ncan implement any desired logic function as described by its truth table with a\nbarrel of NAND gates.\n3."
} |
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"context": "Question: Is there any single two-input logic gate that is logically complete?\nFor example, is the NAND gate logically complete? Hint: Can I implement a\nNOT gate with a NAND gate? If yes, can I then implement an AND gate using a\nNAND gate followed by a NOT gate? If yes, can I implement an OR gate using\njust AND gates and NOT gates?\nIf all of the above is true, then the NAND gate is logically complete, and I\ncan implement any desired logic function as described by its truth table with a\nbarrel of NAND gates.\n3.4 Basic Storage Elements\nRecall our statement at the beginning of Section 3."
} |
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"context": "3.4 Basic Storage Elements\nRecall our statement at the beginning of Section 3.3 that there are two kinds of\nlogic structures, those that involve the storage of information and those that do\nnot. We have discussed three examples of those that do not: the decoder, the mux,\nand the full adder. Now we are ready to discuss logic structures that do include\nthe storage of information.\n3.4."
} |
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0.45449725721703593,
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0.6249544369532175,
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]
} | {
"context": "3.4.1 The R-S Latch\nA simple example of a storage element is the R-S latch. It can store one bit of\ninformation, a 0 or a 1. The R-S latch can be implemented in many ways, the\nsimplest being the one shown in Figure 3.18. Two 2-input NAND gates are con-\nnected such that the output of each is connected to one of the inputs of the other.\nThe remaining inputs S and R are normally held at a logic level 1."
} |
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"context": "Two 2-input NAND gates are con-\nnected such that the output of each is connected to one of the inputs of the other.\nThe remaining inputs S and R are normally held at a logic level 1.\nThe R-S latch\nets its name from the old desi nations for settin\nthe latch\nR\nb\nFigure 3.18\nAn R-S latch.\nThe Quiescent State\nWe describe the quiescent (or quiet) state of a latch as\nthe state when the latch is storing a value, either 0 or 1, and nothing is trying to."
} |
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] | {
"indices": [
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],
"values": [
0.5890053303866941,
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]
} | {
"context": "18\nAn R-S latch.\nThe Quiescent State\nWe describe the quiescent (or quiet) state of a latch as\nthe state when the latch is storing a value, either 0 or 1, and nothing is trying to"
} |
100857 | [
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} | {
"context": "change that value. This is the case when inputs S and R both have the logic value\n1. In Figure 3.18 the letter a designates the value that is currently stored in the\nlatch, which we also refer to as the output of the latch.\nConsider rst the case where the value stored and therefore the output a is\n1. Since that means the value A is 1 (and since we know the input R is 1 because\nwe are in the quiescent state), the NAND gates output b must be 0."
} |
131059 | [
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} | {
"context": "Consider rst the case where the value stored and therefore the output a is\n1. Since that means the value A is 1 (and since we know the input R is 1 because\nwe are in the quiescent state), the NAND gates output b must be 0. That, in turn,\nmeans B must be 0, which results in the output a equal to 1. As long as the inputs\nS and R remain 1, the state of the circuit will not change. That is, the R-S latch\nwill continue to store the value 1 (the value of the output a)."
} |
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] | {
"indices": [
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"values": [
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} | {
"context": "As long as the inputs\nS and R remain 1, the state of the circuit will not change. That is, the R-S latch\nwill continue to store the value 1 (the value of the output a).\nIf, on the other hand, we assume the output a is 0, then A must be 0, and\nthe out ut b must be 1. That, in turn, results in B equal to 1, and combined with\nt S equal to 1 (again due to quiescence), results in the output a equal to\nn, as long as the inputs S and R remain 1, the state of the circuit will not."
} |
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} | {
"context": "If, on the other hand, we assume the output a is 0, then A must be 0, and\nthe out ut b must be 1. That, in turn, results in B equal to 1, and combined with\nt S equal to 1 (again due to quiescence), results in the output a equal to\nn, as long as the inputs S and R remain 1, the state of the circuit will not\n. In this case, we say the R-S latch stores the value 0.\nthe Latch to a 1 or a 0\nThe latch can be set to 1 by momentarily setting\nprovided we keep the value of R at 1."
} |
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} | {
"context": "In this case, we say the R-S latch stores the value 0.\nthe Latch to a 1 or a 0\nThe latch can be set to 1 by momentarily setting\nprovided we keep the value of R at 1. Similarly, the latch can be set to 0\nentarily setting R to 0, provided we keep the value of S at 1. In order for\nthe R-S latch to work properly, both S and R must never be allowed to be set to 0\nat the same time.\nWe use the term set to denote setting a variable to 0 or 1, as in set to 0 or\nset to 1."
