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Digital Circuit I (EEI 101) Ch1 Introduction Electronic circuits can be divided into two broad categories, digital and analog. Digital electronics involves quantities with discrete values, and analog electronics involves quantities with continuous values. An example of both analog and digital representation of a signal is illustrated below: Analog (real) signal digital (Sampled) signal Most systems applications require both digital and analog electronics, thus the interfacing between them is important. An Analog Electronic System A public address system, used to amplify sound so that it can be heard by a large audience is one simple example of an application of analog electronics. The basic diagram is shown below: Dr. Fawzy Hashem Page 1 Digital Circuit I (EEI 101) Sound waves, which are analog in nature, are picked up by a microphone and converted to a small analog voltage called the audio signal. This voltage varies continuously as the volume and/or frequency of the sound changes and is applied to the input of a linear amplifier. The output of the amplifier, which is an increased reproduction of input voltage, goes to the speakers. The speaker changes the amplified audio signal back to sound waves that have a much greater volume than the original sound waves picked up by the microphone. System Using Digital and Analog Methods The compact disk (CD) player is an example of a system in which both digital and analog circuits are used. The simplified block diagram is shown below: Music in digital forms is stored on the compact disk. A laser diode optical system picks up the digital data from the rotating disk and transfers it to the digital-toanalog converter (DAC). The DAC changes the digital data into an analog signal Dr. Fawzy Hashem Page 2 Digital Circuit I (EEI 101) that is an electrical reproduction of the original music. This signal is amplified and sent to the speakers for you to enjoy. When the music was originally recorded on the CD, a process, essentially the reverse of the one described here, using an analog-to-digital converter (ADC) was used. Binary Digits Each of the two digits in the binary system, 1 and 0, is called a bit, which is a contraction of the words binary digit. Groups of bits (combinations of 1s and 0s), called codes, are used to represent numbers, letters, symbols, instructions, and any thing else required in a given application. Logic Levels The voltage used to represent a 1 and a 0 are called logic levels. Generally a 1 is represented by higher voltage, which we will refer to as a HIGH, and a 0 is represented by lower voltage, which we will refer to as a LOW. In practical digital circuits, however, a HIGH and a LOW can be any voltage between a specified minimum value and a specified maximum value. The figure below illustrates the general range of LOW, and HIGH for a digital circuit: Dr. Fawzy Hashem Page 3 Digital Circuit I (EEI 101) The voltage values between VL(max) and VH(min) are unacceptable for proper operation. For example, the HIGH input values for a certain type of digital circuit technology called CMOS may range from 2 V to 3.3 V, and the LOW input values may range from 0 V to 0.8 V. If a voltage of 2.5 V is applied, the circuit will accept it as a HIGH or binary 1. If a voltage of 0.5 V is applied, the circuit will accept it as LOW or binary 0. For this type of circuit, voltages between 0.8 V and 2 V can appear as either a HIGH or LOW which is unacceptable. Digital Waveforms Most waveforms encountered in digital systems are composed of series of pulses, sometimes called pulse trains, and can be classified as either periodic or nonperiodic. A periodic pulse waveform is one that repeats itself at a fixed interval, called a period (T). The frequency (f) is the rate at which it repeats itself and is measured in hertz (Hz). A non-periodic pulse waveform, of course, does not repeat itself at fixed intervals and may be composed of pulses of randomly differing pulse widths and/or randomly differing time intervals between pulses. An example of each type is shown below: The frequency (f) of a pulse (digital) waveforms is the reciprocal of the period (T), thus: f = 1 / T and T = 1/ f. Dr. Fawzy Hashem Page 4 Digital Circuit I (EEI 101) An important characteristic of a periodic digital waveform is its duty cycle, which is the ratio of the pulse width (tw) to the period (T). It can be represented as a percentage: Duty cycle = (tw / T) 100%. Ideal and Practical Pulse Shapes As indicated below a pulse has two edges: a leading (rising) edge that goes from LOW to HIGE, and the trailing (falling) edge that goes from HIGH to LOW. Notice that the pulses are ideal because the rising and falling edges are assumed to change in zero time (instantaneously). In practice, these transitions never occur instantaneously in practice as shown below: Notice that: The rise time (tr) is the time required for a pulse to go from LOW level (10 % of the amplitude) to the HIGH level (90 % of the amplitude). The falling time (tf) is the time required for the transition from HIGH level (90 % of the amplitude) to the LOW level (10 % of the amplitude). Dr. Fawzy Hashem Page 5 Digital Circuit I (EEI 101) The pulse width (tw) is the measure of the duration of the pulse between the 50 % points on the rising and falling edges. The overshoot and undershoot are the produced by stray capacitance and inductive effects. Serial and Parallel Transfer of Binary Data Data refer to a group of bits that convey some type of information. In computer system, binary data are transferred in two ways: serial and parallel as shown below: When bits are transferred in serial form, they are sent one bit at a time along a single line. Thus to transfer eight bits in series, it takes eight time intervals. When bits are transferred in parallel form, all bits in a group are sent out on separate lines at the same time. There is one line for each bit, thus it takes one time interval to transfer the eight. Basic Logic Operations In the 1850s, the Irish mathematician Georg Boole developed a mathematical system for formulating logic statements with symbols so that problems can be written and solved in a manner similar to ordinary algebra. Boolean algebra, as it known today, is applied in the design and analysis of digital systems. Dr. Fawzy Hashem Page 6 Digital Circuit I (EEI 101) Basic Logic Gates Tree basic logic operations (NOT, AND, and OR) are indicated by standard distinctive shape symbols as follows: The NOT gate function The output of NOT gate indicates the opposite condition of its input The AND gate function The output of AND gate is True only if all input conditions are true. The OR gate function The output of OR gate is True only if one or more input conditions are true. Dr. Fawzy Hashem Page 7 Digital Circuit I (EEI 101) System Concept The three basic logic gates AND, OR, and NOT can be combined to form various types of logic functions such as: comparison, arithmetic, code conversion, encoding, data selection, counting, and storage. The comparison function A magnitude comparator compares two quantities and indicates whether or not they are equal in magnitude. One number in binary form is applies to input A, and the other in the same form number is applied to input B. The outputs indicate the relationship of the two numbers by producing a HIGH level on the proper output line, as shown below: Basic arithmetic functions An adder adds two binary numbers (on inputs A and B with a carry input Cin) and generates a sum (∑) and a carry output (Cout), as illustrated below: Dr. Fawzy Hashem Page 8 Digital Circuit I (EEI 101) The encoding function The encoder converts information, such as decimal number or an alphabetic character, into some coded form. For example, one certain type of encoder converts each of the decimal digits, 0 through 9, to a binary code as indicated below: The decoding function The decoder converts coded information, such as binary number, into non-coded form, such as a decimal form. For example, when a particular binary code appears on the decoder inputs, the appropriate output lines are activated and light the proper segments to display the corresponding decimal digit, as show below: The data selection function Two types of circuit that select data are the multiplexer (mux) and the demultiplexer (demux). The mux is a logic circuit that switches digital data from several input lines onto a single output line in a specified time sequence. Dr. Fawzy Hashem Page 9 Digital Circuit I (EEI 101) The demux is a logic circuit that switches digital data from one input line to several output lines in a specified time sequence. Essentially, the demux is a mux in reverse, as illustrated below: Integrated Circuits All the logic elements and functions that have been introduced are generally available in integrated circuit (IC) form. Digital systems have incorporated ICs for many years because of their small size, high reliability, low cost, and low power consumption. A cutaway view of one type IC package with the circuit chip shown within the package is illustrated below: Dr. Fawzy Hashem Page 10 Digital Circuit I (EEI 101) IC Packages IC packages are classified according to the way they are mounted on printed circuit board (PCB), as either through-hole mounted or surface mounted. The most common type of through-hole package is the dual in-line package (DIP), shown in figure (a) below: Another type of IC packages uses surface-mount technology (SMT). The pins of SMT packages are soldered directly to conductors on one side of the board, leaving the other side free for additional circuits. An example of a SMT package is the small-outline integrated circuit (SOIC), shown in figure (b). Complexity Classifications of ICs Digital ICs are classified according to their complexity, as follows: Small-scale integration (SSI), compromises up to 10 equivalent gate circuits on a single chip. Medium-scale integration (MSI), compromises from more than 10 to 100 equivalent gate circuits on a single chip. Large-scale integration (LSI), compromises from more than 100 to 10,000 equivalent gate circuits on a single chip. Very large-scale integration (VLSI), compromises from more than 10,000 to 100,000 equivalent gate circuits on a single chip. Ultra large-scale integration (ULSI), compromises more than 100,000 equivalent gate circuits on a single chip. Dr. Fawzy Hashem Page 11