This is interesting - Circuit design.

           +---------------------------------------+
           |     Theory of electrical circuitry.    |
           +---------------------------------------+

   The purpose of this opus is that I want to share my
 our knowledge and experience in the field of electronics. I hope you read
 The reader will understand everything that will be written and drawn below.
 I will try to describe everything as simply and clearly as possible.        
   I will devote most of the article to digital electronics, but without
 analogue is indispensable, so the latter will also be given attention
 attention. I’ll probably start from the very beginning, since I also dis-
 I can read it for an unprepared reader, but for some it hurts
 familiar, then you can safely press the 'Page Down' button to quickly
 scroll through the 'uninteresting' pages.  I guess I'll end here
 simply translate the editor’s already small memory and re-
 raid directly to the purpose of writing the article.                 
                                          
                                          
     Basic logical elements and synthesis of the simplest combinations
 tion devices.                                             
                                          
   Logic element "N".                                      
 This element implements the logical multiplication function (Conjunction)кция).                                                         
              
              
              
              
              
              
              
              
                                          
   Broken squirrel "NЛN"                                    
 Pages Businesses Media/News Company Movie/Television
 кция).                                                         
               
               
               
               
               
               
               
               
 Logical element "NOT".                                     
 This element implements the logical negation function.          
                   
                   
                   
                   
                   
                   
 All these elements are the main logical basis or basis
 a new functionally complete system of elements.  Based on these
 elements, you can create a circuit that implements any logical
 what function. Simply put, based on the combination of these elements
 You can create any logical device.                     
   The figures shown above show the symbols
 logical elements - "N", "NЛN", "NOT".  Next, for each log-
 of the real element is shown, as is commonly called, the table of truth
 ity, as well as the logical function of each of the elements.  Table-
 The truth value shows the output state for each of
 all possible combinations of states at the inputs of the logical element
 ment (or logical device).                                          
                                          
           Fundamentals and theorems of the algebra of logic.         
                                          
   The principle of duality.                                      
 ----------------                         
   Let's write down the rule for performing the operations "NLN" and "N" by placing
 lines "N" in reverse order.                                
                                          
                       
                         
                         
                         
                         
                         
                                          
   Comparing the operations line by line, you can see that if you change
 all zeros are ones and ones are zeros, and operations are addition
 swap places with multiplication operations, then the rule changes -
 in some places. This is the principle of duality, which
 which can be written in general form as:                           
       _____ _ _ A v B = A ^ B                                            
                                          
   To transform formulas, logic algebras are used, as well as
 in ordinary algebra, brackets.  If there are no parentheses, then first do
 a logical description is carried out over the individual elements, then
 logical multiplication and logical addition. However, if the sign
 version is above the whole expression, then the inversion is performed in
                last thing.                              
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                       Теоремы для одной перенной.            
                              _                                 
   1. A v 0 = A 4. A v A = 1 7. A ^ A = A         
                                                  _             
   2. A v 1 = 1 5. A^0 = 0 8. A^A =         
                                              =                 
   3. A v A = A б. A^1 = A 9. A = A             
                                          
                                          
                   Теоремы для двух более перенных.         
                                          
 10. а) A v В = В v A б) A ^ В = В ^ A                     
                                          
 11. A^В^C = A^(В^C) = (A^В)^C 12. a) A^(B v C) = A^B v A^C b) A v B^C = (A v B)^(A v C)  
                                          
 13. a) A v A^B = A b) A ^ (A v B) = A                     
             _ _                          
 14. a) (A v B) ^ B = A ^ B b) A^B v B = A v B              
              _ _                        
 15. a) A^B v A^B = B b) (A v B)^(A v B) = B               
        _____ _ _ _____ _ _                     
 1b. a) A v B = A ^ B b) A ^ B = A v B                     
                                          
   Each specific combination of elements is called a set. If
 If there are n elements, then there are 2 to the power of n sets.  If
 it is known what values the function takes on all sets it
 is called completely defined if on some tuples
 the value of the function is unknown, it is called underdetermined
 or partially defined, and the combination of elements on which
 a function that is not defined is called a forbidden set.  Meaning
 functions on forbidden sets can be specified at your discretion
 rhenium, i.e. by redefining the function.                               
                                          
