[Hardware Design] Basics of Digital Circuits--Concepts, Classifications and Basic Operations
Preface: Chapters are for simple review of knowledge. Those who want to pass the exam can go to station B to read the special content explanation.
1. Basic concepts of digital circuits
Analog and Digital Signals
- Analog signal: A signal that is continuous in time and has continuous values. Such as speed, pressure, temperature, etc.
- Digital signal: Discrete both in time and in value. Such as the second signal of the electronic watch, the counting signal of the number of parts recorded on the production line, etc.
Digital circuit logic system
A digital signal is one 二值信号that uses two levels ( 高电平and ) to represent two logic values ( and ) 低电平respectively . There are two logical regimes:逻辑1逻辑0
- The positive logic system stipulates that a high level is a logic 1 and a low level is a logic 0.
- The negative logic system stipulates that a low level is a logic 1 and a high level is a logic 0.
The main parameters
2. Classification of digital circuits (understanding)
- Classified by integration: digital circuits can be divided into small-scale (SSI, tens of devices per chip), medium-scale (MSI, hundreds of devices per chip), large-scale (LSI, thousands of devices per chip) and very large-scale (VLSI , the number of devices per chip is greater than 10,000) digital integrated circuits. From the perspective of application, integrated circuits can be divided into two types: general-purpose and special-purpose.
- According to the different manufacturing processes of the devices used: digital circuits can be divided into two types: bipolar (TTL type) and unipolar (MOS type).
- According to the structure and working principle of the circuit, digital circuits can be divided into two types: combinational logic circuits and sequential logic circuits. The combinational logic circuit has no memory function, and its output signal is only related to the input signal at that time, but has nothing to do with the previous state of the circuit. Sequential logic circuit has a memory function, and its output signal is not only related to the input signal at that time, but also related to the previous state of the circuit.
Three, number system
进位制: When expressing a number, it is often not enough to use only one digit, and it is necessary to use the method of carry counting to form a multi-digit number. The composition of each digit of a multi-digit number and the carry rule from low to high are called the carry counting system, referred to as the carry system.基数: The base of the base system is the number of digits that may be used in the base system.位权（位的权数）: In a number in a certain base system, the size of each bit corresponds to the number on that bit multiplied by a fixed number, and this fixed number is the weight of this bit.weight is a power。
Several common counting systems:
- Decimal (Decimal)
- Binary
- Octal (Octal)
- Hexadecimal
Conversion between different number systems
Convert binary to decimal
Problem: Convert the binary number 10011.101 to a decimal number.
Solution: Multiply each binary number by the bit weight, and then add them up to get 10011.101=1×2 4 + 0×2 3 +0×2 2 +1×2 1 +1×2 0 +1×2 -1 + 0×2-2 + 1×2-3 = (19.625)d
Decimal to Binary
Problem: Convert the decimal number 23 to a binary number. Solution: Convert (23)D=(10111)B
with the method of "dividing by 2 and taking the remainder"
Conversion between binary and hexadecimal
(1101 1011) B=(db)H
Note: Four binary numbers represent a hexadecimal number
Base Correspondence Table
BCD code
The BCD code uses binary code to represent ten numbers from 0 to 9 in decimal system.
Use at least 4 binary digits.
4. Diode and tertiary tubes in digital circuits
4.1 Diode
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Static characteristics of diodes
(1) When the forward voltage is applied, the diode conducts, and the tube voltage drop voltage can be ignored. A diode acts as a closed switch.
(2 When the reverse voltage is applied, the diode is cut off, and the reverse current is negligible. The diode is equivalent to an open switch.
Dynamic Characteristics of Diodes
When a square wave signal is given to the diode, the waveform is as follows:
The reverse recovery time is the time required for the stored charge to dissipate, that is, the time required to change from a negative level to a positive level.
4.2 Triode
Three working states of the triode:
cut-off area
When V I is less than the dead-zone voltage of the emitter junction of the triode, I B = I CB is approximately equal to 0, I C = I CE is approximately equal to 0, V CE is approximately equal to V CC , and the triode works in the cut-off region, corresponding to point A in the figure.
The conditions for the triode to work in the cut-off state are:The emitter junction is reverse biased or less than the dead zone voltage
Amplified area
When VI is positive and greater than the dead zone voltage, the transistor is turned on. Yes
At this point, if you adjust R B ↓, then I B ↑, I C , V CE ↓, the working point moves upward along the load line from point A → point B → point C → point D. During this period, the triode works in the amplification area,
Its characteristic is I C =β I B .
The conditions for the triode to work in the amplified state are:The emitter junction is forward biased and the collector junction is reverse biased
Saturation zone
Saturation state: V I remains unchanged, and R b continues to decrease . When V CE =0.7V, the collector junction becomes zero-biased, which is called critical saturation state, corresponding to point E. At this time, the collector current is represented by I CS , and the base current is represented by I BS , as follows:
If R b is further reduced , I B will continue to increase, but I C will not increase any more, and the triode will enter a saturated state. The V CE voltage at saturation is called the saturation voltage drop V CES , and its typical value is: V CES is approximately equal to 0.3V.
The current condition for the triode to work in saturation is: I B > I BS
The voltage conditions are:Both collector and emitter junctions are forward biased
5. Logical operations
5.1 Logical AND
The equivalent circuit is as follows:
Suppose the switch is closed = "1", the switch is not closed = "0", the light is on, L=1, the light is not on, L=0.
The following figure can be formed:
converted into a truth table:
thereforelogic andThe logic is:
only when all the conditions of a thing are met, this thing will happen.
5.2 Logical OR
The equivalent circuit is as follows:
the event table and the truth table are obtained as follows:
when one or more conditions are met among the several conditions for determining one thing, this thing will happen.
5.3 non
The equivalent circuit is as follows:
the event table and the truth table are obtained as:
Whether or not something happens depends only on one condition, and it is the negation of that condition. That is, things do not happen when the conditions are met; things happen when the conditions are not met.
5.4 Logical circuits
and non
or non-
exclusive or
same-or
5.5 Basic formula
5.6 Basic Rules
Substitution rules
For any equation containing a certain variable, if all occurrences of this variable in the equation are replaced by a logic function, the equation is still valid.
2. Inversion rules
For any logical function F, do the following:
- If the operator "·" in the formula is replaced with "+", "+" is replaced with "·"
- The constant "0" is replaced with "1", and "1" is replaced with "0";
- The original variable is replaced by the opposite variable, and the opposite variable is replaced by the original variable
3. Duality rule
- If the operator "·" in the formula is replaced with "+", "+" is replaced with "·";
- The constant "0" is replaced with "1", and "1" is replaced with "0"
- The new functional formula is obtained as the dual formula F' of the original functional formula F.
- If two functional forms are equal, their corresponding dual forms are also equal. That is, if F1=F2, then F1'=F2'.
5.7 Expressions of Logical Functions
Definition : The logical relationship between the input logical variable and the output logical variable.
Features : Input variables and output variables only have two values of logic 0 and logic 1.
Representation method :
Truth table:
Logical expression:
Logic Diagram:
Timing Diagram:
Mutual conversion of logic functions
Truth table→expression→logic diagram
Logic diagram→expression→truth table
