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] | {
"indices": [
3326792864,
2578007438,
1059781460,
2484513939,
358389376,
286434387,
1628150701,
3530670207,
75456649,
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1031134330,
2514386435
],
"values": [
0.524346980836124,
0.6879627636333991,
0.767826220966833,
0.8852765014403581,
0.6879627636333991,
0.6879627636333991,
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]
} | {
"context": " In other words, the output of XOR is\n1 if the two sources are dierent. The output is 0 if the two sources are the same.\nThe truth table for the XOR function is\nA\nB\nXOR\n0\n0\n0\n0\n1\n1\n1\n0\n1\n1\n1\n0"
} |
730943 | [
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] | {
"indices": [
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"values": [
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} | {
"context": "In the same way that we applied the logical operation AND to two m-bit patterns,\nwe can apply the XOR operation bit-wise to two m-bit patterns.\nExample 2.9\nIf a and b are 16-bit patterns as before, then c (shown here) is the XOR of a and b.\na: 0011101001101001\nb: 0101100100100001\nc: 0110001101001000\nNote the distinction between the truth table for XOR shown here and the truth table\nfor OR shown earlier."
} |
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] | {
"indices": [
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],
"values": [
0.45021338715555703,
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]
} | {
"context": "9\nIf a and b are 16-bit patterns as before, then c (shown here) is the XOR of a and b.\na: 0011101001101001\nb: 0101100100100001\nc: 0110001101001000\nNote the distinction between the truth table for XOR shown here and the truth table\nfor OR shown earlier. In the case of exclusive-OR, if both source operands are 1, the\noutput is 0. That is, the output is 1 if the rst operand is 1 but the second operand is\nnot 1 or if the second operand is 1 but the rst operand is not 1."
} |
997518 | [
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"indices": [
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"values": [
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} | {
"context": "In the case of exclusive-OR, if both source operands are 1, the\noutput is 0. That is, the output is 1 if the rst operand is 1 but the second operand is\nnot 1 or if the second operand is 1 but the rst operand is not 1. The term exclusive\nis used because the output is 1 if only one of the two sources is 1. The OR function,\non the other hand, produces an output 1 if only one of the two sources is 1, or if both\nsources are 1."
} |
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} | {
"context": "The term exclusive\nis used because the output is 1 if only one of the two sources is 1. The OR function,\non the other hand, produces an output 1 if only one of the two sources is 1, or if both\nsources are 1. Ergo, the name inclusive-OR.\nExample 2.10\nSuppose we wish to know if two patterns are identical. Since the XOR function pro-\nduces a 0 only if the corresponding pair of bits is identical, two patterns are identical\nif the output of the XOR is all 0s."
} |
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} | {
"context": "10\nSuppose we wish to know if two patterns are identical. Since the XOR function pro-\nduces a 0 only if the corresponding pair of bits is identical, two patterns are identical\nif the output of the XOR is all 0s.\n2.6.6 DeMorgans Laws\nThere are two well-known relationships between AND functions and OR func-\nt\n\n1\n0\n1\n0\n0\n0\n0\n1\n1\n1\n0\n1\nFigure 2.2\nDeMorgans Law."
} |
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} | {
"context": "the\nB =\nfun\nrepr\nA AND B = A OR B\nWe can also state this behavior in English:\nIt is not the case that both A and B are false is equivalent to saying At least\none of A and B is true.\nThis equivalence is known as one of two DeMorgans Laws. Question: Is there\na similar result if one inverts both inputs to an OR function, and then inverts the\noutput?\n2.6.7 The Bit Vector\nWe have discussed the AND, OR, and NOT functions performed on m-bit pat-\nterns, where each of the m bits is a logical value (0 or 1) and the operations are per-\nformed bit-wise (i."
} |
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} | {
"context": "6.7 The Bit Vector\nWe have discussed the AND, OR, and NOT functions performed on m-bit pat-\nterns, where each of the m bits is a logical value (0 or 1) and the operations are per-\nformed bit-wise (i.e., individually and independently). We have also discussed the\nuse of an m-bit bit mask, where our choice of 0 or 1 for each bit allows us to isolate\nthe bits we are interested in focusing on and ignore the bits that dont matter."
} |
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} | {
"context": ", individually and independently). We have also discussed the\nuse of an m-bit bit mask, where our choice of 0 or 1 for each bit allows us to isolate\nthe bits we are interested in focusing on and ignore the bits that dont matter.\nAn m-bit pattern where each bit has a logical value (0 or 1) independent of\nthe other bits is called a bit vector. It is a convenient mechanism for identifying\na property such that some of the bits identify the presence of the property and\nother bits identify the absence of the property."
} |
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"indices": [
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} | {
"context": "An m-bit pattern where each bit has a logical value (0 or 1) independent of\nthe other bits is called a bit vector. It is a convenient mechanism for identifying\na property such that some of the bits identify the presence of the property and\nother bits identify the absence of the property.\nThere are many uses for bit vectors. The most common use is a bit mask,\nas we saw in Example 2.7."
} |
784926 | [
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0.6249544369532175,
0.45449725721703593,
0.45449725721703593,
0.7691962589732724,
0.45449725721703593,
0.45449725721703593,
0.6249544369532175,
0.6249544369532175,
0.45449725721703593,
0.45449725721703593,
0.6249544369532175,
0.45449725721703593,
0.45449725721703593,
0.45449725721703593,
0.45449725721703593,
0.45449725721703593,
0.45449725721703593,
0.45449725721703593,
0.45449725721703593,
0.45449725721703593,
0.45449725721703593,
0.45449725721703593
]
} | {
"context": "The most common use is a bit mask,\nas we saw in Example 2.7. In that example, we had an eight-bit value, and we\nwanted to focus on bit 1 and bit 0 of that value. We did not care about the other\nbits. Performing the AND of that value with the bit mask 00000011 caused bit 7\nthrough bit 2 to be ignored, resulting in the AND function producing 00000000,\n00000001, 00000010, or 00000011, depending on the values of bit 1 and bit 0."
} |
129517 | [
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] | {
"indices": [
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"values": [
0.6504870267441352,
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} | {
"context": "We did not care about the other\nbits. Performing the AND of that value with the bit mask 00000011 caused bit 7\nthrough bit 2 to be ignored, resulting in the AND function producing 00000000,\n00000001, 00000010, or 00000011, depending on the values of bit 1 and bit 0.\nThe bit mask is a bit vector, where the property of each of the bits is whether or\nnot we care about that bit. In Example 2."
} |
491498 | [
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} | {
"context": "The bit mask is a bit vector, where the property of each of the bits is whether or\nnot we care about that bit. In Example 2.7, we only cared about bit 1 and bit 0.\nAnother use of a bit mask could involve a 16-bit 2s complement integer.\nSuppose the only thing we cared about was whether the integer was odd or even\nand whether it was positive or negative. The bit vector 1000000000000001 has a 1 in\nbit 15 that is used to identify a number as positive or negative, and a 1 in bit 0 that is\nused to identify if the integer is odd or even."
