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Structure of sequential machines in .NET Draw QR Code 2d barcode in .NET Structure of sequential machines

Structure of sequential machines using vs .net toencode qr code 2d barcode with asp.net web,windows application iPhone OS Example For machine M1 , the Visual Studio .NET QR partitions 1 = {A, B; C, D} and 2 = {A, C; B, D} are closed. Since y1 in assignment has been assigned to distinguish the blocks of 1 , it is independent of y2 .

Similarly, since y2 has been assigned to distinguish the blocks of 2 , it is independent of y1 . Theorem 12.1 actually states a necessary and suf cient condition for the decomposition of sequential machines.

The existence of a partition and a closed partition on the set of states of a machine M, such that = (0) guarantees that M can be composed of two component machines connected in series. The rst component in the connection consists of log2 #( ) memory elements (and their excitation circuitry), corresponding to the state variables assigned to distinguish the blocks of . Since these variables are independent of the remaining variables, the rst component is often referred to as the independent component.

The second component in the serial connection, also referred to as the dependent component, contains log2 #( ) memory elements, corresponding to the state variables assigned to distinguish the blocks of . We shall refer to the independent component as the predecessor machine and the dependent component as the successor machine. It is often convenient to view the predecessor machine as the component that distinguishes between the blocks of , and the successor machine as the component that distinguishes between the states within the blocks of .

The existence of two closed partitions on the states of M such that their product is zero, i.e., 1 2 = (0), implies that M can be composed of two components operating in parallel, independently of each other.

One component consists of log2 #( 1 ) memory elements, corresponding to the variables assigned to distinguish the blocks of 1 . The second component consists of log2 #( 2 ) memory elements, corresponding to the variables assigned to distinguish the blocks of 2 . The preceding arguments can thus be summarized as follows.

. An n-state machine M can be decomposed into two independent components operating in parallel if and only if there exist two nontrivial closed partitions 1 and 2 on the states of M such that 1 2 = (0). This decomposition requires a minimal number (i.e.

, log2 n ) of state variables if and only if log2 #( 1 ) + log2 #( 2 ) = log2 n . Example Consider the machine M2 given in Table 12.3.

It can be shown that M2 has seven closed partitions, which are listed in Fig. 12.4.

Since M2 has eight states, three state variables are needed for an assignment. The existence of the closed partition 5 suggests that M2 can be realized as two component machines connected in series. The predecessor component has two state variables, y1 and y2 , which are assigned to the blocks of 5 and,.

12.2 State assignments using partitions Table 12.3 Machine M2 NS PS A B C D E F G H x=0 H F G E A C B D x=1 B A D C C D A B z 0 0 0 1 0 0 0 0. 0 = {A; B; C ; D; E ;F ; G; VS .NET QR Code 2d barcode H } = (0), 1 = {A, B, C , D; E , F , G, H }, 2 = {A, D, E , H ; B, C , F , G}, 3 = {A, D; B, C , F , G; E , H }, 4 = {A, D, E , H ; B, C ; F , G}, 5 = {A, D; B, C ; E , H ; F , G}, 6 = {A, B, C , D, E , F , G, H } = (I )..

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