Digital Design and Computer Architecture. Edition No. 2,Readership
SECOND Edition Features - Covers the fundamentals of digital logic design and reinforces logic concepts through the design of a MIPS microprocessor. - Features side-by-side examples of the two most prominent Hardware Description - - Languages (HDLs)-SystemVerilog and VHDL-which illustrate and compare the ways each can be used in the design of digital systems Computer Systems Design and Architecture Uploaded by sancristall Copyright: Attribution Non-Commercial (BY-NC) Available Formats Download as PDF or read online from Scribd Download Digital Design And Computer Architecture, Second Edition [PDF] Type: PDF Size: MB Download as PDF Download Original PDF This document was uploaded by user Computer Systems Design and Architecture (2nd Edition) - Google Docs Computer Systems Design and Architecture (2nd Edition) The version of the browser you are using is no ABOUT THE BOOK Digital Design And Computer Architecture 2nd Edition PDF free download. Digital Design and Computer Architecture, Second Edition, takes a unique and modern ... read more
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Books to Borrow Open Library. Featured All Books All Texts This Just In Smithsonian Libraries FEDLINK US Genealogy Lincoln Collection. Top American Libraries Canadian Libraries Universal Library Project Gutenberg Children's Library Biodiversity Heritage Library Books by Language Additional Collections. A device engineer cannot make wise trade-offs in transistor design without understanding the circuits in which the transistors will be used. We hope that by the time you finish reading this book, you can pick the level of abstraction appropriate to solving your problem and evaluate the impact of your design choices on other levels of abstraction.
Using interchangeable parts is a familiar application of discipline. One of the first examples of interchangeable parts was in flintlock rifle manufacturing. Until the early 19th century, rifles were individually crafted by hand. Components purchased from many different craftsmen were carefully filed and fit together by a highly skilled gunmaker. The discipline of interchangeable parts revolutionized the industry. By limiting the components to a standardized set with well-defined tolerances, rifles could be assembled and repaired much faster and with less skill. The gunmaker no longer concerned himself with lower levels of abstraction such as the specific shape of an individual barrel or gunstock. In the context of this book, the digital discipline will be very important. Digital circuits use discrete voltages, whereas analog circuits use continuous voltages. Therefore, digital circuits are a subset of analog circuits and in some sense must be capable of less than the broader class of analog circuits.
However, digital circuits are much simpler to design. By limiting 5 Each chapter in this book begins with an abstraction icon indicating the focus of the chapter in deep blue, with secondary topics shown in lighter shades of blue. For example, digital televisions, compact disks CDs , and cell phones are replacing their analog predecessors. These principles apply to both software and hardware systems. Captain Meriwether Lewis of the Lewis and Clark Expedition was one of the early advocates of interchangeable parts for rifles. In , he explained: The guns of Drewyer and Sergt. Pryor were both out of order. The first was repared with a new lock, the old one having become unfit for use; the second had the cock screw broken which was replaced by a duplicate which had been prepared for the lock at Harpers Ferry where she was manufactured. But for the precaution taken in bringing on those extra locks, and parts of locks, in addition to the ingenuity of John Shields, most of our guns would at this moment be entirely unfit for use; but fortunately for us I have it in my power here to record that they are all in good order.
See Elliott Coues, ed. Common modules are reused many times, reducing the number of distinct modules that must be designed. A flintlock rifle was one of the most intricate objects in common use in the early 19th century. Using the principle of hierarchy, we can break it into components shown in Figure 1. The barrel is the long metal tube through which the bullet is fired. The lock is the firing mechanism. And the stock is the wooden body that holds the parts together and provides a secure grip for the user. In turn, the lock contains the trigger, hammer, flint, frizzen, and pan. Each of these components could be hierarchically described in further detail. Modularity teaches that each component should have a well-defined function and interface.
A function of the stock is to mount the barrel and lock. Its interface consists of its length and the location of its mounting pins. In a modular rifle design, stocks from many different manufacturers can be used with a particular barrel as long as the stock and barrel are of the correct length and have the proper mounting mechanism. A function of the barrel is to impart spin to the bullet so that it travels more accurately. Modularity dictates that there should be no side effects: the design of the stock should not impede the function of the barrel. Regularity teaches that interchangeable parts are a good idea. With regularity, a damaged barrel can be replaced by an identical part. The barrels can be efficiently built on an assembly line, instead of being painstakingly hand-crafted.