} |
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"context": "Suppose the only thing we cared about was whether the integer was odd or even\nand whether it was positive or negative. The bit vector 1000000000000001 has a 1 in\nbit 15 that is used to identify a number as positive or negative, and a 1 in bit 0 that is\nused to identify if the integer is odd or even. If we perform the AND of this bit vector\nwith a 16-bit 2s complement integer, we would get one of four results, depending\non whether the integer was positive or negative and odd or even:\n0000000000000000\n0000000000000001\n1000000000000000\n1000000000000001\nAnother common use of bit vectors involves managing a complex system\nmade up of several units, each of which is individually and independently either."
} |
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] | {
"indices": [
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"values": [
0.7700206310784536,
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} | {
"context": " The bit vector 1000000000000001 has a 1 in\nbit 15 that is used to identify a number as positive or negative, and a 1 in bit 0 that is\nused to identify if the integer is odd or even. If we perform the AND of this bit vector\nwith a 16-bit 2s complement integer, we would get one of four results, depending\non whether the integer was positive or negative and odd or even:\n0000000000000000\n0000000000000001\n1000000000000000\n1000000000000001\nAnother common use of bit vectors involves managing a complex system\nmade up of several units, each of which is individually and independently either"
} |
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"context": "busy or available. The system could be a manufacturing plant where each unit is\na particular machine. Or the system could be a taxicab network where each unit\nis a particular taxicab. In both cases, it is important to identify which units are\nbusy and which are available so that work can be properly assigned.\nSay we have m such units. We can keep track of these m units with a bit\nvector, where a bit is 1 if the unit is free and 0 if the unit is busy."
} |
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} | {
"context": "Say we have m such units. We can keep track of these m units with a bit\nvector, where a bit is 1 if the unit is free and 0 if the unit is busy.\nExample 2.11\nSuppose we have eight machines that we want to monitor with respect to their avail-\nability. We can keep track of them with an eight-bit BUSYNESS bit vector, where a\nbit is 1 if the unit is free and 0 if the unit is busy. The bits are labeled, from right to\nleft, from 0 to 7."
} |
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} | {
"context": "We can keep track of them with an eight-bit BUSYNESS bit vector, where a\nbit is 1 if the unit is free and 0 if the unit is busy. The bits are labeled, from right to\nleft, from 0 to 7.\nThe BUSYNESS bit vector 11000010 corresponds to the situation where only\nunits 7, 6, and 1 are free and therefore available for work assignment.\nSuppose work is assigned to unit 7. We update our BUSYNESS bit vector by per-\nforming the logical AND, where our two sources are the current bit vector 11000010\nand the bit mask 01111111."
} |
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"indices": [
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"values": [
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} | {
"context": "Suppose work is assigned to unit 7. We update our BUSYNESS bit vector by per-\nforming the logical AND, where our two sources are the current bit vector 11000010\nand the bit mask 01111111. The purpose of the bit mask is to clear bit 7 of the\nBUSYNESS bit vector, while leaving alone the values corresponding to all the other\nunits. The result is the bit vector 01000010, indicating that unit 7 is now busy."
} |
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} | {
"context": "The purpose of the bit mask is to clear bit 7 of the\nBUSYNESS bit vector, while leaving alone the values corresponding to all the other\nunits. The result is the bit vector 01000010, indicating that unit 7 is now busy.\nSuppose unit 5 nishes its task and becomes idle. We can update the\nBUSYNESS bit vector by performing the logical OR of it with the bit mask\n00100000. The result is 01100010, indicating that unit 5 is now available."
} |
179606 | [
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} | {
"context": "We can update the\nBUSYNESS bit vector by performing the logical OR of it with the bit mask\n00100000. The result is 01100010, indicating that unit 5 is now available.\n2.7 Other Representations\nThere are many other representations of information that are used in computers.\nTwo that are among the most useful are the oating point data type and ASCII\ncodes. We will describe both in this section."
} |
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} | {
"context": "Two that are among the most useful are the oating point data type and ASCII\ncodes. We will describe both in this section. We will also describe a notation\ncalled hexadecimal that, although not a data type, is convenient for humans to\nuse when dealing with long strings of 0s and 1s.\n2.7.1 Floating Point Data Type (Greater Range, Less Precision)\nMost of the arithmetic in this book uses integer values."
} |
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} | {
"context": "7.1 Floating Point Data Type (Greater Range, Less Precision)\nMost of the arithmetic in this book uses integer values. The LC-3 computer, which\nyou will start studying in Chapter 4, uses the 16-bit, 2s complement integer data\ntype. That data type provides one bit to identify whether the number is positive\nor negative and 15 bits to represent the magnitude of the value. With 16 bits used\nin this way, we can express integer values between 32,768 and +32,767, that\nis, between 215 and +215 1."
} |
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} | {
"context": "That data type provides one bit to identify whether the number is positive\nor negative and 15 bits to represent the magnitude of the value. With 16 bits used\nin this way, we can express integer values between 32,768 and +32,767, that\nis, between 215 and +215 1. We say the precision of our value is 15 bits, and\nthe range is 216. As you learned in high school chemistry class, sometimes we\nneed to express much larger numbers, but we do not require so many digits of\nprecision."
} |
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] | {
"indices": [
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],
"values": [
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0.616883240004695,
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]
} | {
"context": "We say the precision of our value is 15 bits, and\nthe range is 216. As you learned in high school chemistry class, sometimes we\nneed to express much larger numbers, but we do not require so many digits of\nprecision. In fact, recall the value 6.0221023, which you may have been required\nto memorize back then. The range needed to express the value 1023 is far greater\nthan the largest value 2151 that is available with 16-bit 2s complement integers."
} |
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] | {
"indices": [
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"values": [
0.518653437244768,
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]
} | {
"context": "0221023, which you may have been required\nto memorize back then. The range needed to express the value 1023 is far greater\nthan the largest value 2151 that is available with 16-bit 2s complement integers.\nOn the other hand, the 15 bits of precision available with 16-bit 2s complement\nintegers are overkill"
} |
797838 | [
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] | {
"indices": [
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"values": [
0.45886343419922815,
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]
} | {
"context": "In fact, recall the value 6.0221023, which you may have been required\nto memorize back then. The range needed to express the value 1023 is far greater\nthan the largest value 2151 that is available with 16-bit 2s complement integers.\nOn the other hand, the 15 bits of precision available with 16-bit 2s complement\nintegers are overkill. We need only enough bits to express four signicant decimal\ndigits (6022)."
} |
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] | {
"indices": [
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],
"values": [
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]
} | {
"context": "\nOn the other hand, the 15 bits of precision available with 16-bit 2s complement\nintegers are overkill. We need only enough bits to express four signicant decimal\ndigits (6022)."
} |
163650 | [
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} | {
"context": "So we have a problem. We have more bits than we need for precision. But we\ndont have enough bits to represent the range.\nThe oating point data type solves the problem. Instead of using all the bits\nto represent the precision of a value, the oating point data type allocates some of\nthe bits to the range of values (i.e., how big or how small) that can be expressed.\nThe rest of the bits (except for the sign bit) are used for precision."
