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The digital system (also known as the binary system) is based on counting in 1's. Thus it has only two digits (known as "bits")  0 (zero) and 1 (one)  which are very easy to manipulate electronically. It only needs a simple onoff switch, for example, to count in this manner. The switch is either "off" (showing zero as far as the circuit is concerned) or "on" (representing a count of 1). It can continue to count in l's, or even multiply, divide, etc, in association with other simple types of switches. The fastaslight speed at which electronic devices can count makes the digital system very suitable for building computer circuits, particularly as only a few basic operations have to be performed. The fact that these operations, using simple logic circuits or gates in suitable combinations, may have to be repeated very many times is no problem either. The decimal system expresses a number in powers of 10. In other words individual digits, depending on their order represent the digit value x 10°, digit value x 10, digit value x 10^2, etc, reading from right to left. Putting this the correct way round, and taking an actual numbersay 124: 124 = 1 x 10^2 + 2 x 10^1 + 4 x 10^0 = 100 + 20 + 4 The binary system expresses a number in powers of 2 using only the two digits 1 and 0. Thus 1011 = 1 x 2^3 + 0 x 2^2 + 0 x 2^1 + 1 x 2°= 8 + 0 + 2 + 1= 11 Thus a binary number is longer, written down, than its corresponding decimal number, and can get very long indeed with large decimal numbers (e.g., 10,000 = 1010100010000) but this does not matter at all as far as electronics "counting" is concerned. It only makes it difficult for people to convert decimal numbers to binary numbers, and vice versa. Here are two basic rules. CONVERTING DECIMAL TO BINARY Write the decimal number on the righthand side, divide by two and write down the result, placing the remainder (0 or 1) underneath this number. Divide the number obtained in the top line by 2 and carry the remainder (0 or 1) down to make a next step to the left. Repeat this operation, progressing further to the left each time, until you are left with a 0 in the top line. For example, convert the decimal number 19 to binary. 19/2 = 9, remainder 1, 9/2 = 4, remainder 1 4/2 = 2, remainder 0 2/2 = 1, remainder 0 1/2 = 0, remainder 1 Written as described above, we have: decimal numbers: 0 1 2 4 9 19 remainders: 1 0 0 1 1 and the remainders put together gives us the number 19 converted to binary, 10011. CONVERTING BINARY TO DECIMAL Write down progressively from right to left as many powers of 2 as there are digits in the binary number. Write the binary num be underneath. Determine the powers of 2 in each column where a 1 appears under the heading and then add all these up. Example Binary number 10101, which has 5 digits, so write down five stages of powers of 2 starting with 2° and reading from right to left. Powers of two 2^4 2^3 2^2 2^1 2° Write down binary number 1 0 1 0 1 Convert to decimal 16 0 4 0 1 Add 16 + 4 + 1 = 21 LOGIC Logic systems also work on the binary number process, commonly based on the difference between two dc voltage levels. If the more positive voltage signifies 1, then the system employs positive logic. If the more negative voltage signifies 1, then the system employs negative logic. It should be noted that in both cases, al though the lower or higher voltage respectively signifies 0, this is not necessarily a zero voltage level, so the actual voltage values have no real significance. There is another system, known as pulselogic, where a "bit" is recognized by the presence or absence of a pulse (positive pulse in the case of a positivelogic system and negative pulse in the case of a negativelogic system). GATES Logic functions are performed by logic gates. The three basic logic functions are OR, AND, and NOT. All are designed to accept two or more input signals and have a single output lead. The presence of a signal is signaled by 1 and the absence of a signal by 0. The four possible states of an OR gate with two inputs (A and B) are shown in Fig. 1. There is an output signal whenever there is an input signal applied to input A OR input B (and also with in put at A and B simultaneously). This applies regardless of the actual number of inputs the gate is designed to accept. The behavior of an OR gate (again written for only two inputs) is expressed by the following truth table: A B output(Y) 0 0 0 0 1 1 1 0 1 1 1 1
It can also be expressed in terms of Boolean algebra, calling the output Y Y=A+B+...+N where N is the number of gates The important thing to remember is that in Boolean algebra the sign + does not mean "plus" but OR. The AND gate again has two or more inputs and one output, but this time the output is 1 only if all the inputs are also 1. The truth table in this case is quite differentFig. 2. The corresponding equation of an AND gate is: Y=AB...N or Y=AxB...xN This time the or x sign does not mean "multiplied by" as in conventional arithmetic, but AND.
The NOT gate has a single input and a single outputFig. 103, with output always opposite to the input, i.e., if A = 1, Y = 0 and if A = 0, Y = 1. In other words it inverts the sense of the output with respect to the input and is thus commonly called an inverter.