We will return to these principles of hierarchy, modularity, and regularity throughout the book. net © Flint Cock String Spring Pan Expanded view of Lock 1. For example, the voltage on a wire, the frequency of an oscillation, or the position of a mass are all continuous quantities. Digital systems, on the other hand, represent information with discrete-valued variables—that is, variables with a finite number of distinct values. Babbage labored from to ,1 designing and attempting to build this mechanical computer. The Analytical Engine used gears with ten positions labeled 0 through 9, much like a mechanical odometer in a car. Charles Babbage, — Attended Cambridge University and married Georgiana Whitmore in Also invented the cowcatcher and the universal postage rate. Interested in lock-picking, but abhorred street musicians image courtesy of Fourmilab Switzerland, www. Babbage chose 25 rows of gears, so the machine has digit precision.
He wrote An Investigation of the Laws of Thought , which introduced binary variables and the three fundamental logic operations: AND, OR, and NOT image courtesy of the American Institute of Physics. Indeed, the word bit is short for binary digit. A continuous signal theoretically contains an infinite amount of information because it can take on an infinite number of values. In practice, noise and measurement error limit the information to only 10 to 16 bits for most continuous signals. If the measurement must be made rapidly, the information content is lower e. George Boole developed a system of logic operating on binary variables that is now known as Boolean logic.
Electronic computers commonly use a positive voltage to represent '1' and zero volts to represent '0'. In this book, we will use the terms '1', TRUE, and HIGH synonymously. Similarly, we will use '0', FALSE, and LOW interchangeably. On the other hand, understanding the details of the hardware allows the programmer to optimize the software better for that specific computer. In the next section, we examine how groups of bits can be used to represent numbers. In later chapters, we will also use groups of bits to represent letters and programs. This section introduces the various number systems that will be used throughout the rest of the book. Just as you probably have ten fingers, there are ten decimal digits: 0, 1, 2, …, 9. Decimal digits are joined together to form longer decimal numbers. Each column of a decimal number has ten times the weight of the previous column.
From right to left, the column weights are 1, 10, , , and so on. Decimal numbers are referred to as base The base is indicated by a subscript after the number to prevent confusion when working in more than one base. For example, Figure 1. This is called the range of the number. For example, a three-digit decimal number represents one of possibilities in the range of 0 to Each column of a binary number has twice the weight of the previous column, so binary numbers are base 2. In binary, the 1's column 10's column 's column 's column Figure 1. Table 1. Example 1. Solution: Figure 1. Solution: Determine whether each column of the binary result has a 1 or a 0.
We can do this starting at either the left or the right column. Working from the left, start with the largest power of 2 less than or equal to the number in this case, Hence, it is sometimes more convenient to work in base 16, called hexadecimal. Hexadecimal numbers use the digits 0 to 9 along with the letters A to F, as shown in Table 1. Columns in base 16 have weights of 1, 16, or , or , and so on. Solution: Conversion between hexadecimal and binary is easy because each hexadecimal digit directly corresponds to four binary digits. Conversion to decimal requires the arithmetic shown in Figure 1. A more proper term would use the Latin sexa six , but sexadecimal sounded too risqué. Solution: Again, conversion is easy. Start reading from the right. Solution: Like decimal to binary conversion, decimal to hexadecimal conversion can be done from the left or the right. Working from the left, start with the largest power of 16 less than or equal to the number in this case, Now it is easy to convert from hexadecimal to binary, as in Example 1.
Working from the right, repeatedly divide the number by The remainder goes in each column. Again, the result is 14D The size of objects stored in computer memories is customarily measured in bytes rather than bits. A group of four bits, or half a byte, is called a nibble. One hexadecimal digit stores one nibble and two hexadecimal digits store one full byte. Nibbles are no longer a commonly used unit, but the term is cute. Microprocessors handle data in chunks called words. The size of a word depends on the architecture of the microprocessor.
When this chapter was written in , most computers had bit processors, indicating that they operate on bit words. At the time, older computers handling bit words were also widely available. Simpler microprocessors, especially those used in gadgets such as toasters, use 8- or bit words. Similarly, within a word, the bytes are identified as least significant byte LSB through most significant byte MSB , as shown in Figure 1. A microprocessor is a processor built on a single chip. Intel introduced the first 4-bit microprocessor, called the , in Now, even the most sophisticated supercomputers are built using microprocessors. We will use the terms microprocessor and processor interchangeably throughout this book.
Hence, the term kilo Greek for thousand indicates For example, bytes is one kilobyte 1 KB. Solution: Split the exponent into a multiple of ten and the remainder. Similarly, MB, Mb, GB, and Gb are used for millions and billions of bytes and bits. Memory capacity is usually measured in bytes. As in decimal addition, if the sum of two numbers is greater than what fits in a single digit, we carry a 1 into the next column. In the right-most column of Figure 1. For example, in the right-most column of Figure 1. For obvious reasons, the bit that is carried over to the neighboring column is called the carry bit. The carries are indicated in blue. We can check our work by repeating the computation in decimal. Addition is said to overflow if the result is too big to fit in the available digits. A 4-bit number, for example, has the range [0, 15]. The fifth bit is discarded, producing an incorrect result in the remaining four bits. Overflow can be detected by checking for a carry out of the most significant column.