} |
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} | {
"context": ", how big or how small) that can be expressed.\nThe rest of the bits (except for the sign bit) are used for precision.\nMost ISAs today specify more than one oating point data type. One of them,\nusually called oat, consists of 32 bits, allocated as follows:\nI\nFigure 2.3\nThe 32-bit oating point data type.\n2.7.1.1 Normalized Form\nLike Avogadros number that you learned years ago, the oating point data type\nrepresents numbers expressed in scientic notation, and mostly in normalized\nform:\nN = (1)S 1."
} |
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2484513939,
697231871,
1982334159,
3987636988,
457071384,
212512720,
2774602186,
4040544333,
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2846288729
],
"values": [
0.38803680267519547,
0.7172218223916194,
0.7172218223916194,
0.38803680267519547,
0.38803680267519547,
0.7172218223916194,
0.38803680267519547,
0.38803680267519547,
0.38803680267519547,
0.5591160146868198,
0.5591160146868198,
0.5591160146868198,
0.5591160146868198,
0.5591160146868198,
0.38803680267519547,
0.38803680267519547,
0.38803680267519547,
0.5591160146868198,
0.38803680267519547,
0.6554404077166195,
0.38803680267519547,
0.5591160146868198,
0.38803680267519547,
0.6554404077166195,
0.6554404077166195,
0.38803680267519547,
0.38803680267519547,
0.38803680267519547,
0.38803680267519547,
0.38803680267519547,
0.38803680267519547,
0.38803680267519547,
0.38803680267519547,
0.38803680267519547,
0.38803680267519547,
0.38803680267519547,
0.38803680267519547,
0.38803680267519547,
0.38803680267519547
]
} | {
"context": "1.1 Normalized Form\nLike Avogadros number that you learned years ago, the oating point data type\nrepresents numbers expressed in scientic notation, and mostly in normalized\nform:\nN = (1)S 1. fraction 2exponent127, 1 exponent 254\nwhere S, fraction, and exponent are the binary numbers in the elds of Figure 2.3.\nWe say mostly in normalized form because (as noted in the equation) the data\ntype represents a oating point number in normalized form only if the eight-bit\nexponent is restricted to the 254 unsigned integer values, 1 (00000001) through\n254 (11111110)."
} |
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"indices": [
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"values": [
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} | {
"context": "3.\nWe say mostly in normalized form because (as noted in the equation) the data\ntype represents a oating point number in normalized form only if the eight-bit\nexponent is restricted to the 254 unsigned integer values, 1 (00000001) through\n254 (11111110).\nAs you know, with eight bits, one can represent 256 values uniquely. For the\nother two integer values 0 (00000000) and 255 (11111111), the oating point\ndata type does not represent normalized numbers."
} |
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} | {
"context": "As you know, with eight bits, one can represent 256 values uniquely. For the\nother two integer values 0 (00000000) and 255 (11111111), the oating point\ndata type does not represent normalized numbers. We will explain what it does\nrepresent in Section 2.7.1.2 and Section 2.7.1.3.\nRecall again Avogadros number: (a) an implied + sign (often left out when\nthe value is positive), (b) four decimal digits 6."
} |
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],
"values": [
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]
} | {
"context": "3.\nRecall again Avogadros number: (a) an implied + sign (often left out when\nthe value is positive), (b) four decimal digits 6.022 in normalized form (one non-\nzero decimal digit 6 before the decimal point) times (c) the radix 10 raised to\nthe power 23. The computers 32-bit oating point data type, on the other hand,\nconsists of (a) a sign bit (positive or negative), (b) 24 binary digits in normalized\nform (one non-zero binary digit to the left of the binary point) times (c) the radix\n2 raised to an exponent expressed in eight bits."
} |
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} | {
"context": "022 in normalized form (one non-\nzero decimal digit 6 before the decimal point) times (c) the radix 10 raised to\nthe power 23. The computers 32-bit oating point data type, on the other hand,\nconsists of (a) a sign bit (positive or negative), (b) 24 binary digits in normalized\nform (one non-zero binary digit to the left of the binary point) times (c) the radix\n2 raised to an exponent expressed in eight bits.\nWe determine the value of the 32-bit oating point representation shown in\nFigure 2."
} |
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} | {
"context": "The computers 32-bit oating point data type, on the other hand,\nconsists of (a) a sign bit (positive or negative), (b) 24 binary digits in normalized\nform (one non-zero binary digit to the left of the binary point) times (c) the radix\n2 raised to an exponent expressed in eight bits.\nWe determine the value of the 32-bit oating point representation shown in\nFigure 2.3 by examining its three parts."
} |
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0.1212208941578865,
0.793633222579956,
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0.33065035939216614,
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0.7993999719619751
]
] | {
"indices": [
3510466679,
3005552705,
3041551381,
3445939484,
648501015,
1731862276,
976803442,
818459139,
758380041,
1758470515,
1296924235,
28501148
],
"values": [
0.6446506032632968,
0.6446506032632968,
0.6446506032632968,
0.6446506032632968,
0.6446506032632968,
0.6446506032632968,
0.6446506032632968,
0.6446506032632968,
0.6446506032632968,
0.6446506032632968,
0.6446506032632968,
0.6446506032632968
]
} | {
"context": "\nWe determine the value of the 32-bit oating point representation shown in\nFigure 2.3 by examining its three parts."
} |
718349 | [
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] | {
"indices": [
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"values": [
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} | {
"context": "The sign bit S is just a single binary digit, 0 for positive numbers, 1 for neg-\native numbers. The formula contains the factor 1S, which evaluates to +1 if\nS = 0, and 1 if S = 1.\nThe 23 fraction bits form the 24-bit quantity 1.fraction, where normalized\nform demands exactly one non-zero binary digit to the left of the binary point.\nSince there exists only one non-zero binary digit (i."
} |
602940 | [
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} | {
"context": "fraction, where normalized\nform demands exactly one non-zero binary digit to the left of the binary point.\nSince there exists only one non-zero binary digit (i.e., the value 1), it is unneces-\nsary to explicitly store that bit in our 32-bit oating point format. In fact that is\nhow we get 24 bits of precision, the 1 to the left of the binary point that is always\npresent in normalized numbers and so is unnecessary to store, and the 23 bits of\nfraction that are actually part of the 32-bit data type."
} |
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0.40446581128347797,
0.40446581128347797,
0.40446581128347797,
0.5759710318813028,
0.40446581128347797,
0.5759710318813028,
0.5759710318813028,
0.5759710318813028,
0.40446581128347797,
0.40446581128347797,
0.40446581128347797,
0.40446581128347797,
0.40446581128347797,
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0.40446581128347797,
0.40446581128347797,
0.40446581128347797,
0.40446581128347797
]
} | {
"context": ", the value 1), it is unneces-\nsary to explicitly store that bit in our 32-bit oating point format. In fact that is\nhow we get 24 bits of precision, the 1 to the left of the binary point that is always\npresent in normalized numbers and so is unnecessary to store, and the 23 bits of\nfraction that are actually part of the 32-bit data type.\nThe eight exponent bits are encoded in what we call an excess code, named\nfor the notion that one can get the *real* exponent by treating the code as\nan unsigned integer and subtracting the excess (sometimes called the bias)."
