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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:
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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
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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:
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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.
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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).
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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.
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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.
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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:
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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.
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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:
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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.
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