Its Boolean equation is: Y = (Y equals NOT A) Inverting the output of an AND gate gives us a NAND (Not AND) gate. A NAND gate is illustrated in Fig. 104. It is just the opposite of an AND gate. The output of a NAND gate is 0 if, and only if, both of the inputs are 1's.
Another variation on the OR gate is the XOR (eXclusive OR) gate, which is illustrated in Fig. 6. The output is a 1 when only one of the inputs is a 1. This gate could also be considered a logical difference detector. If the two inputs are equal, the output is 0. If the inputs are at different logic levels, the output will be a 1. Diodelogic (DL) circuits for an OR gate and an AND gate are shown in Fig. 7. Both are shown for negative logic and are identical except for the polarity of the diodes. In fact, a positivelogic DL or OR gate becomes a negativelogic AND gate; and a positivelogic AND gate a negativelogic OR gate.
The simple NOT gate or inverter shown in Fig. 108 is based on a transistor logican NPN transistor for positivelogic and a PNP transistor for negativelogic. The capacitor across the input resistance is added to improve the transient response.
PRACTICAL GATES Most logic gates are produced in the form of integrated circuits, from which various "family" names are derived. NAND and NOR gates, for example, are a combination of AND or, OR gates, respectively, with a NOT gate inverter. From the basic circuits just described, such functions can be performed by diodetransistor logic or DTL gates. Faster and better performance can be realized with transistortransistorlogic gates (TTL). During the early 1970's DTL and TTL represented the bulk of the IC digital productions, but since then various other IC families have appeared, each offering specific advantages and more functions for particular applications. These are: RTL (resistortransistor logic) which can be made very small even by microelectronic standardsand is capable of performing a large number of functions. DCTL (directcoupledtransistor logic), which employs the same type of circuit as RTL but with the base resistors omitted. This gate, which can perform NOR or NAND functions, has the advantage of needing only one low voltage supply and has lowpower classification. HTL (high threshold logic) is based on diodetransistor logic similar to DTL but also incorporates a zener diode to stabilize the circuit and provide high immunity to "noise." It is usually chosen for applications where this feature is important. MOS (metal oxide semiconductor logic), based entirely on field effect transistors (FETs) to the complete exclusion of diodes, resistors and capacitors, yielding NAND and NOR gates. CMOS (complementary metaloxidesemiconductor logic) using complementary enhancement devices on the same IC chip, reducing the power dissipation to very low levels. The basic CMOS circuit is a NOT gate (inverter), but more complicated NAND and NOR gates and also flipflops can be formed from combinations of smaller circuits (again in a single chip). ECL (emittercoupled logic) also known as CML (currentmode logic). This family is based on a differential amplifier which is basically an analog device. Nevertheless it has important application in digital logic and is the fastest of all the logic families with delay times as low as 1 nanosecond per gate.
GATE DEMONSTRATION CIRCUITS To give you a better understanding of how digital gates work, we will present several demonstration circuits built around the CD4011 quad NAND gate. Any digital gate can be constructed from NAND gates. In Fig. 9 we have the basic NAND circuit. The LED will be lit (logic 1) if one or both inputs (A or B) are grounded (logic 0). If both of the switches is moved to the + V line (logic 1), the LED will be dark (logic 0). By shorting the two inputs together into a single input line, as shown in Fig. 10 we have a simple inverter demonstrator. If the input is logic 1 (V + ), the output will be logic 0 (LED dark). If the input is logic 0 (ground), then the output will be logic 1 (LED lit). Inverting the output of a NAND gate produces an AND gate. This can be done with two NAND gate stages, as illustrated in Fig. 11. On the other hand, inverting the inputs of a NAND gate simulates an OR gate. A demonstration circuit for this is shown in Fig. 12. Simply adding a fourth stage (as an inverter) creates a NOR gate, as illustrated in Fig. 13. A number of nonstandard gating schemes can also be created. For example, the circuit shown in Fig. 1014 is a combined AND/OR gate. The output is a logic 1 if A and B are 1's or C and D are 1's. If all four inputs are l's, the output will also be a 1.
Fig. 12. This circuit demonstrates how an OR gate can be created from three NAND gates.