Does overflow occur? This result overflows the range of a 4-bit binary number. If it must be stored as four bits, the most significant bit is discarded, leaving the incorrect result of If the computation had been done using numbers with five or more bits, the result would have been correct. We will often want to represent both positive and negative numbers, requiring a different binary number system. The failure was caused when the computer controlling the rocket overflowed its bit range and crashed. The code had been extensively tested on the Ariane 4 rocket. However, the Ariane 5 had a faster engine that produced larger values for the control computer, leading to the overflow.
A sign bit of 0 indicates positive and a sign bit of 1 indicates negative. Both indicate zero. As you may expect, it can be troublesome to have two different representations for the same number. Notice that positive numbers have a 0 in the most significant position and negative numbers have a 1 in this position, so the most significant bit can be viewed as the sign bit. The process consists of inverting all of the bits in the number, then adding 1 to the least significant bit position. This is useful to find the representation of a negative number or to determine the magnitude of a negative number. Inverting produces Solution: has a leading 1, so it must be negative. To find its magnitude, invert the bits and add 1. Recall that when adding N-bit numbers, the carry out of the Nth bit i. The fifth bit is discarded, leaving the correct 4-bit result Note that the carry out of the most significant position is discarded because the result is stored in four bits. Zero is considered positive because its sign bit is 0.
However the values are split between positive and negative numbers. For example, a 4-bit unsigned number represents 16 values: 0 to Hence, this negative number has no positive counterpart. Adding a positive number to a negative number never causes overflow. Unlike unsigned numbers, a carry out of the most significant column does not indicate overflow. Instead, overflow occurs if the two numbers being added have the same sign bit and the result has the opposite sign bit. Does the result overflow? This process is called sign extension. They are sign-extended to seven bits by copying the sign bit into the three new upper bits to form and , respectively. Subtraction is performed by negating the second number i. Unsigned numbers span the range [0, 15] in regular binary order. The nonnegative numbers [0, 7] share the same encodings as unsigned numbers. The most significant bit is the sign bit.
The positive numbers [1, 7] share the same encodings as unsigned numbers. The negative numbers are symmetric but have the sign bit set. Logic gates are simple digital circuits that take one or more binary inputs and produce a binary output. Logic gates are drawn with a symbol showing the input or inputs and the output. Digital designers typically use letters near the beginning of the alphabet for gate inputs and the letter Y for the gate output. The relationship between the inputs and the output can be described with a truth table or a Boolean equation. A truth table lists inputs on the left and the corresponding output on the right. It has one row for each possible combination of inputs.
A Boolean equation is a mathematical expression using binary variables. If A is FALSE, then Y is TRUE. If A is TRUE, then Y is FALSE. This relationship is summarized by the truth table and Boolean equation in the figure. It simply copies the input to the output. From the logical point of view, a buffer is no different from a wire, so it might seem useless. However, from the analog point of view, the buffer might have desirable characteristics such as the ability to deliver large amounts of current to a motor or the ability to quickly send its output to many gates. This is an example of why we need to consider multiple levels of abstraction to fully understand a system; the digital abstraction hides the real purpose of a buffer. The triangle symbol indicates a buffer. A circle on the output is called a bubble and indicates inversion, as was seen in the NOT gate symbol of Figure 1. The AND gate shown in Figure 1. Otherwise, the output is FALSE.
By convention, the inputs are listed in the order 00, 01, 10, 11, as if you were counting in binary. Any gate can be followed by a bubble to invert its operation. The NAND gate performs NOT AND. Its output is TRUE unless both inputs are TRUE. The NOR gate performs NOT OR. Its output is TRUE if neither A nor B is TRUE. An N-input XOR gate is sometimes called a parity gate and produces a TRUE output if an odd number of inputs are TRUE. As with two-input gates, the input combinations in the truth table are listed in counting order. Complete the truth table. The XNOR output is TRUE if both inputs are FALSE or both inputs are TRUE. The two-input XNOR gate is sometimes called an equality gate because its output is TRUE when the inputs are equal.
The most common are AND, OR, XOR, NAND, NOR, and XNOR. An N-input OR gate produces a TRUE output when at least one input is TRUE. The output is TRUE only if none of the inputs are TRUE. Create a truth table. The output is TRUE only if all of the inputs are TRUE. However, the variables are represented by continuous physical quantities such as the voltage on a wire, the position of a gear, or the level of fluid in a cylinder. Hence, the designer must choose a way to relate the continuous value to the discrete value. For example, consider representing a binary signal A with a voltage on a wire. Any real system must tolerate some noise, so 4. But what about 4. table 1. The highest voltage in the system comes from the power supply and is usually called VDD.
