# Coding of states of a control automaton, Construction...

## Coding the states of the control automaton

To fix the states of the control automaton we will use triggers. To each state a of the control automaton we assign a certain code combination, which is mapped by the state of the Q-outputs of the triggers. The number n of the code bits, or triggers, can be selected based on the condition K & lt; 2 n, where K - is the number of states of the control automaton. For the case under consideration, K = 3, n = 2. The selected codes for the states of the control automaton are given in Table. 4.10.

Table 4.10

 Status Code i   0 0 0 1 0 1 2 1 0

The block diagram of the control automaton shown in Fig. 4.26, contains: Fig. 4.26. Block diagram of the control automaton with circuit logic

• two? 5-flip-flop , which form the register of information storage for fixing the current state of the control automaton with the output signals ;

• a decoder designed to convert a two-bit code to status signals ;

• A combination circuit that generates the control signals for the operating machine and signals for triggers based on the input signals , i.e. has five inputs and seven outputs.

The next task is to compose the combination scheme of the control automaton for each of the algorithms considered. First, we construct the transition graph of the control automaton.

## Constructing a transition graph

Such a graph is constructed on the basis of a marked graph-scheme of the algorithm (see Figure 4.25). The transition graph (Figure 4.27) provides complete information about all possible changes in the processor states, as well as control signals (micro-commands) and logical conditions that are used at each transition. To construct such a graph, we introduce the notion paths from the mark to the mark (from the initial state to the final state): (4.13) Fig. 4.27. Conversion graphs of the control automaton

where is the conjunction (logical product) of all the logical conditions corresponding to the vertexes in this path, with is taken in a straightforward form if from the given vertex the path goes along the arrow marked with the value 1, and in inverse form if the path goes along the arrow marked with the value 0; - microinstruction (the set of microoperations), indicated in the single operator vertex through which this path passes.

The path must not contain the same logical condition in direct and inverse forms. Possible paths that contain several conditional vertices or do not contain any, as well as paths that do not contain an operator vertex. The set of paths (4.13) determines the set of transitions between the states a n and a s of the automaton. When constructing the transition graph for each mark a x in the graph-scheme of the algorithm or the state a {of the control automaton, the vertex of the graph is put in correspondence, and to each path (4.13) - an arc directed from the vertex a n to the vertex a s. The arc reflects the transition of the automaton from the state a n to the state a \$, is marked by a conjunct and a control signal . If there are no logical vertices in the path under consideration, then is assumed (ie, an unconditional transition is made); if there is no operator vertex, then we assume that is an empty operator meaning preservation of the state, since no micro-operation is performed.

The transition graphs constructed in accordance with the above procedure (see Figure 4.27) determine the law of functioning and the structure of the control automaton.

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