} |
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] | {
"indices": [
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"values": [
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} | {
"context": "In order for\nthe R-S latch to work properly, both S and R must never be allowed to be set to 0\nat the same time.\nWe use the term set to denote setting a variable to 0 or 1, as in set to 0 or\nset to 1. In addition, we often use the term clear to denote the act of setting a\nvariable to 0.\nIf we set S to 0 for a very brief period of time, this causes a to equal 1, which\nin turn causes A to equal 1."
} |
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} | {
"context": "In addition, we often use the term clear to denote the act of setting a\nvariable to 0.\nIf we set S to 0 for a very brief period of time, this causes a to equal 1, which\nin turn causes A to equal 1. Since R is also 1, the output at b must be 0. This causes\nB to be 0, which in turn makes a equal to 1. If, after that very brief period of time,\nwe now return S to 1, it does not aect a. Why? Answer: Since B is also 0, and\nsince only one input 0 to a NAND gate is enough to guarantee that the output of\nthe NAND gate is 1, the latch will continue to store a 1 long after S returns to 1."
} |
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} | {
"context": "If, after that very brief period of time,\nwe now return S to 1, it does not aect a. Why? Answer: Since B is also 0, and\nsince only one input 0 to a NAND gate is enough to guarantee that the output of\nthe NAND gate is 1, the latch will continue to store a 1 long after S returns to 1.\nIn the same way, we can clear the latch (set the latch to 0) by setting R to 0\nfor a very short period of time."
} |
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} | {
"context": "Why? Answer: Since B is also 0, and\nsince only one input 0 to a NAND gate is enough to guarantee that the output of\nthe NAND gate is 1, the latch will continue to store a 1 long after S returns to 1.\nIn the same way, we can clear the latch (set the latch to 0) by setting R to 0\nfor a very short period of time.\nWe should point out that if both S and R were allowed to be set to 0 at the same\ntime, the outputs a and b would both be 1, and the nal state of the latch would\ndepend on the electrical properties of the transistors making up the gates and\nnot on the logic being performed."
} |
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"context": "In the same way, we can clear the latch (set the latch to 0) by setting R to 0\nfor a very short period of time.\nWe should point out that if both S and R were allowed to be set to 0 at the same\ntime, the outputs a and b would both be 1, and the nal state of the latch would\ndepend on the electrical properties of the transistors making up the gates and\nnot on the logic being performed. How the electrical properties of the transistors\nwould determine the nal state in this case is a subject we will have to leave for\na later semester."
} |
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} | {
"context": "\nWe should point out that if both S and R were allowed to be set to 0 at the same\ntime, the outputs a and b would both be 1, and the nal state of the latch would\ndepend on the electrical properties of the transistors making up the gates and\nnot on the logic being performed. How the electrical properties of the transistors\nwould determine the nal state in this case is a subject we will have to leave for\na later semester"
} |
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} | {
"context": "We should point out that if both S and R were allowed to be set to 0 at the same\ntime, the outputs a and b would both be 1, and the nal state of the latch would\ndepend on the electrical properties of the transistors making up the gates and\nnot on the logic being performed. How the electrical properties of the transistors\nwould determine the nal state in this case is a subject we will have to leave for\na later semester. :-(\nFinally, we should note that when a digital circuit is powered on, the latch\ncan be in either of its two states, 0 or 1."
} |
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} | {
"context": "How the electrical properties of the transistors\nwould determine the nal state in this case is a subject we will have to leave for\na later semester. :-(\nFinally, we should note that when a digital circuit is powered on, the latch\ncan be in either of its two states, 0 or 1. It does not matter which state since we\nnever use that information until after we have set it to 1 or 0.\n3.4.2 The Gated D Latch\nTo be useful, it is necessary to control when a latch is set and when it is cleared."
} |
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} | {
"context": "4.2 The Gated D Latch\nTo be useful, it is necessary to control when a latch is set and when it is cleared.\nA simple way to accomplish this is with the gated latch.\nFigure 3.19 shows a logic circuit that implements a gated D latch. It consists\nof the R-S latch of Figure 3.18, plus two additional NAND gates that allow the"
} |
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"values": [
0.7325014542133561,
0.47720054860988836,
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0.47720054860988836,
0.7849979036300037,
0.47720054860988836,
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0.7325014542133561,
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0.47720054860988836,
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]
} | {
"context": "R\nFigure 3.19\nA gated D latch.\nlatch to be set to the value of D, but only when WE is asserted (i.e., when WE\nequals 1). WE stands for write enable. When WE is not asserted (i.e., when WE\nequals 0), the outputs S and R are both equal to 1. Since S and R are inputs to the\nR-S latch, if they are kept at 1, the value stored in the latch remains unchanged,\nas we explained in Section 3.4."