As chips have progressed to smaller transistors, VDD has dropped to 3. The first gate is called the driver and the second gate is called the receiver. The output of the driver is 23 1. The driver produces a LOW 0 output in the range of 0 to VOL or a HIGH 1 output in the range of VOH to VDD· If the receiver gets an input in the range of 0 to VIL, it will consider the input to be LOW. If the receiver gets an input in the range of VIH to VDD, it will consider the input to be HIGH. VOH,VOL, VIH, and VIL are called the output and input high and low logic levels.
Thus, even if the output of the driver is contaminated by some noise, the input of the receiver will still detect the correct logic level. The noise margin is the amount of noise that could be added to a worst-case output such that the signal can still be interpreted as a valid input. As can be seen in Figure 1. VO1 is the output voltage of inverter I1, and VI2 is the input voltage of inverter I2. What are the inverter low and high noise margins? Can the circuit tolerate 1 V of noise between VO1 and VI2? VDD stands for the voltage on the drain of a metal-oxidesemiconductor transistor, used to build most modern chips.
The power supply voltage is also sometimes called V CC , standing for the voltage on the collector of a bipolar junction transistor used to build chips in an older technology. Ground is sometimes called VSS because it is the voltage on the source of a metal-oxidesemiconductor transistor. See Section 1. DC indicates behavior when an input voltage is held constant or changes slowly enough for the rest of the system to keep up. In contrast, the transient response of a circuit is the behavior when an input voltage changes rapidly. Section 2. The DC transfer characteristics of a gate describe the output voltage as a function of the input voltage when the input is changed slowly enough that the output can keep up. They are called transfer characteristics because they describe the relationship between input and output voltages. A real inverter changes more gradually between the extremes, as shown in Figure 1. This raises the question of how to define the logic levels.
These two points are called the unity gain points. Choosing logic levels at the unity gain points usually maximizes the noise margins. If VIL were reduced, VOH would only increase by a small amount. But if VIL were increased, VOH would drop precipitously. The static discipline requires that, given logically valid inputs, every circuit element will produce logically valid outputs. By conforming to the static discipline, digital designers sacrifice the freedom of using arbitrary analog circuit elements in return for the simplicity and robustness of digital circuits. They raise the level of abstraction 25 1. The choice of VDD and logic levels is arbitrary, but all gates that communicate must have compatible logic levels. Therefore, gates are grouped into logic families such that all gates in a logic family obey the static discipline when used with other gates in the family.
Logic gates in the same logic family snap together like Legos in that they use consistent power supply voltages and logic levels. Their logic levels are compared in Table 1. Since then, logic families have balkanized with a proliferation of even lower power supply voltages. Appendix A. Solution: Table 1. Note that a 5 V logic family such as TTL or CMOS may produce an output voltage as HIGH as 5 V. If this 5 V signal drives the input of a 3. Born in Burlington, Iowa. Received a B. in physics from Grinnell College and a Ph. in physics from MIT. Cofounded Fairchild Semiconductor in and Intel in Coinvented the integrated circuit.
Many engineers from his teams went on to found other seminal semiconductor companies © , Intel Corporation. Reproduced by permission. Modern computers use transistors because they are cheap, small, and reliable. Transistors are electrically controlled switches that turn ON or OFF when a voltage or current is applied to a control terminal. In , Jack Kilby at Texas Instruments built the first integrated circuit containing two transistors. In , Robert Noyce at Fairchild Semiconductor patented a method of interconnecting multiple transistors on a single silicon chip. Thanks to more than three decades of unprecedented manufacturing advances, engineers can now pack roughly one billion MOSFETs onto a 1 cm2 chip of silicon, and these transistors cost less than 10 microcents apiece.
The capacity and cost continue to improve by an order of magnitude every 8 years or so. MOSFETs are now the building blocks of almost all 27 1. In this section, we will peer beneath the digital abstraction to see how logic gates are built from MOSFETs. Silicon Si is a group IV atom, so it has four electrons in its valence shell and forms bonds with four adjacent atoms, resulting in a crystalline lattice. In the figure, a line represents a covalent bond. By itself, silicon is a poor conductor because all the electrons are tied up in covalent bonds. However, it becomes a better conductor when small amounts of impurities, called dopant atoms, are carefully added. If a group V dopant such as arsenic As is added, the dopant atoms have an extra electron that is not involved in the bonds. The electron carries a negative charge, so we call arsenic an n-type dopant.