} |
112875 | [
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} | {
"context": "In fact that is\nhow we get 24 bits of precision, the 1 to the left of the binary point that is always\npresent in normalized numbers and so is unnecessary to store, and the 23 bits of\nfraction that are actually part of the 32-bit data type.\nThe eight exponent bits are encoded in what we call an excess code, named\nfor the notion that one can get the *real* exponent by treating the code as\nan unsigned integer and subtracting the excess (sometimes called the bias). In\nthe case of the IEEE Floating Point that almost everyone uses, that excess (or\nbias) is 127 for 32-bit oating point numbers."
} |
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} | {
"context": "The eight exponent bits are encoded in what we call an excess code, named\nfor the notion that one can get the *real* exponent by treating the code as\nan unsigned integer and subtracting the excess (sometimes called the bias). In\nthe case of the IEEE Floating Point that almost everyone uses, that excess (or\nbias) is 127 for 32-bit oating point numbers. Thus, an exponent eld contain-\ning 10000110 corresponds to the exponent +7 (since 10000110 represents the\nunsigned integer 134, from which we subtract 127, yielding +7)."
} |
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],
"values": [
0.4261152563889012,
0.4261152563889012,
0.4261152563889012,
0.5975888056451725,
0.4261152563889012,
0.4261152563889012,
0.4261152563889012,
0.4261152563889012,
0.4261152563889012,
0.6901655924291842,
0.4261152563889012,
0.4261152563889012,
0.4261152563889012,
0.4261152563889012,
0.7481134113278183,
0.5975888056451725,
0.4261152563889012,
0.4261152563889012,
0.5975888056451725,
0.5975888056451725,
0.5975888056451725,
0.5975888056451725,
0.5975888056451725,
0.5975888056451725,
0.5975888056451725,
0.4261152563889012,
0.5975888056451725,
0.5975888056451725,
0.4261152563889012,
0.5975888056451725,
0.5975888056451725,
0.4261152563889012
]
} | {
"context": "In\nthe case of the IEEE Floating Point that almost everyone uses, that excess (or\nbias) is 127 for 32-bit oating point numbers. Thus, an exponent eld contain-\ning 10000110 corresponds to the exponent +7 (since 10000110 represents the\nunsigned integer 134, from which we subtract 127, yielding +7). An exponent\neld containing 00000111 corresponds to the exponent 120 (since 00000111\nrepresents the unsigned integer 7, from which we subtract 127, yielding 120)."
} |
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] | {
"indices": [
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],
"values": [
0.40446581128347797,
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0.40446581128347797,
0.40446581128347797,
0.40446581128347797,
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]
} | {
"context": "Thus, an exponent eld contain-\ning 10000110 corresponds to the exponent +7 (since 10000110 represents the\nunsigned integer 134, from which we subtract 127, yielding +7). An exponent\neld containing 00000111 corresponds to the exponent 120 (since 00000111\nrepresents the unsigned integer 7, from which we subtract 127, yielding 120).\nThe exponent eld gives us numbers as large as 2+127 for an exponent eld con-\ntaining 254 (11111110) and as small as 2126 for an exponent eld containing\n1 (00000001)."
} |
389635 | [
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"indices": [
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"values": [
0.7930325315818297,
0.7540182209966191,
0.6051599098019981,
0.6051599098019981,
0.43385612017797237,
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0.43385612017797237,
0.43385612017797237,
0.43385612017797237,
0.43385612017797237,
0.43385612017797237,
0.43385612017797237,
0.43385612017797237,
0.43385612017797237,
0.43385612017797237,
0.43385612017797237,
0.43385612017797237,
0.43385612017797237,
0.43385612017797237,
0.43385612017797237,
0.43385612017797237,
0.43385612017797237,
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]
} | {
"context": "An exponent\neld containing 00000111 corresponds to the exponent 120 (since 00000111\nrepresents the unsigned integer 7, from which we subtract 127, yielding 120).\nThe exponent eld gives us numbers as large as 2+127 for an exponent eld con-\ntaining 254 (11111110) and as small as 2126 for an exponent eld containing\n1 (00000001).\nExample 2.12\nWhat does the oating point data type\n00111101100000000000000000000000\nrepresent?\nThe leading bit is a 0."
} |
444729 | [
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0.4633143131816905,
0.721437915187976,
0.6332396382760778,
0.4633143131816905,
0.4633143131816905,
0.721437915187976,
0.4633143131816905,
0.4633143131816905,
0.4633143131816905,
0.4633143131816905,
0.4633143131816905,
0.4633143131816905,
0.4633143131816905,
0.4633143131816905,
0.4633143131816905,
0.4633143131816905,
0.4633143131816905,
0.4633143131816905,
0.4633143131816905,
0.4633143131816905,
0.4633143131816905,
0.4633143131816905,
0.4633143131816905,
0.4633143131816905,
0.4633143131816905
]
} | {
"context": "Example 2.12\nWhat does the oating point data type\n00111101100000000000000000000000\nrepresent?\nThe leading bit is a 0. This signies a positive number. The next eight bits\nrepresent the unsigned number 123. If we subtract 127, we get the actual expo-\nnent 4. The last 23 bits are all 0. Therefore, the number being represented is\n+1.000000000000000000000000 24, which is 1\n16.\nExample 2."
} |
979049 | [
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"indices": [
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"values": [
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} | {
"context": "000000000000000000000000 24, which is 1\n16.\nExample 2.13\nHow is the number 6 5\n8 represented in the oating point data type?\nFirst, we express 6 5\n8 as a binary number: 110.101.\n(1 22 + 1 21 + 0 20 + 1 21 + 0 22 + 1 23)\nThen we normalize the value, yielding 1.10101 22.\nThe sign bit is 1, reecting the fact that 6 5\n8 is a negative number. The exponent\neld contains 10000001, the unsigned number 129, reecting the fact that the real\nexponent is +2 (129127 = +2)."
} |
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] | {
"indices": [
1622730881,
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],
"values": [
0.4418834306199022,
0.6129253186992035,
0.7037231194242516,
0.6129253186992035,
0.6129253186992035,
0.6129253186992035,
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0.4418834306199022,
0.7600169847832969,
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0.6129253186992035,
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]
} | {
"context": "The sign bit is 1, reecting the fact that 6 5\n8 is a negative number. The exponent\neld contains 10000001, the unsigned number 129, reecting the fact that the real\nexponent is +2 (129127 = +2). The fraction is the 23 bits of precision, after remov-\ning the leading 1. That is, the fraction is 10101000000000000000000. The result is\nthe number 6 5\n8, expressed as a oating point number:\n1 10000001 10101000000000000000000."
} |
628584 | [
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"context": " That is, the fraction is 10101000000000000000000. The result is\nthe number 6 5\n8, expressed as a oating point number:\n1 10000001 10101000000000000000000"
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"indices": [
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"values": [
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} | {
"context": "Example 2.14\nThe following three examples provide further illustrations of the interpretation of\nthe 32-bit oating point data type according to the rules of the IEEE standard.\n0 10000011 00101000000000000000000 is 1.00101 24 = 18.5\nThe exponent eld contains the unsigned number 131. Since 131 127 is 4, the\nexponent is +4. Combining a 1 to the left of the binary point with the fraction eld\nto the right of the binary point yields 1."