 +---------+-----------+-----------+            
 |   | A B C | F F' F"| +---+-----------+-----------+            
 | 0 | 0 0 0 | 0 - 0 |            
 | 1 | 0 0 1 | 0 0 0 |            
 | 2 | 0 1 0 | 0 0 0 |            
 | 3 | 0 1 1 | 1 1 0 |            
 | 4 | 1 0 0 | 0 0 0 |            
 | 5 | 1 0 1 | 1 1 0 |            
 | 6 | 1 1 0 | 1 1 0 |            
 | 7 | 1 1 1 | 1 - 1 |            
 +---------+-----------+-----------+            
     F is a fully defined set.                          
   The 3-argument function takes the value "1"                
   if any two elements or all 3 are equal to "1".                 
     F' is an underdetermined function.                              
   The 3-argument function takes the value "1"                
   if any 2 arguments are equal to "1" and takes the value            
   value "0" in all other cases except cases            
   equivalence of all 3 arguments.                          
     Sets 0 and 7 are prohibited sets.                         
                                          
   To consider the minimization of a function, we introduce the following definitions:  
 divisions:                                                       
 1. The constituent of a unit is a function of n arguments, which  
 which takes the value "1" only on one set.           
   2. Constituent of zerois a function with n arguments that 
 takes the value "0" on only one set.                 
                                          
   The perfect disjunctive normal form of a function is called
 disjunction of constituents equal to "1" on the same sets as for-
 this function.  The transition from the table to this form is carried out
 as follows:                                             
             for each set on which the function is equal to "1" for-
             elementary works of all arguments are written
             tov, and if the value of the argument is "0", then be-
             root its negation, then produce a logical word
             the production of these works.                           










                                          
   Minimization is performed using algebra theoremslogic.
 The most effective techniques are to bracket out the
 members, the use of double negation, the principle of duality
 ity, laws of absorption and gluing (formulas - 13, 14,15).
 Along with complete gluing, incomplete gluing is often used.
 when one or both members involved in this operation are
 are hiding.                                                        






















                                          
   To record the functions of logical devices you can use,
 also the perfect conjunctive normal form of the function. When- 
 the move to it from the table occurs as follows:            
                                          
             for those sets for which the function is equal to zero co- 
             put the elementary logical sum of all elements 
             ntov, and if the argument in the set has a value
             "1", then its negation is written, then these logical
             Calcical sums are combined by the operation of multiplication.     
                                     _ _ _          
       F(ABC) = (A v B v C)^(A v B v C)^(A v B v C)^(A v B v C) 
                                          
 Then you can minimize it.                                  
                                          
                                          
                                          
   The underlying logical basis is not minimal because 
 logical element "N" or logical element "NLN" can be expressed
 pass through two other logical functions._____ _____                  
                 _ _ _ _                  
         A ^ B = A v B A v B = A ^ B                  
                                          
   There are bases and the corresponding logical elements of the
 holding only one function: “N-NOT” and “NLN-NOT”. The basis is based
 based on the logical element "N-NOT" It is called the Schaeffer basis.  
                                          





















                                          
                                          
                                          
   Кроме базиса "N-НЕ" используется базис "NЛN-НЕ",  который на-
 зывается базисом Пирса.                                        
                                          















When minimizing logical functions, they often use
 called "Carnot maps".  Carnot map - broken rectangle
 into squares, the number of which is equal to the number of sets of the considered
 functions. The cells are placed so that the sets for which it is possible
 Our adjacent constituents ended up in neighboring cells.  When
 When completing the Karnaugh map, enter the value of the function in the cell for
 of the corresponding set. Usually only cells containing
 pressing unit.                                                 





























                                          
                                          
   Карта Карно для функции F'будет выглядеть следующим образом: 
                                          

















                                          
   Underspecification of a function means that forbidden sets
 will never appear during operation of the device, following
 It is true that if we define this function either by zero or by one
 face, this will not affect the operation of the device in any way, therefore
 in Carnaugh maps, units are placed in the corresponding sets
 only in those cells that facilitate the union of units.     