On the other hand, if a group III dopant such as boron B is added, the dopant atoms are missing an electron, as shown in Figure 1. This missing electron is called a hole. In a similar fashion, the hole can migrate around the lattice. The hole is a lack of negative charge, so it acts like a positively charged particle. Hence, we call boron a p-type dopant. Because the conductivity of silicon changes over many orders of magnitude depending on the concentration of dopants, silicon is called a semiconductor. The p-type region is called the anode and the n-type region is called the cathode, as illustrated in Figure 1. But when the anode voltage is lower than the voltage on the cathode, the diode is reverse biased, and no current flows.
The diode symbol intuitively shows that current only flows in one direction. The capacitance is proportional to the size of the conductors and inversely proportional to the distance between them. The symbol for a capacitor is shown in Figure 1. Capacitance is important because charging or discharging a conductor takes time and energy. More capacitance means that a circuit will be slower and require more energy to operate. Speed and energy will be discussed throughout this book. A pin dual-inline package DIP contains a small chip scarcely visible in the center that is connected to 40 metal pins, 20 on a side, by gold wires thinner than a strand of hair photograph by Kevin Mapp.
A MOSFET is a sandwich of several layers of conducting and insulating materials. MOSFETs are built on thin flat wafers of silicon of about 15 to 30 cm in diameter. The manufacturing process begins with a bare wafer. The process involves a sequence of steps in which dopants are implanted into the silicon, thin films of silicon dioxide and silicon are grown, and metal is deposited. Between each step, the wafer is patterned so that the materials appear only where they are desired. Because transistors are a fraction of a micron2 in length and the entire wafer is processed at once, it is inexpensive to manufacture billions of transistors at a time. Once processing is complete, the wafer is cut into rectangles called chips or dice that contain thousands, millions, or even billions of transistors. The chip is tested, then placed in a plastic or ceramic package with metal pins to connect it to a circuit board.
The MOSFET sandwich consists of a conducting layer called the gate on top of an insulating layer of silicon dioxide SiO2 on top of the silicon wafer, called the substrate. Historically, the gate was constructed from metal, hence the name metal-oxide-semiconductor. Modern manufacturing processes use polycrystalline silicon for the gate because it does not melt during subsequent high-temperature processing steps. Silicon dioxide is better known as glass and is often simply called oxide in the semiconductor industry. The metal-oxide-semiconductor sandwich forms a capacitor, in which a thin layer of insulating oxide called a dielectric separates the metal and semiconductor plates.
The n-type transistors, called nMOS, have regions of n-type dopants adjacent to the gate called the source and the drain and are built on a p-type semiconductor substrate. The pMOS transistors are just the opposite, consisting of p-type source and drain regions in an n-type substrate. A MOSFET behaves as a voltage-controlled switch in which the gate voltage creates an electric field that turns ON or OFF a connection between the source and drain. The term field effect transistor comes from this principle of operation. Let us start by exploring the operation of an nMOS transistor. The substrate of an nMOS transistor is normally tied to GND, the lowest voltage in the system.
First, consider the situation when the gate is also at 0 V, as shown in Figure 1. The diodes between the source or drain and the substrate are reverse biased because the source or drain voltage is nonnegative. Hence, there is no path for current to flow between the source and drain, so the transistor is OFF. Now, consider when the gate is raised to VDD, as shown in Figure 1. When a positive voltage is applied to the top plate of a capacitor, it establishes an electric field that attracts positive charge on the top plate and negative charge to the bottom plate. If the voltage is sufficiently large, so much negative charge is attracted to the underside of the gate that the region inverts from p-type to effectively become n-type. This inverted region is called the channel. Now the transistor has a continuous path from the n-type source through the n-type channel to the n-type drain, so electrons can flow from source to drain.
The transistor is ON. The gate voltage required to turn on a transistor is called the threshold voltage,Vt, and is typically 0. However, we say that charge flows from the source to the drain. In an nMOS transistor, the charge is carried by electrons, which flow from negative voltage to positive voltage. In a pMOS transistor, the charge is carried by holes, which flow from positive voltage to negative voltage. If we draw schematics with the most positive voltage at the top and the most negative at the bottom, the source of negative charges in an nMOS transistor is the bottom terminal and the source of positive charges in a pMOS transistor is the top terminal. A technician holds a inch wafer containing hundreds of microprocessor chips © , Intel Corporation. Born in San Francisco.