} |
118454 | [
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] | {
"indices": [
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"values": [
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} | {
"context": "Since 131 127 is 4, the\nexponent is +4. Combining a 1 to the left of the binary point with the fraction eld\nto the right of the binary point yields 1.00101. If we move the binary point four\npositions to the right, we get 10010.1, which is 18.5.\n1 10000010 00101000000000000000000 is 1 1.00101 23 = 9.25\nThe sign bit is 1, signifying a negative number. The exponent is 130, signifying an\nexponent of 130 127, or +3."
} |
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] | {
"indices": [
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],
"values": [
0.45021338715555703,
0.6208926095194913,
0.45021338715555703,
0.6208926095194913,
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0.45021338715555703,
0.45021338715555703,
0.45021338715555703,
0.45021338715555703,
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0.45021338715555703,
0.45021338715555703,
0.45021338715555703,
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]
} | {
"context": "25\nThe sign bit is 1, signifying a negative number. The exponent is 130, signifying an\nexponent of 130 127, or +3. Combining a 1 to the left of the binary point with\nthe fraction eld to the right of the binary point yields 1.00101. Moving the binary\npoint three positions to the right, we get 1001.01, which is 9.25.\n0 11111110 11111111111111111111111 is 2128\nThe sign is +. The exponent is 254 127, or +127."
} |
536530 | [
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"indices": [
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"values": [
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]
} | {
"context": "0 11111110 11111111111111111111111 is 2128\nThe sign is +. The exponent is 254 127, or +127. Combining a 1 to the left\nof the binary point with the fraction eld to the right of the binary point yields\n1.11111111 1, which is approximately 2. Therefore, the result is approximately\n2128.\n2.7.1.2 Innities\nWe noted above that the oating point data type represented numbers expressed\nin scientic notation in normalized form provided the exponent eld does not\ncontain 00000000 or 11111111."
} |
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] | {
"indices": [
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],
"values": [
0.4460095183914834,
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0.616883240004695,
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]
} | {
"context": "1.2 Innities\nWe noted above that the oating point data type represented numbers expressed\nin scientic notation in normalized form provided the exponent eld does not\ncontain 00000000 or 11111111.\nIf the exponent eld contains 11111111, we use the oating point data type to\nrepresent various things, among them the notion of innity. Innity is represented\nby the exponent eld containing all 1s and the fraction eld containing all 0s."
} |
410045 | [
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] | {
"indices": [
457071384,
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],
"values": [
0.6129253186992035,
0.7037231194242516,
0.7037231194242516,
0.4418834306199022,
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0.6129253186992035,
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0.6129253186992035,
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]
} | {
"context": "If the exponent eld contains 11111111, we use the oating point data type to\nrepresent various things, among them the notion of innity. Innity is represented\nby the exponent eld containing all 1s and the fraction eld containing all 0s. We\nrepresent positive innity if the sign bit is 0 and negative innity if the sign bit is 1.\n2.7.1.3 Subnormal Numbers\nThe smallest number that can be represented in normalized form is\nN = 1."
} |
665198 | [
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] | {
"indices": [
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],
"values": [
0.4869299023387813,
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]
} | {
"context": "1.3 Subnormal Numbers\nThe smallest number that can be represented in normalized form is\nN = 1.00000000000000000000000 2126\nWhat about numbers smaller than 2126 but larger than 0? We call such num-\nbers subnormal numbers because they cannot be represented in normalized form.\nThe largest subnormal number is\nN = 0.11111111111111111111111 2126\nThe smallest subnormal number is\nN = 0.00000000000000000000001 2126, i."
} |
361515 | [
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] | {
"indices": [
1793842459,
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3327252652,
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964114575,
112807804,
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],
"values": [
0.5748286596828066,
0.8439443830554441,
0.5748286596828066,
0.7300205722679514,
0.7300205722679514,
0.5748286596828066,
0.5748286596828066,
0.5748286596828066,
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0.7300205722679514,
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0.5748286596828066,
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]
} | {
"context": "11111111111111111111111 2126\nThe smallest subnormal number is\nN = 0.00000000000000000000001 2126, i.e., 223 2126 which is 2149.\nNote that the largest subnormal number is 2126 minus 2149. Do you see why\nthat is the case?"
} |
345071 | [
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] | {
"indices": [
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],
"values": [
0.46785238308125726,
0.7250884400239858,
0.46785238308125726,
0.46785238308125726,
0.46785238308125726,
0.46785238308125726,
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0.6374651681242771,
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0.7785999733411075,
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0.46785238308125726,
0.46785238308125726,
0.46785238308125726,
0.46785238308125726,
0.46785238308125726,
0.46785238308125726,
0.46785238308125726,
0.46785238308125726,
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0.6374651681242771,
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]
} | {
"context": "Subnormal numbers are numbers of the form\nN = (1)S 0. fraction 2126\nWe represent them with an exponent eld of 00000000. The fraction eld is\nrepresented in the same way as with normalized numbers. That is, if the expo-\nnent eld contains 00000000, the exponent is 126, and the signicant digits are\nobtained by starting with a leading 0, followed by a binary point, followed by the\n23 bits of the fraction eld."
} |
210948 | [
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] | {
"indices": [
1982334159,
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],
"values": [
0.6208926095194913,
0.7107036060130572,
0.45021338715555703,
0.45021338715555703,
0.45021338715555703,
0.7107036060130572,
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0.45021338715555703,
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0.6208926095194913,
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0.45021338715555703,
0.45021338715555703,
0.45021338715555703,
0.45021338715555703,
0.45021338715555703,
0.6208926095194913,
0.7107036060130572,
0.7107036060130572,
0.45021338715555703,
0.6208926095194913,
0.45021338715555703,
0.45021338715555703,
0.45021338715555703,
0.45021338715555703,
0.45021338715555703,
0.45021338715555703,
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0.45021338715555703
]
} | {
"context": "The fraction eld is\nrepresented in the same way as with normalized numbers. That is, if the expo-\nnent eld contains 00000000, the exponent is 126, and the signicant digits are\nobtained by starting with a leading 0, followed by a binary point, followed by the\n23 bits of the fraction eld.\nExample 2.15\nWhat number corresponds to the following oating point representation?\n0 00000000 00001000000000000000000\nAnswer: The leading 0 means the number is positive."
