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E D0 Data inputs D1 D2 D3 I0 I1 4-to-1 MUX Output F F
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Data select block diagram of 4-to-1 MUX I1 0 0 1 1 I0 0 1 0 1 F D0 D1 D2 D3
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Truth table of 4-to-1 MUX
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Figure 1355 4-to-1 MUX
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D1 F D2 F
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Figure 1356 Internal structure of the 4-to-1 MUX Table 1313 I1 0 0 0 0 1 1 1 1 I0 0 0 1 1 0 0 1 1 D3 x x x x x x 0 1 D2 x x x x 0 1 x x D1 x x 0 1 x x x x D0 0 1 x x x x x x F 0 1 0 1 0 1 0 1
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Data inputs D0 D1 D2 D3 I0
4-to-1 MUX
Output
Select lines
Figure 1357 Functional diagram of four-input MUX
I1 and I0 , assuming that I0 is the least signi cant bit As an example, I1 I0 = 10 selects D2 , which means that the output, F , will select the value of the data line D2 Therefore F = 1 if D2 = 1 and F = 0 if D2 = 0 Read-Only Memory (ROM) Another common technique for implementing logic functions uses a read-only memory, or ROM As the name implies, a ROM is a logic circuit that holds in storage ( memory ) information in the form of binary numbers that cannot be altered but can be read by a logic circuit A ROM is an array of memory cells, each of which can store either a 1 or a 0 The array consists of 2m n cells, where n is the number of bits in each word stored in ROM To access the information stored in ROM, m address lines are required When an address is selected, in a fashion similar to the operation of the MUX, the binary word corresponding to the address selected appears at the output, which consists of n bits, that is, the same number of bits as the stored words In some sense, a ROM can be thought of as a MUX that has an output consisting of a word instead of a single bit Figure 1358 depicts the conceptual arrangement of a ROM with n = 4 and m = 2 The ROM table has been lled with arbitrary 4-bit words, just for the
ROM address I1 0 0 1 1 I0 0 1 0 1
ROM content (4-bit words) b3 b2 b1 b0 0 1 0 1 1 0 1 1 1 0 1 1 0 W0 1 W1 0 W2 1 W3
I1 Address lines
22 4 ROM
b1 b2 b3
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Figure 1358 Read-only memory
Wi = output word
13
Digital Logic Circuits
purpose of illustration In Figure 1358, if one were to select an enable input of 0 (ie, on) and values for the address lines of I0 = 0 and I1 = 1, the output word would be W2 = 0110, so that b0 = 0, b1 = 1, b2 = 1, b3 = 0 Depending on the content of the ROM and the number of address and output lines, one could implement an arbitrary logic function Unfortunately, the data stored in read-only memories must be entered during fabrication and cannot be altered later A much more convenient type of readonly memory is the erasable programmable read-only memory (EPROM), the content of which can be easily programmed and stored and may be changed if needed EPROMs nd use in many practical applications, because of their exibility in content and ease of programming The following example illustrates the use of an EPROM to perform the linearization of a nonlinear function
FOCUS ON MEASUREMENTS
EPROM-Based Lookup Table for Automotive Fuel Injection System Control
One of the most common applications of EPROMs is the arithmetic lookup table A lookup table is similar in concept to the familiar multiplication table and is used to store precomputed values of certain functions, eliminating the need for actually computing the function A practical application of this concept is present in every automobile manufactured in the United States since the early 1980s, as part of the exhaust emission control system In order for the catalytic converter to minimize the emissions of exhaust gases (especially hydrocarbons, oxides of nitrogen, and carbon monoxide), it is necessary to maintain the air-to-fuel ratio (A/F) as close as possible to the stoichiometric value, that is, 147 parts of air for each part of fuel Most modern engines are equipped with fuel injection systems that are capable of delivering accurate amounts of fuel to each individual cylinder thus, the task of maintaining an accurate A/F amounts to measuring the mass of air that is aspirated into each cylinder and computing the corresponding mass of fuel Many automobiles are equipped with a mass air ow sensor, capable of measuring the mass of air drawn into each cylinder during each engine cycle Let the output of the mass air ow sensor be denoted by the variable MA , and let this variable represent the mass of air (in g) actually entering a cylinder during a particular stroke It is then desired to compute the mass of fuel, MF (also expressed in g), required to achieve and A/F of 147 This computation is simply: MA 147 Although the above computation is a simple division, its actual calculation in a low-cost digital computer (such as would be used on an automobile) is rather complicated It would be much simpler to tabulate a number of values of MA , to precompute the variable MF , and then to store the result of this computation into an EPROM If the EPROM address were made to correspond to the tabulated values of air mass, and the content at each address to the corresponding fuel mass (according to the precomputed values of the expression MF = MA /147), it would not be necessary to perform the division by 147 For each measurement of air mass into one MF =
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