in chemistry from UC Berkeley and a Ph. in chemistry and physics from Caltech. Cofounded Intel in with Robert Noyce. Observed in that the number of transistors on a computer chip doubles every year. Since , transistor counts have doubled every two years. Semiconductor sales have also increased exponentially. Unfortunately, power consumption has increased exponentially as well © , Intel Corporation. pMOS transistors work in just the opposite fashion, as might be guessed from the bubble on their symbol shown in Figure 1. The substrate is tied to VDD. When the gate is also at VDD, the pMOS transistor is OFF. When the gate is at GND, the channel inverts to p-type and the pMOS transistor is ON. Unfortunately, MOSFETs are not perfect switches. However, we will see that it is possible to build logic gates that use transistors only in their good mode. nMOS transistors need a p-type substrate, and pMOS transistors need an n-type substrate. To build both flavors of transistors on the same chip, manufacturing processes typically start with a p-type wafer, then implant n-type regions called wells where the pMOS transistors should go.
These processes that provide both flavors of transistors are called Complementary MOS or CMOS. CMOS processes are used to build the vast majority of all transistors fabricated today. In summary, CMOS processes give us two types of electrically controlled switches, as shown in Figure 1. The voltage at the gate g regulates the flow of current between the source s and drain d. nMOS transistors are OFF when the gate is 0 and ON when the gate is 1. The triangle indicates GND, and the flat bar indicates VDD; these labels will be omitted from future schematics. The nMOS transistor, N1, is connected between GND and the Y output. The pMOS transistor, P1, is connected between VDD and the Y output. Both transistor gates are controlled by the input, A. Hence, Y is connected to VDD but not to GND, and is pulled up to a logic 1. P1 passes a good 1. N1 passes a good 0. Checking against the truth table in Figure 1. In schematic diagrams, wires are always joined at three-way junctions. They are joined at four-way junctions only if a dot is shown.
The nMOS transistors N1 and N2 are connected in series; both nMOS transistors must be ON to pull the output down to GND. The pMOS transistors P1 and P2 are in parallel; only one pMOS transistor must be ON to pull the output up to VDD. P1 is OFF, but P2 is ON, creating a path from VDD to Y. Therefore, Y is pulled up to 1. pMOS transistors are Table 1. They confirm this theory with the observation that if the magic smoke is ever let out of the device, it ceases to work. The networks may consist of transistors in series or in parallel. When transistors are in parallel, the network is ON if either transistor is ON. When transistors are in series, the network is ON only if both transistors are ON. The slash across the input wire indicates that the gate may receive multiple inputs.
If both the pull-up and pull-down networks were ON simultaneously, a short circuit would exist between VDD and GND. The output of the gate might be in the forbidden zone and the transistors would consume large amounts of power, possibly enough to burn out. On the other hand, if both the pull-up and pull-down networks were OFF simultaneously, the output would be connected to neither VDD nor GND. We say that the output floats. Its value is again undefined. Floating outputs are usually undesirable, but in Section 2. In a properly functioning logic gate, one of the networks should be ON and the other OFF at any given time, so that the output is pulled HIGH or LOW but not shorted or floating. We can guarantee this by using the rule of conduction complements. When nMOS transistors are in series, the pMOS transistors must be in parallel.
When nMOS transistors are in parallel, the pMOS transistors must be in series. Y A B Solution: The NAND gate should produce a 0 output only when all three inputs are 1. Hence, the pull-down network should have three nMOS transistors in series. By the conduction complements rule, the pMOS transistors must be in parallel. Such a gate is shown in Figure 1. C Figure 1. gate schematic A B Y Figure 1. Hence, the pull-down network should have two nMOS transistors in parallel. By the conduction complements rule, the pMOS transistors must be in series. However, building NAND and NOT gates is easy. Thus, the best way to build an AND gate using CMOS transistors is to use a NAND followed by a NOT, as shown in Figure 1. A B Y Figure 1. Recall that nMOS transistors are good at passing 0 and pMOS transistors are good at passing 1, so the parallel combination of the two passes both values well. The two sides of the switch are called A and B because a switch is bidirectional and has no preferred input or output side.
The control signals are called enables, EN and EN. Hence, the transmission gate is OFF or disabled, so A and B are not connected. EN A B EN Figure 1. Transistors in series are slower than transistors in parallel, just as resistors in series have more resistance than resistors in parallel. Moreover, pMOS transistors are slower than nMOS transistors because holes cannot move around the silicon lattice as fast as electrons. Therefore the parallel nMOS transistors are fast and the series pMOS transistors are slow, especially when many are in series. Pseudo-nMOS logic replaces the slow stack of pMOS transistors with a single weak pMOS transistor that is always ON, as shown in Figure 1.