} |
693707 | [
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-0.7714351415634155,
-0.12124285846948624,
-0.1765289157629013,
1.0350019931793213
]
] | {
"indices": [
2035475614,
3165358105,
1308688855,
737551030,
3551371075,
3445939484,
648501015,
1731862276,
3530670207,
2565335819,
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],
"values": [
0.45021338715555703,
0.45021338715555703,
0.7661119630911921,
0.45021338715555703,
0.45021338715555703,
0.45021338715555703,
0.6208926095194913,
0.45021338715555703,
0.7107036060130572,
0.45021338715555703,
0.45021338715555703,
0.45021338715555703,
0.45021338715555703,
0.6208926095194913,
0.45021338715555703,
0.45021338715555703,
0.45021338715555703,
0.7107036060130572,
0.45021338715555703,
0.6208926095194913,
0.45021338715555703,
0.45021338715555703,
0.45021338715555703,
0.45021338715555703,
0.45021338715555703,
0.45021338715555703,
0.45021338715555703,
0.45021338715555703,
0.6208926095194913,
0.45021338715555703,
0.45021338715555703,
0.45021338715555703,
0.45021338715555703
]
} | {
"context": "Example 2.15\nWhat number corresponds to the following oating point representation?\n0 00000000 00001000000000000000000\nAnswer: The leading 0 means the number is positive. The next eight bits, a zero\nexponent, means the exponent is 126, and the bit to the left of the binary point is 0.\nThe last 23 bits form the number 0.00001000000000000000000, which equals 25.\nThus, the number represented is 25 2126, which is 2131."
} |
755594 | [
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} | {
"context": "00001000000000000000000, which equals 25.\nThus, the number represented is 25 2126, which is 2131.\nIncluding subnormal numbers allows very, very tiny numbers to be repre-\nsented.\nA detailed understanding of IEEE Floating Point Arithmetic is well beyond\nwhat should be expected in this rst course. Our purpose in including this sec-\ntion in the textbook is to at least let you know that there is, in addition to 2s\ncomplement integers, another very important data type available in almost all\nISAs, which is called oating point; it allows very large and very tiny numbers to\nbe expressed at the cost of reducing the number of binary digits of precision."
} |
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} | {
"context": "A detailed understanding of IEEE Floating Point Arithmetic is well beyond\nwhat should be expected in this rst course. Our purpose in including this sec-\ntion in the textbook is to at least let you know that there is, in addition to 2s\ncomplement integers, another very important data type available in almost all\nISAs, which is called oating point; it allows very large and very tiny numbers to\nbe expressed at the cost of reducing the number of binary digits of precision.\n2."
} |
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} | {
"context": "Our purpose in including this sec-\ntion in the textbook is to at least let you know that there is, in addition to 2s\ncomplement integers, another very important data type available in almost all\nISAs, which is called oating point; it allows very large and very tiny numbers to\nbe expressed at the cost of reducing the number of binary digits of precision.\n2.7.2 ASCII Codes\nAnother representation of information is the standard code that almost all com-\nputer equipment manufacturers have agreed to use for transferring characters\nbetween the main computer processing unit and the input and output devices."
} |
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} | {
"context": "7.2 ASCII Codes\nAnother representation of information is the standard code that almost all com-\nputer equipment manufacturers have agreed to use for transferring characters\nbetween the main computer processing unit and the input and output devices.\nThat code is an eight-bit code referred to as ASCII. ASCII stands for Ameri-\ncan Standard Code for Information Interchange. It (ASCII) greatly simplies the\ninterface between a keyboard manufactured by one company, a computer made\nby another company, and a monitor made by a third company."
} |
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} | {
"context": "ASCII stands for Ameri-\ncan Standard Code for Information Interchange. It (ASCII) greatly simplies the\ninterface between a keyboard manufactured by one company, a computer made\nby another company, and a monitor made by a third company.\nEach key on the keyboard is identied by its unique ASCII code. So, for\nexample, the digit 3 is represented as 00110011, the digit 2 is 00110010, the\nlowercase e is 01100101, and the ENTER key is 00001101."
} |
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} | {
"context": "Each key on the keyboard is identied by its unique ASCII code. So, for\nexample, the digit 3 is represented as 00110011, the digit 2 is 00110010, the\nlowercase e is 01100101, and the ENTER key is 00001101. The entire set of\neight-bit ASCII codes is listed in Figure E.2 of Appendix E. When you type a key\non the keyboard, the corresponding eight-bit code is stored and made available to\nthe computer."
} |
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} | {
"context": "2 of Appendix E. When you type a key\non the keyboard, the corresponding eight-bit code is stored and made available to\nthe computer. Where it is stored and how it gets into the computer are discussed\nin Chapter 9.\nMost keys are associated with more than one code. For example, the ASCII\ncode for the letter E is 01000101, and the ASCII code for the letter e is 01100101."
} |
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} | {
"context": "Both are associated with the same key, although in one case the Shift key is also\ndepressed while in the other case, it is not.\nIn order to display a particular character on the monitor, the computer must\ntransfer the ASCII code for that character to the electronics associated with the\nmonitor. That, too, is discussed in Chapter 9.\n2.7.3 Hexadecimal Notation\nWe have seen that information can be represented as 2s complement integers,\nas bit vectors, in oating point format, or as an ASCII code."
} |
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"values": [
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} | {
"context": "7.3 Hexadecimal Notation\nWe have seen that information can be represented as 2s complement integers,\nas bit vectors, in oating point format, or as an ASCII code. There are other\nrepresentations also, but we will leave them for another book. However, before\nwe leave this topic, we would like to introduce you to a representation that is used\nmore as a convenience for humans than as a data type to support operations being\nperformed by the computer."
} |
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} | {
"context": "There are other\nrepresentations also, but we will leave them for another book. However, before\nwe leave this topic, we would like to introduce you to a representation that is used\nmore as a convenience for humans than as a data type to support operations being\nperformed by the computer. This is the hexadecimal notation. As we will see, it\nevolves nicely from the positional binary notation and is useful for dealing with\nlong strings of binary digits without making errors."
} |
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} | {
"context": "This is the hexadecimal notation. As we will see, it\nevolves nicely from the positional binary notation and is useful for dealing with\nlong strings of binary digits without making errors.\nIt will be particularly useful in dealing with the LC-3 where 16-bit binary\nstrings will be encountered often.\nAn example of such a binary string is\n0011110101101110\nLets try an experiment. Cover the preceding 16-bit binary string of 0s and 1s\nwith one hand, and try to write it down from memory."
} |
304014 | [
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] | {
"indices": [
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"values": [
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0.673936010434824,
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0.5794647210550786,
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]
} | {
"context": "An example of such a binary string is\n0011110101101110\nLets try an experiment. Cover the preceding 16-bit binary string of 0s and 1s\nwith one hand, and try to write it down from memory. How did you do? Hex-\nadecimal notation is about being able to do this without making mistakes. We\nshall see how.\nIn general, a 16-bit binary string takes the form\na15 a14 a13 a12 a11 a10 a9 a8 a7 a6 a5 a4 a3 a2 a1 a0\nwhere each of the bits ai is either 0 or 1."
} |
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} | {
"context": "We\nshall see how.\nIn general, a 16-bit binary string takes the form\na15 a14 a13 a12 a11 a10 a9 a8 a7 a6 a5 a4 a3 a2 a1 a0\nwhere each of the bits ai is either 0 or 1.\nIf we think of this binary string as an unsigned integer, its value can be\ncomputed as\na15 215 + a14 214 + a13 213 + a12 212 + a11 211 + a10 210\n+ a9 29 + a8 28 + a7 27 + a6 26 + a5 25 + a4 24 + a3 23\n+ a2 22 + a1 21 + a0 20\nWe can factor 212 from the rst four terms, 28 from the second four terms, 24\nfrom the third set of four terms, and 20 from the last four terms, yielding\n212(a15 23 + a14 22 + a13 21 + a12 20)\n+ 28(a11 23 + a10 22 + a9 21 + a8 20)\n+ 24(a7 23 + a6 22 + a5 21 + a4 20)\n+ 20(a3 23 + a2 22 + a1 21 + a0 20)\nNote that the largest value inside a set of parentheses is 15, which would be the\ncase if each of the four bits is 1."
