# Algorithmic Method for the Design of Sequential Circuits with the Use of Logic Elements
## 2 Algorithmic Method of Sequential Circuit Design
The arches coming out of the vertices are assigned signals informing that the desired state has been reached. These signals are, therefore, the signals causing a change in the state of the element to which they enter. For example, in the case of the presented graph, the signal coming from the B\(-\) vertex is a signal b0 informing the retraction of the B actuator and a signal that goes to the C+ vertex, which will cause the C actuator to extend. State S\(\pm\) (system start) is drawn in a double circle as a stable state, and other states, as transient states, are drawn in a single circle. The graph obtained in this way is divided into groups. Each group comprises a segment of the graph circle selected so that the same element occurs only once. The segments are made of as many elements as possible in a clockwise direction. The section is created starting from the stable state of the system. The division of groups is created radially, by running a line from the centre of the circle outside, so that each group is located between two lines. The number of groups determines the selection of a memory block--the number of inputs/outputs must be equal to the number of groups. Each created group is marked with k1, k2,..., kn starting from the group with the S\(\pm\) signal as shown in Figure 4. Each drawn line dividing the groups is marked with an index letter (e.g., x1, x2,..., xn), starting from the line closing the first group. Group division signals (x1, x2,..., xn) are generated by the last output signal in the group, e.g., x2 is generated by the product of the k2 and c1 signal, which is the last signal in the k2 group. The resulting signal causes the system to move to the next state of memory, i.e., x2 causes the transition to the state of k3, while x3 to the state of k4, etc. The first element in a given group is always forced by the state it is in, e.g., B\(-\) being the first state in groups k2 and k4 is forced by each of them. The graph after division into states has been presented in Figure 4.  
Figure 3: System graph. General rules for creating the graph:  
1. The graph is drawn based on the operating conditions of the system--the connection formula. 2. The graph is divided into groups in such a way that in each group the state of individual elements occurs only once. 3. Each separate group is numbered from k1 to kn, starting with the group with the start signal \"S\". 4. The division lines of groups have been marked from x1 to xn, where x1 corresponds to the end of the group k1, while xn to the end of group kn. 5. Arrows are drawn for each dividing line: from the last circle towards the dividing line. 6. The arch between the dividing line and the next state is designated as the state in which the arch is located. 7. The arch between the state and the dividing line directed to the dividing line is designated as signals coming out of that state. 8. Each dividing line is described by an equation in which we multiply the signals from the arc directed to the dividing line with the value of the state before the dividing line.