# Algorithmic Method for the Design of Sequential Circuits with the Use of Logic Elements
## 2 Algorithmic Method of Sequential Circuit Design  
The algorithmic method is used, among others, for systems with actuators cooperating with distributors controlled pneumatically, hydraulically or electrically on both sides. A separate dedicated timing unit has been used to perform memory functions. Its operation is based on successive states, in such a way that the next state deletes the previous one. The basis for designing the system is a description of the device's operation and specifying the conditions necessary for the proper operation [11]. The simplest way to describe the system operation is a control narrative, which is transformed into descriptionsin the form of an operating cycle diagram or connection formula. The connection formula defines the order of actuations of driver elements, in this case actuators. Indeed, the algorithmic method uses the description in the form of a connection formula. When adopting this method of description, several assumptions should be made, namely:  
* the driver element (actuator) used in the project is marked with a capital letter of the alphabet starting from A-Z;
* the sign \"+\" after the symbol of a given driver element (actuator) means activation (full extension of the piston);
* the sign \"\(-\)\" next to the symbol of a given driver element (actuator) means deactivation of the driver element (extension of the piston);
* the sign \"\(\pm\)\" next to the symbol of a given element means a short-term actuation of the element;
* each cylinder is equipped with sensors detecting the position of the cylinder piston;
* the position of the driver element (actuator) in the ON state is indicated by the symbol of the given element with the index 0--from logical state 0 (e.g., for element A symbol a0);
* the position of the driver element (actuator) in the OFF state is indicated by the symbol of the given element with the index 1--from logical state 1 (e.g., for element B symbol b1). Based on the description of the operation of individual driver elements (actuators) and the adopted markings, a formula is created that shows the operation of the automaton, i.e., the order of operation of the actuators. If in the formula there are two symbols of the actuators one above the other, it means that they operate at the same time. The connection formula on the example of which the system design will be discussed is as follows  
\[\text{S}\pm\text{A}+\text{B}+\text{B}-\text{C}+\text{B}+\text{B}- \begin{array} []{c}\text{A}-\\ \text{C}-\end{array} \]  
On the basis of the connection formula, the operating cycle diagram of the process unit is presented in Figure 2.  
The selected sequence is based on three actuators and is as follows:  
* in the initial state all actuators A, B and C are retracted,
* after pressing the S button, the actuator A begins to extend,
* after the actuator A is extended, the actuator B begins to extend,
* after the actuator B is extended, it is retracted again,
* after the actuator B is retracted, the actuator C begins to extend,
* after the actuator C is extended, the actuator B begins to extend,
* after the actuator B is extended, it is retracted again,
* after the actuator B is retracted, the actuators A and C start to retract simultaneously. At this stage, the sequence is completed and the system is waiting for the S button to be pressed again. Based on the connection formula, a diagram of the system is created, which is shown in Figure 3. Such a graph is created by placing on its circle as many circles showing the state of the system as there are elements in the connection formula. Each  
Figure 2: System operating cycle diagram. state circle will be the vertex of the system graph. The system graph is described in such a way that the vertices of the graph are assigned symbols denoting a change in the state of elements in the order according to the connection formula, while the arches of the graph circle directed to the vertices of the graph are assigned the signals that cause a change in the state of the element.