                                          
   When minimizing, it is necessary to remember that Carnaugh maps are
 cyclic (see last example).                           
   You can combine not only in pairs, but also in 4.8, i.e. 2 in
 degree n.                                                     
                                          



























                                          
                                          
                                          
                                          
                 Виды кодирования двоичных цифр.                
                                          
   По виду кодирования двоичных электрическими на
 входах выххтото“​​​​” делятся на
 Black and white.  В потенциальных нулю и
 Be the first to receive a cover in the picture-
 So, snowflake ("1") and snowflake ("0") pages:         
                                          
                  
                  
                  
                  
                  
                  
                  
                                          
   В импульсных элементах возможны следующие варианты  кодирова-
 ния:                                                           
                                          
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
                                          
   In addition, there are elements that react to a front or a recession
 impulse.                                                      
   Information entering a particular digital device
 represents a discrete code (from "0" and "1").  On transfer
 signal is allocated a finite period of time, which is called
 tact. In the case of serial data transmission in 1 clock cycle
 1 digit of the number is given, in the case of parallel - the entire number is sequential
 face.                                                         
   In general, the input of the device receives a set of binary
 variables X, and a set of binary variables is removed from the output
 variable Y. The device carries out a certain logical function
 tion between input and output variables.                   
   Devices are divided into combinational and sequential.
 In combinational devices, the Y value during each cycle
 It is determined by the value of X only in the same clock cycle.  In subsequent
 In relativity devices, the value of Y determines the value of X as
 during the considered cycle, and the values of the existing
 shih in a number of previous measures, i.e. these devices include
 dyat memory elements.Typical components of digital devices.       
                                          
 I). Triggers are the simplest, elementary, finite  
     automata with memory. In more complex devices   
     They are used to store one bit of binary     
     numbers.                                                     
                                          
          Triggers are characterized by the following properties:       
     1). The number of possible internal states is 2 (0 or 1),    
         which corresponds to the internal variable Q.             
     2). Number of output variables - 1, output variable     
         matches the Q value.                              
     3). The number of input variables depends on the type of trigger.     
                                          
                                          
   In addition to the output Q, called direct, the trigger has an inverse
       _                                                        
 output Q, but the state of the flip-flop is determined by the state of the direct
                                          
 exit.  Change in trigger state under the influence of input
                                          
 signalshappens spasmodically. Triggers can be implemented
                                          
 baths on transistors, universal logic elements and
                                          
 integral design.                                       
                                          
                                          
   According to their functionality, triggers are divided into 4 main ones:   
   type:                                                        
     1). Triggers with two setting inputs, RS - triggers. 
     2). Delay flip-flops with one input, D - flip-flops.        
     3). Flip-flops with one counting input, T - flip-flops.         
     4). Universal with multiple inputs.                   
                                          
 In addition, triggers can be synchronous or asynchronous. B
 in asynchronous flip-flops, a change in the output signal occurs
 directly with the arrival of input signals. In synchronous trig-
 gerah only when a synchronizing pulse is applied to the input.    
                                          
                       This figure shows a conditional
                     designation of a synchronous RS flip-flop.       
                               
                               
                               
                               
                               
 Inputs that control voltage levels are called static
 mi, and the inputs that control level differences are dynamic.     
   Dynamic inputs are indicated by triangles if the vertex
 triangle is directed inward (>) of the trigger, then it is triggered
 occurs when the input signal changes from “0” to “1”, if the vertex
 no outward ( < ), then - from “1” to “0”.                           
   In addition to marking dynamic inputs with a triangle, it is permissible
 There is another form of notation that is more convenient for drawing
 reading circuits using a computer:                               
                                          
                                          
  
  
  
  
  
                                          
   This figure shows the conditionaldesignations            
 T- and D-triggers.                                             
                                          
#############################################################
                                          
   That's all for now, the continuation will be published next
 issue of the magazine where I plan to describe each trigger
 in more detail, as well as talk about counters, registers and
 adders.                                                    
                                          
 R. S. I express my deep gratitude to Steel Drugon/HWC and       
  Mongol/LGC for assistance in restoration         
  of this article and other materials that were          
  are lost in the inter-disk space of the CP/M format.       
                                          
                                          
 (c) Melted Snov, 11/15/1999