} |
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} | {
"context": "In general, a 16-bit binary string takes the form\na15 a14 a13 a12 a11 a10 a9 a8 a7 a6 a5 a4 a3 a2 a1 a0\nwhere each of the bits ai is either 0 or 1.\nIf we think of this binary string as an unsigned integer, its value can be\ncomputed as\na15 215 + a14 214 + a13 213 + a12 212 + a11 211 + a10 210\n+ a9 29 + a8 28 + a7 27 + a6 26 + a5 25 + a4 24 + a3 23\n+ a2 22 + a1 21 + a0 20\nWe can factor 212 from the rst four terms, 28 from the second four terms, 24\nfrom the third set of four terms, and 20 from the last four terms, yielding\n212(a15 23 + a14 22 + a13 21 + a12 20)\n+ 28(a11 23 + a10 22 + a9 21 + a8 20)\n+ 24(a7 23 + a6 22 + a5 21 + a4 20)\n+ 20(a3 23 + a2 22 + a1 21 + a0 20)\nNote that the largest value inside a set of parentheses is 15, which would be the\ncase if each of the four bits is 1. If we replace what is inside each square bracket."
} |
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"indices": [
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"values": [
0.2775524672493006,
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0.4345065652714821,
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0.4345065652714821,
0.2775524672493006,
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]
} | {
"context": "\nIf we think of this binary string as an unsigned integer, its value can be\ncomputed as\na15 215 + a14 214 + a13 213 + a12 212 + a11 211 + a10 210\n+ a9 29 + a8 28 + a7 27 + a6 26 + a5 25 + a4 24 + a3 23\n+ a2 22 + a1 21 + a0 20\nWe can factor 212 from the rst four terms, 28 from the second four terms, 24\nfrom the third set of four terms, and 20 from the last four terms, yielding\n212(a15 23 + a14 22 + a13 21 + a12 20)\n+ 28(a11 23 + a10 22 + a9 21 + a8 20)\n+ 24(a7 23 + a6 22 + a5 21 + a4 20)\n+ 20(a3 23 + a2 22 + a1 21 + a0 20)\nNote that the largest value inside a set of parentheses is 15, which would be the\ncase if each of the four bits is 1. If we replace what is inside each square bracket"
} |
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0.5031633058386022,
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0.33615110305703677,
0.33615110305703677,
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]
} | {
"context": "with a symbol representing its value (from 0 to 15), and we replace 212 with its\nequivalent 163, 28 with 162, 24 with 161, and 20 with 160, we have\nh3 163 + h2 162 + h1 161 + h0 160\nwhere h3, for example, is a symbol representing\na15 23 + a14 22 + a13 21 + a12 20\nSince the symbols must represent values from 0 to 15, we assign symbols to these\nvalues as follows: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F. That is, we represent\n0000 with the symbol 0, 0001 with the symbol 1, 1001 with 9, 1010 with A,\n1011 with B, 1111 with F. The resulting notation is called hexadecimal, or\nbase 16."
} |
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} | {
"context": "That is, we represent\n0000 with the symbol 0, 0001 with the symbol 1, 1001 with 9, 1010 with A,\n1011 with B, 1111 with F. The resulting notation is called hexadecimal, or\nbase 16.\nSo, for example, if the hex digits E92F represent a 16-bit 2s complement\ninteger, is the value of that integer positive or negative? How do you know?\nNow, then, what is this hexadecimal representation good for, anyway? It\nseems like just another way to represent a number without adding any benet."
} |
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} | {
"context": "The resulting notation is called hexadecimal, or\nbase 16.\nSo, for example, if the hex digits E92F represent a 16-bit 2s complement\ninteger, is the value of that integer positive or negative? How do you know?\nNow, then, what is this hexadecimal representation good for, anyway? It\nseems like just another way to represent a number without adding any benet.\nLets return to the exercise where you tried to write from memory the string\n0011110101101110\nIf we had rst broken the string at four-bit boundaries\n0011\n1101\n0110\n1110\nand then converted each four-bit string to its equivalent hex digit\n3\nD\n6\nE\nit would have been no problem to jot down (with the string covered) 3D6E."
} |
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} | {
"context": "So, for example, if the hex digits E92F represent a 16-bit 2s complement\ninteger, is the value of that integer positive or negative? How do you know?\nNow, then, what is this hexadecimal representation good for, anyway? It\nseems like just another way to represent a number without adding any benet.\nLets return to the exercise where you tried to write from memory the string\n0011110101101110\nIf we had rst broken the string at four-bit boundaries\n0011\n1101\n0110\n1110\nand then converted each four-bit string to its equivalent hex digit\n3\nD\n6\nE\nit would have been no problem to jot down (with the string covered) 3D6E.\nIn summary, although hexadecimal notation can be used to perform base-\n16 arithmetic, it is mainly used as a convenience for humans."
} |
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} | {
"context": "Lets return to the exercise where you tried to write from memory the string\n0011110101101110\nIf we had rst broken the string at four-bit boundaries\n0011\n1101\n0110\n1110\nand then converted each four-bit string to its equivalent hex digit\n3\nD\n6\nE\nit would have been no problem to jot down (with the string covered) 3D6E.\nIn summary, although hexadecimal notation can be used to perform base-\n16 arithmetic, it is mainly used as a convenience for humans. It can be used to\nrepresent binary strings that are integers or oating point numbers or sequences\nof ASCII codes, or bit vectors."
} |
228536 | [
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} | {
"context": "In summary, although hexadecimal notation can be used to perform base-\n16 arithmetic, it is mainly used as a convenience for humans. It can be used to\nrepresent binary strings that are integers or oating point numbers or sequences\nof ASCII codes, or bit vectors. It simply reduces the number of digits by a factor\nof\nres\n2.1\n2.\n2.\nrequiring additional bits for each students unique bit pattern?."
} |
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} | {
"context": "\n2.\nrequiring additional bits for each students unique bit pattern?"
} |
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} | {
"context": "ital Logic Structures\nI\nn Chapter 1, we stated that computers were built from very large numbers\nof very simple structures. For example, Intels Broadwell-E5 microproces-\nsor, introduced in 2016, contained more than seven billion transistors. Similarly,\nIBMs Power9 microprocessor, introduced in 2017, contained eight billion tran-\nsistors. In this chapter, we will explain how the MOS transistor works (as a logic\nelement), show how these transistors are connected to form logic gates, and then\nshow how logic gates are interconnected to form larger units that are needed to\nconstruct a computer."
