Chapter1 Digital Concepts

Analog & Digital Quantities

Analog Quantity

An analog quantity is one having continuous values (in time domain). And it takes on all the infinite values in between [a, b].

Sampled Value

Discrete in time domain
Continues values

Digital Quantity

Discrete in time domain
Discrete values

Basic Concepts about Digital Circuit

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.
In digital circuits, two different voltage levels are used to represent the two bits. The higher/lower voltage level is referred to as a HIGH/LOW, or H/L.
- HIGH = 1
- LOW = 0
Groups of bits, called codes, are used to represent numbers, letters, symbols, instructions, and anything else required in a given application.

Logic Levels

The voltages used to represent a 1 and a 0 are called logic levels.
Ideally, one voltage level represents a HIGH and another voltage level represents a LOW.
In a practical digital circuit, a HIGH can be any voltage between a specified minimum value and a specified maximum value. Likewise, a LOW can be any voltage between a specified minimum and a specified maximum

Digital Waveforms

Digital waveforms consists of voltage levels that are changing back and forth between the HIGH and LOW levels or states.

A single positive-going pulse is generated when the voltage goes from its normally LOW level to its HIGH level and then back to its LOW level.
Notice the definition of Rising edge (上升沿) and Falling edge (下降沿) in the picture

Amplitude ( $V_m$ ): Height from baseline.
Rise time ( $t_r$ ): The time for a pulse to go from 10% to 90% of the pulse amplitude
Fall time ( $t_f$ ): The time for a pulse to go from 90% to 10% of the pulse amplitude
Pulse width ( $t_w$ ): A measure of the duration of the pulse and is often defined as the time interval between the 50% points on the rising and falling edges.

Periodic Pulse

A periodic 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). The relationship between f and T is expressed as follows:

Period: $T_1 = T_2 = T_3 = T_n$
Frequency: $f = \frac{1}{T}$

The duty cycle (占空比) is defined as the ratio of the pulse width ( $t_w$ ) to the period (T) and can be expressed as a percentage.

Duty Cycle: $q = \left(\frac{t_w}{T}\right) \times 100 \%$

Timing Diagram

A timing diagram is a graph of digital waveforms showing the actual time relationship of two or more waveforms and how each waveform changes in relation to the others.

Data Transfer

Parallel Transfer: When bits are transferred in serial form from one point to another, they are sent one bit at a time along a single conductor. To transfer n bits in series, it takes n time intervals.
Serial Transfer: When bits are transferred in serial form from one point to another, they are sent one bit at a time along a single conductor. To transfer n bits in series, it takes n time intervals.

Basic Logic Operations

The term logic is applied to digital circuits used to implement logic functions. Several kinds of digital logic circuits are the basic elements that form the building blocks for such complex digital systems as the computer.
In Boolean algebra, there are three basic logic operations: NOT, AND, and OR.
The standard distinctive shape symbols for the three basic logic operations are shown below.

A circuit that performs a specified basic logic operation is called a logic gate.
The true/false statements mentioned earlier are represented by a HIGH (true) and a LOW (false).
AND and OR gates can have any number of inputs.
Each of the three basic logic operations produces a unique response (output) to a given set of conditions (inputs).