} |
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} | {
"context": "Since S and R are inputs to the\nR-S latch, if they are kept at 1, the value stored in the latch remains unchanged,\nas we explained in Section 3.4.1. When WE is momentarily set to 1, exactly one\nof the outputs S or R is set to 0, depending on the value of D. If D equals 1, then S\nis set to 0. If D equals 0, then both inputs to the lower NAND gate are 1, resulting\nin R being set to 0."
} |
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] | {
"indices": [
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],
"values": [
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]
} | {
"context": "If D equals 1, then S\nis set to 0. If D equals 0, then both inputs to the lower NAND gate are 1, resulting\nin R being set to 0. As we saw earlier, if S is set to 0, the R-S latch is set to 1. If R\nis set to 0, the R-S latch is set to 0. Thus, the R-S latch is set to 1 or 0 according\nto whether D is 1 or 0. When WE returns to 0, S and R return to 1, and the value\nstored in the R-S latch persists."
} |
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"context": "Thus, the R-S latch is set to 1 or 0 according\nto whether D is 1 or 0. When WE returns to 0, S and R return to 1, and the value\nstored in the R-S latch persists.\n3.5 The Concept of Memory\nWe now have all the tools we need to describe one of the most important struc-\ntures in the electronic digital computer, its memory. We will see in Chapter 4\nhow memory ts into the basic scheme of computer processing, and you will see\nthroughout the rest of the book and indeed the rest of your work with computers\nhow important the concept of memory is to computing."
} |
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} | {
"context": "5 The Concept of Memory\nWe now have all the tools we need to describe one of the most important struc-\ntures in the electronic digital computer, its memory. We will see in Chapter 4\nhow memory ts into the basic scheme of computer processing, and you will see\nthroughout the rest of the book and indeed the rest of your work with computers\nhow important the concept of memory is to computing.\nMemory is made up of a (usually large) number of locations, each uniquely\nidentiable and each having the ability to store a value."
} |
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} | {
"context": "We will see in Chapter 4\nhow memory ts into the basic scheme of computer processing, and you will see\nthroughout the rest of the book and indeed the rest of your work with computers\nhow important the concept of memory is to computing.\nMemory is made up of a (usually large) number of locations, each uniquely\nidentiable and each having the ability to store a value. We refer to the unique\nidentier associated with each memory location as its address."
} |
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} | {
"context": "Memory is made up of a (usually large) number of locations, each uniquely\nidentiable and each having the ability to store a value. We refer to the unique\nidentier associated with each memory location as its address. We refer to the\nnumber of bits of information stored in each location as its addressability.\nFor example, an advertisement for a laptop computer might say, This com-\nputer comes with 2 gigabytes of memory."
} |
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} | {
"context": "We refer to the\nnumber of bits of information stored in each location as its addressability.\nFor example, an advertisement for a laptop computer might say, This com-\nputer comes with 2 gigabytes of memory. Actually, most ads generally use\nthe abbreviation 2 GB (or, often: 2 Gig). This statement means, as we will\nexplain momentarily, that the laptop includes two billion memory locations, each\ncontaining one byte of information."
} |
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"context": "Actually, most ads generally use\nthe abbreviation 2 GB (or, often: 2 Gig). This statement means, as we will\nexplain momentarily, that the laptop includes two billion memory locations, each\ncontaining one byte of information.\n3.5.1 Address Space\nWe refer to the total number of uniquely identiable locations as the memorys\naddress space. A 2 GB memory, for example, refers to a memory that consists of\ntwo billion uniquely identiable memory locations."
} |
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] | {
"indices": [
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],
"values": [
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]
} | {
"context": "1 Address Space\nWe refer to the total number of uniquely identiable locations as the memorys\naddress space. A 2 GB memory, for example, refers to a memory that consists of\ntwo billion uniquely identiable memory locations."
} |
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"context": "Actually, the number two billion is only an approximation, due to the way we\nspecify memory locations. Since everything else in the computer is represented\nby sequences of 0s and 1s, it should not be surprising that memory locations are\nidentied by binary addresses as well. With n bits of address, we can uniquely\nidentify 2n locations. Ten bits provide 1024 locations, which is approximately\n1000."
} |