} |
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} | {
"context": "Similarly,\nIBMs Power9 microprocessor, introduced in 2017, contained eight billion tran-\nsistors. In this chapter, we will explain how the MOS transistor works (as a logic\nelement), show how these transistors are connected to form logic gates, and then\nshow how logic gates are interconnected to form larger units that are needed to\nconstruct a computer. In Chapter 4, we will connect those larger units and form\na computer."
} |
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"values": [
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} | {
"context": "In this chapter, we will explain how the MOS transistor works (as a logic\nelement), show how these transistors are connected to form logic gates, and then\nshow how logic gates are interconnected to form larger units that are needed to\nconstruct a computer. In Chapter 4, we will connect those larger units and form\na computer.\nBut rst, the transistor.\n3.1 The Transistor\nMost computers today or rather most microprocessors (which form the core of the\ncomputer) are constructed out of MOS transistors."
} |
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} | {
"context": "3.1 The Transistor\nMost computers today or rather most microprocessors (which form the core of the\ncomputer) are constructed out of MOS transistors. MOS stands for metal-oxide\nsemiconductor. The electrical properties of metal-oxide semiconductors are well\nbeyond the scope of what we want to understand in this course. They are below\nour lowest level of abstraction, which means that if somehow transistors start\nmisbehaving, we are at their mercy."
} |
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} | {
"context": "The electrical properties of metal-oxide semiconductors are well\nbeyond the scope of what we want to understand in this course. They are below\nour lowest level of abstraction, which means that if somehow transistors start\nmisbehaving, we are at their mercy. However, it is unlikely in this course that we\nwill have any problems from the transistors.\nStill, it is useful to know that there are two types of MOS transistors: P-type\nand N-type."
} |
322747 | [
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} | {
"context": "However, it is unlikely in this course that we\nwill have any problems from the transistors.\nStill, it is useful to know that there are two types of MOS transistors: P-type\nand N-type. They both operate logically, very similar to the way wall switches\nwork.\nFigure 3.1 shows the most basic of electrical circuits. It consists of (1) a\npower supply (in this case, the 120 volts that come into your house if you live in\nthe United States, or the 220 volts if you live in most of the rest of the world),\n(2) a wall switch, and (3) a lamp (plugged into an outlet in the wall)."
} |
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} | {
"context": "1 shows the most basic of electrical circuits. It consists of (1) a\npower supply (in this case, the 120 volts that come into your house if you live in\nthe United States, or the 220 volts if you live in most of the rest of the world),\n(2) a wall switch, and (3) a lamp (plugged into an outlet in the wall). In order for\nthe lamp to glow, electrons must ow; in order for electrons to ow, there must be\na closed circuit from the power supply to the lamp and back to the power supply."
} |
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} | {
"context": "It consists of (1) a\npower supply (in this case, the 120 volts that come into your house if you live in\nthe United States, or the 220 volts if you live in most of the rest of the world),\n(2) a wall switch, and (3) a lamp (plugged into an outlet in the wall). In order for\nthe lamp to glow, electrons must ow; in order for electrons to ow, there must be\na closed circuit from the power supply to the lamp and back to the power supply.."
} |
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] | {
"indices": [
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"values": [
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} | {
"context": " In order for\nthe lamp to glow, electrons must ow; in order for electrons to ow, there must be\na closed circuit from the power supply to the lamp and back to the power supply."
} |
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} | {
"context": "Figure 3.1\nA simple electric circuit showing the use of a wall switch.\nThe lamp can be turned on and o by simply manipulating the wall switch to\nmake or break the closed circuit.\nInstead of the wall switch, we could use an N-type or a P-type MOS transistor\nto make or break the closed circuit. Figure 3.2 shows a schematic rendering of\nan N-type transistor (a) by itself, and (b) in a circuit."
} |
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"indices": [
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"values": [
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} | {
"context": "Figure 3.2 shows a schematic rendering of\nan N-type transistor (a) by itself, and (b) in a circuit. Note (Figure 3.2a) that\nthe transistor has three terminals. They are called the gate, the source, and the\ndrain. The reasons for the names source and drain are not of interest to us in this\ncourse. What is of interest is the fact that if the gate of the N-type transistor is\nsupplied with 1."
} |
180546 | [
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} | {
"context": "The reasons for the names source and drain are not of interest to us in this\ncourse. What is of interest is the fact that if the gate of the N-type transistor is\nsupplied with 1.2 volts, the connection from source to drain acts like a piece of\nwire. We say (in the language of electricity) that we have a short circuit between\nthe source and drain. If the gate of the N-type transistor is supplied with 0 volts,\nthe connection between the source and drain is broken."
} |
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] | {
"indices": [
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"values": [
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} | {
"context": "We say (in the language of electricity) that we have a short circuit between\nthe source and drain. If the gate of the N-type transistor is supplied with 0 volts,\nthe connection between the source and drain is broken. We say that between the\nsource and drain we have an open circuit.\nFigure 3.2 shows the N-type transistor in a circuit with a battery and a bulb.\nWhen the gate is supplied with 1."
} |
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"indices": [
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"values": [
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} | {
"context": "2 shows the N-type transistor in a circuit with a battery and a bulb.\nWhen the gate is supplied with 1.2 volts, the transistor acts like a piece of wire,\ncompleting the circuit and causing the bulb to glow. When the gate is supplied\nFigure 3.2\nThe N-type MOS transistor."
} |
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] | {
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"values": [
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]
} | {
"context": "Figure 3.2c is a shorthand notation for describing the circuit of Figure 3.2b.\nRather than always showing the power supply and the complete circuit, electri-\ncal engineers usually show only the terminals of the power supply. The fact that\nthe power supply itself provides the completion of the completed circuit is well\nunderstood, and so is not usually shown.\nThe P-type transistor works in exactly the opposite fashion from the N-type\ntransistor."
} |
158895 | [
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"values": [
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} | {
"context": "The fact that\nthe power supply itself provides the completion of the completed circuit is well\nunderstood, and so is not usually shown.\nThe P-type transistor works in exactly the opposite fashion from the N-type\ntransistor. Figure 3.3 shows the schematic representation of a P-type transistor.\nWhen the gate is supplied with 0 volts, the P-type transistor acts (more or less)\nlike a piece of wire, closing the circuit."
} |
801837 | [
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] | {
"indices": [
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"values": [
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0.801011887420441,
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]
} | {
"context": "3 shows the schematic representation of a P-type transistor.\nWhen the gate is supplied with 0 volts, the P-type transistor acts (more or less)\nlike a piece of wire, closing the circuit. When the gate is supplied with 1.2 volts,\nthe P-type transistor acts like an open circuit. Because the P-type and N-type\nt\ns\nDrain\nFigure 3.3\nA P-type MOS transistor.\n3.2 Logic Gates\nOne step up from the transistor is the logic gate."
} |
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"context": "3.2 Logic Gates\nOne step up from the transistor is the logic gate. That is, we construct basic logic\nstructures out of individual MOS transistors. In Chapter 2, we studied the behav-\nior of the AND, the OR, and the NOT functions. In this chapter, we construct\ntransistor circuits that implement each of these functions. The corresponding\ncircuits are called AND, OR, and NOT gates.\n3.2."
} |