Digital logic and digital system personal notes (exam review)

Chapter One Number System and Symbology

1. Digital and analog
analog signal: a continuous signal in time and value.
Digital signal: discrete
digital system advantages:
1. Communication: strong anti-interference ability, good confidentiality
2. Audio, TV: good fidelity, easy to store
3. Instrument: high precision, strong function, easy to automate, intelligent, Reliability: Small size
4. High integration; device size is getting smaller and smaller.
Binary conversion to octal system looks at three digits.
Binary to hexadecimal system looks at four digits.
* Cyclic code is a typical Gray code
feature: adjacent, cyclic, Reflective
8421 code: expressed by a four-digit binary number, the
remaining three codes differ from the 8421 code by three

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Example:
Decimal (380) = 8421BCD (0011 1000 0000)
(0001) 8421BCD + (1001) 8421BCD = (0001 0000) 8421BCD
(add 6 to modify 0110) In the same way, subtract 0110

Chapter 2 Fundamentals of Logical Algebra

1. Logic function
Representation method: truth table, logic function formula, logic diagram, waveform diagram
and NOR non-
exclusive OR: same as zero
Same or: same as 1

Methods of simplification of logical functions

• ** Formula simplification method **
  1. Coordination method: A+non-A=1
  2. Absorption method: A+AB=A, A+non(A) B=A+B (emphasis)
  3. Coordination method: A= A(B+non-B)
  4. Eliminate redundant items: AB+non(A) C+BC=AB+non-AC (emphasis)
  standard expression
• Minimum term: In the logic function of n variables, including the product term of all n variables (each variable must and can only appear in the form of original variable or inverse variable once) n variables have 2^n minimum terms (abc )=111
• Maximum term: In the logic function of n variables, the sum term of all n variables is included (each variable must and can only appear once in the form of the original variable or the inverse variable) abc=000
• The nature of the minimum term:
  1·n variable function has 2^n minimum or maximum terms.
  2. For the minimum term, there is only a combination of values ​​of a set of variables, so that its value is one, and the rest are all 0.
  3·All minimum terms The sum is-
  4. The product of any two smallest terms is always equal to zero.
  5. The product of any smallest term and another smallest term is always equal to the smallest term.
• The properties of the largest term:
  1. For any largest term, there is only a combination of values ​​of a set of variables, so that its value is 0
  2. The product of all the largest terms is equal to 0
  3. The sum of any two largest terms is always equal to 1.
  4. The sum of any largest term and another largest term is always equal to the largest term.
  The largest item and the smallest item with the same P number are opposite to each other
  
• Carrot diagram simplification
• The composition of Karuotu: Let the smallest items in the truth table of the logic function be rearranged into a matrix form, and the values ​​of the logic variables in the horizontal and vertical directions of the matrix are arranged in the order of Gray code, so that the formed image is a card. If the picture.
• Properties:
  1. Any two adjacent minimum items of standard position 1 can be combined into one item, and one variable can be eliminated (eliminate the factors that are opposite to each other, and keep the common factor)
  2. The number of adjacent minimum items must be 2 ^i can be combined into one item, and i variables can be eliminated. The greater the number of minimum items included, that is, the larger the circle formed by these minimum items, the more variables are eliminated, and the simpler the resulting logical expression. This is the basic principle of using Karnaugh map to simplify logic functions.
• The main items with substantive small items are necessary items, and the ones that are not redundant items (all ones are necessary)

Chapter 3 Integrated Logic Gate Circuit

• Digital integrated circuits are classified according to the degree of integration:
  IC: The components are made on the same silicon chip, and some functions of the circuit have been realized.
  SSI: <=10 gate circuits
  MSI: 10-100
  LSI: 1000-10000
  VLSI:>=10000
• According to the manufacturing process:
  bipolar type: TTL triode-triode logic. ECL emitter coupled logic. I^2L integrated injection logic
  MOS type: PMOS, P-channel metal oxide semiconductor field effect transistor. NMOS: N-channel MOS tube. CMOS: Complementary MOS logic
  Bi-CMOS type: Bipolar CMOS
• Diode: The reverse recovery time of the diode limits the switching rate of the diode.
• Triode: cut off, amplify, saturate.
• The switching characteristics of the field effect tube: cut off, on.
• MOS tube: variable resistance area, cut-off area, constant current area
  

TTl gate circuit

• Integrated circuit advantages: small size, light weight, high reliability, low power consumption
• TTL: Triode-Triode logic
• TTL gate circuit: The input stage is composed of multi-emitter transistor T1, diodes D1, D2 and resistor R1. Realize the AND operation of input variables A and B
• The input terminals are all connected to high level, and the output is low level.
• When at least one input terminal is connected to low level, the output is high level
• The relationship between output and input satisfies the NAND relationship: F=(A*B) non
• Input current calculation: IIL is the same as only one grounding time after parallel connection, IIH: each value is the same, doubled after parallel connection