This pMOS transistor is often called a weak pull-up. The physical dimensions of the pMOS transistor are selected so that the pMOS transistor will pull the output Y HIGH weakly—that is, only if none of the nMOS transistors are ON. But if any nMOS transistor is ON, it overpowers the weak pull-up and pulls Y down close enough to GND to produce a logic 0. The advantage of pseudo-nMOS logic is that it can be used to build fast NOR gates with many inputs. Pseudo-nMOS gates are useful for certain memory and logic arrays discussed in Chapter 5. The disadvantage is that a short circuit exists between VDD and GND when the output is LOW; the weak pMOS and nMOS transistors are both ON.
The short circuit draws continuous power, so pseudo-nMOS logic must be used sparingly. weak Y inputs nMOS pull-down network Figure 1. A weak nMOS transistor was used to pull the output HIGH because pMOS transistors were not available. Power consumption is of great importance in digital systems. The battery life of portable systems such as cell phones and laptop computers is limited by power consumption. Power is also significant for systems that are plugged in, because electricity costs money and because the system will overheat if it draws too much power. Digital systems draw both dynamic and static power. Dynamic power is the power used to charge capacitance as signals change between 0 and 1. Static power is the power used even when signals do not change and the system is idle.
Logic gates and the wires that connect them have capacitance. The energy drawn from the power supply to charge a capacitance C to voltage VDD is CVDD2. If the voltage on the capacitor switches at frequency f i. Discharging does not draw energy from the power supply, so the dynamic power consumption is 1 1. When transistors are OFF, they leak a small amount of current. Some circuits, such as the pseudo-nMOS gate discussed in Section 1. The total static current, IDD, is also called the leakage current or the quiescent supply current flowing between VDD and GND.
When in use, it also broadcasts 3 W of power out of its antenna. When the phone is not in use, the dynamic power drops to almost zero because the signal processing is turned off. But the phone also draws 40 mA of quiescent current whether it is in use or not. Determine the battery life of the phone a if it is not being used, and b if it is being used continuously. Together with the static and broadcast power, the total active power is 2. This example somewhat oversimplifies the actual operation of a cell phone, but it illustrates the key ideas of power consumption. This chapter has introduced principles for understanding and designing complex systems. Although the real world is analog, digital designers discipline themselves to use a discrete subset of possible signals. In particular, binary variables have just two states: 0 and 1, also called FALSE and TRUE or LOW and HIGH.
Logic gates compute a binary output from one or more binary inputs. nMOS transistors turn ON when the gate is 1. pMOS transistors turn ON when the gate is 0. In Chapters 2 through 5, we continue the study of digital logic. Chapter 2 addresses combinational logic, in which the outputs depend only on the current inputs. The logic gates introduced already are examples of combinational logic. You will learn to design circuits involving multiple gates to implement a relationship between inputs and outputs specified by a truth table or Boolean equation. Chapter 3 addresses sequential logic, in which the outputs depend on both current and past inputs. Registers are common sequential elements that remember their previous input. Finite state machines, built from registers and combinational logic, are a powerful way to build complicated systems in a systematic fashion.
We also study timing of digital systems to analyze how fast a system can operate. Chapter 4 describes hardware description languages HDLs. HDLs are related to conventional programming languages but are used to simulate and 35 36 CHAPTER ONE From Zero to One build hardware rather than software. Most digital systems today are designed with HDLs. SystemVerilog and VHDL are the two prevalent languages, and they are covered side-by-side in this book. Chapter 5 studies other combinational and sequential building blocks such as adders, multipliers, and memories. Chapter 6 shifts to computer architecture. It describes the MIPS processor, an industry-standard microprocessor used in consumer electronics, some Silicon Graphics workstations, and many communications systems such as televisions, networking hardware, and wireless links. The MIPS architecture is defined by its registers and assembly language instruction set. You will learn to write programs in assembly language for the MIPS processor so that you can communicate with the processor in its native language.
Chapters 7 and 8 bridge the gap between digital logic and computer architecture. Chapter 7 investigates microarchitecture, the arrangement of digital building blocks, such as adders and registers, needed to construct a processor. In that chapter, you learn to build your own MIPS processor. Indeed, you learn three microarchitectures illustrating different trade-offs of performance and cost. Processor performance has increased exponentially, requiring ever more sophisticated memory systems to feed the insatiable demand for data. Chapter 8 delves into memory system architecture and also describes how computers communicate with peripheral devices such as keyboards and printers.