Digital gates can be used for more than simple logic switching applications. The circuit in Fig. 1015 is a simple low frequency square wave oscillator. When the input is a logic 1 (connected to V + ), the circuit will oscillate. The LED will blink on and off once or twice a second. A logic 0 at the input (grounded) disables the oscillator. Try different capacitor values to create other frequencies. If the frequency is too high, the eye will not be able to distinguish between the separate blinks. The LED will appear to stay continuously lit when the oscillator is enabled. Try routing the output to a small speaker when using a smaller capacitor. (A 0.1 µF capacitor would be a good choice.) You will hear a tone from the speaker when the oscillator is enabled. FLIPFLOPS A flipflop is a bistable circuit and another important element in digital logic. Since it is capable of storing one bit of information it is functionally a 1bit memory unit. Because this information is locked or "latched" in place, a flipflop is also known as a latch. A combination of n flipflops can thus store an nbit word, such a unit being referred to as a register. A basic flipflop circuit is formed by crosscoupling two NOT gates, the output of each gate being connected back to the input of the other gate. The NOT gates can be created from NAND gates as described earlier, and the final circuit will look like Fig. 16. However, to be able to preset or clear the state of the flipflop, two NAND gates are necessary, each preceded by a NOT gate, or a NAND gate with its inputs joined. See Fig. 17.
When the flipflop is used in a pulsed or clocked system the preceding gates are known as the steering gates with the crosscoupled twoinput gates forming the latch. This particular configuration is also known as a SR or RS flipflop. Two other variations of the flipflop are also produced as integrated circuits: PK flipflopwhich is an SR flipflop preceded by two AND gates. This configuration removes any ambiguity in the truth table. It can be used as a Ttype flipflop by connecting the J and K inputs together (see Fig. 18 for connections). Dtype flipflopwhich is a JK flipflop modified by the addition of an inverter (see Fig. 19). It functions as a 1bit delay device.
FLIPFLOP DEMONSTRATION CIRCUITS One of the most common applications for a flipflop is frequency division. The frequency at the output of a flipflop stage will be one half the frequency of a square wave input signal. Figure 1020 shows a simple demonstration circuit for this type of application. It consists of two stages. The first stage (IC1 and its associated components) is a simple 555 astable multivibrator (see Section 7). With the component values listed, it will produce a near square wave with a frequency of about 1 Hz. The second stage (IC2) is one half a dual D type flipflop IC (CD4013). The frequency is divided by two in this stage. LED1 will blink on and off approximately once a second, while LED2 (the output) will blink once every other time LED1 (the in put) blinks. Any number of flipflop stages can be strung together. By looking at each stage output, a binary counter can be created. A simple modulo8 counter circuit is shown in Fig. 21. This circuit will count from 0 (0000) to 8 (1000), then cycle back to 0 and start over. That is: 0001 0010 0011 0100 0101 0110 0111 1000 0000 0001 0010 … and so forth.
See Fig. 22. Here only one LED will be lit (logic 1) at any given moment. The circuit will step through the four outputs repeatedly, activating one at a time. This type of circuit is sometimes called a 1of4 sequencer. It can be extended to include as many output stages as desired. FANIN AND FANOUT The terms fanin and fanout are used with IC logic devices. Fanin refers to the number of separate inputs to a logic gate. Fanout is the number of circuit loads the output can accommodate, or in other words the number of separate outputs provided. Fanout is commonly 10, meaning that the output of the gate can be connected to 10 standard inputs on matching gates. Each separate in put represents a load, the higher the number of separate loads the higher the current output of the device providing fanout needs to be in order to provide the standard load on each input, i.e., passing enough current to drop each input voltage to the design figure. It is possible to increase fanout by replacing diode(s) with transistor(s) in the device concerned, so 10 is by no means a maximum number. ROM ROM stands for ReadOnlyMemory, a system capable of converting one code into another. The best known application is to convert the reading of a digital instrument such as an electronic calculator into a numerical readout via an LED (light emitting di ode) display. The advantage of a ROM is that it is programmable and thus adaptable to different readout systems. It does not follow, however, that it uses the minimum number of components to match a particular application. Special IC chips designed for a specific application may be more economic in this respect, but not necessarily in cost, unless there is a very large demand for that particular IC. The calculator market is a case in point where a special chip can offer advantages over a ROM. RAM RAM stands for RandomAccess Memory and is basically a collection of flipflops or similar devices capable of memorizing information in binary form. Information can be writtenin or read out in a random manner.
THE SHAPE OF DIGITAL ICs In physical appearance, most digital ICs look like any other dual inline (or sometimes quad inline) IC package, or ceramic flat pack ages. They are not readily identified as digital ICs, therefore, (except by type number) although their function is quite specific. The more complicated digital ICs may, however, have considerably more pins than usual. It is also common practice to give pin dia grams which not only define the pin positions but also their specific function (Fig. 23).

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