Exercises Exercises Exercise 1. b chemists studying the composition of matter. Exercise 1. b businesses to manage their operations. Explain how he can use the principles of hierarchy, modularity, and regularity to save time and money during construction. If it can be measured with an accuracy of ±50 mV, at most how many bits of information does it convey? a If you can read the hour hand to the nearest 15 minutes, how many bits of information does the clock convey about the time? b If you know whether it is before or after noon, how many additional bits of information do you know about the time? How many bits of information is conveyed with one sexagesimal digit? How do you write the number in sexagesimal? Show your work. a b c d Exercise 1. Exercises Exercise 1. a A b 3B16 c FFFF16 d D Exercise 1. a 4E16 b 7C16 c ED3A16 d FB Exercise 1. a b Exercise 1. Convert each of the numbers from Exercise 1. a b c d 41 42 CHAPTER ONE From Zero to One Exercise 1.
How many are less than 0? How many nibbles are in the word? How many bytes can it receive in 1 minute? How many bytes can it send in 1 minute? How many real GBs of music can you store on a 50 GB hard disk? Estimate how many bits it has without using a calculator. Indicate whether or not the sum overflows a 4-bit result. Indicate whether or not the sum overflows an 8-bit result. Indicate whether or not the sum overflows a 6-bit result. Indicate whether or not the sum overflows an 8-bit two hex digit result. Indicate whether or not the difference overflows a 5-bit result. Indicate whether or not the difference overflows a 6-bit result.
For example, for 5-bit numbers with a bias of 15, the number 0 is represented as , 1 as , and so forth. Biased number systems are sometimes used in floating point mathematics, which will be discussed in Chapter 5. Consider a biased 8-bit binary number system with a bias of · a What decimal value does the binary number represent? b What binary number represents the value 0? c What is the representation and value of the most negative number? d What is the representation and value of the most positive number? For example, is written as BCD.
a Write in BCD b Convert BCD to decimal c Convert BCD to binary d Explain why BCD might be a useful way to represent numbers Exercise 1. a Write in BCD b Convert BCD to decimal c Convert BCD to binary d Explain the disadvantages of BCD when compared to binary representations of numbers Exercise 1. If this equation is correct, how many fingers would you expect Martians to have? Hacker are having an argument. Hacker are having another argument. When the first 1 is found, invert each subsequent bit. The user should type in an unsigned binary number. The program should print the decimal equivalent. Support bases up to 16, using the letters of the alphabet for digits greater than 9. The user should enter b1, b2, and then the number to convert in base b1. The program should print the equivalent number in base b2. Complete a truth table for the three-input majority gate shown in Figure 1.
A B MAJ Y C Figure 1. Complete a truth table for the gate. Otherwise it produces a TRUE output. List each truth table. Give each one a short descriptive name such as OR, NAND, and so on. If so, what are the input and output low and high levels VIL, VOL, VIH, and VOH and noise margins NML and NMH? If not, explain why not. Vout 5 4 Figure 1. If so, what are the input and output low and high levels VIL,VOL,VIH, and VOH and noise margins NML and NMH? Will it work? Why or why not? He would like to advertise that it is compatible with LVCMOS and LVTTL logic.
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ABOUT THE BOOK Digital Design And Computer Architecture 2nd Edition PDF free download. Digital Design and Computer Architecture, Second Edition, takes a unique and modern Computer Systems Design and Architecture (2nd Edition) - Google Docs Computer Systems Design and Architecture (2nd Edition) The version of the browser you are using is no A tag already exists with the provided branch name. Many Git commands accept both tag and branch names, so creating this branch may cause unexpected behavior Vincent P. Heuring, Harry F. Jordan-Computer Systems Design and Architecture (Conservative)-Prentice Hall () Click the start the download DOWNLOAD PDF Report Computer Systems Design and Architecture Uploaded by sancristall Copyright: Attribution Non-Commercial (BY-NC) Available Formats Download as PDF or read online from Scribd Online Library Computer Systems Design And Architecture 2nd Edition Computer Architecture and Implementation reviews the state of the art in nanoelectronic device design ... read more
However, some errors undoubtedly do remain. Silicon Si is a group IV atom, so it has four electrons in its valence shell and forms bonds with four adjacent atoms, resulting in a crystalline lattice. Note that a 5 V logic family such as TTL or CMOS may produce an output voltage as HIGH as 5 V. The advantage of pseudo-nMOS logic is that it can be used to build fast NOR gates with many inputs. Thanks to the power of abstraction, your grandmother can surf the Web without any regard for the quantum vibrations of electrons or the organization of the memory in her computer. The truth table should have two inputs, A and B. The user should type in an unsigned binary number.
Therefore, digital circuits are a subset of analog circuits and in some sense must be capable of less than the broader class of analog circuits. Note that a 5 V logic family such as TTL or CMOS may produce an output voltage as HIGH as 5 V. Utku Diril Nvidia Corporation Digital Design and Computer Architecture Second Edition About the Authors David Money Harris is a professor of engineering at Harvey Mudd College. Show your work. Most digital systems today are designed with HDLs. Multicycle Processor.
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