Help with binary code

good I ask a question that has nothing to do at the moment with programming in Matlab, but with statistical issues and wonder if anyone can help,

My purpose is predicting the following number of binary string. For this, I have a sequence of binary digits that is:

s= 1(1) 0(2) 1(3) 1(4) 0(5) 0(6) 1(7) 0(8) 0(9) 1(10) 1(11) 1(12) 1(13) 0(14) 0(15) 0(16) 1(17) 1(18) 1(19) 0(20).

What I did then is creating substrings produced as follows:

1) 1 (1) 0 (2) 1 (3) 1 (4) --- [1 0 1 1]

2) 1 (1) 1 (3) 0 (5) 1 (7) --- [1 1 0 1]

3) 1 (1) 1 (4) 1 (7) 1 (10) --- [1 1 1 1]

4) 1 (1) 0 (5) 0 (9) 1 (13) --- [1 0 0 1]

5) 1 (1) 0 (6) 1 (11) 0 (16) --- [1 0 1 0]

6) 1 (1) 1 (7) 1 (13) 1 (19) --- [1 1 1 1]

7) 0 (2) 1 (3) 1 (4) 0 (5) --- [0 1 1 0]

8) 0 (2) 1 (4) 0 (6) 0 (8) --- [0 1 0 0]

9) 0 (2) 0 (5) 0 (8) 1 (11) --- [0 0 0 1]

10) 0 (2) 0 (6) 1 (10) 0 (14) --- [0 0 1 0]

11) 0 (2) 1 (7) 1 (12) 1 (17) --- [0 1 1 1]

12) 0 (2) 0 (8) 0 (14) 0 (20) --- [0 0 0 0]

13) 1 (3) 1 (4) 0 (5) 0 (6) --- [1 1 0 0]

14) 1 (3) 0 (5) 1 (7) 0 (9) --- [1 0 1 0]

15) 1 (3) 0 (6) 0 (9) 1 (12) --- [1 0 0 1]

16) 1 (3) 1 (7) 1 (11) 0 (15) --- [1 1 1 0]

17) 1 (3) 0 (8) 1 (13) 1 (18) --- [1 0 1 1]

18) 1 (4) 0 (5) 0 (6) 1 (7) --- [1 0 0 1]

19) 1 (4) 0 (6) 0 (8) 1 (10) --- [1 0 0 1]

20) 1 (4) 1 (7) 1 (10) 1 (13) --- [1 1 1 1]

21) 1 (4) 0 (8) 1 (12) 0 (16) --- [1 0 1 0]

22) 1 (4) 0 (9) 0 (14) 1 (19) --- [1 0 0 1]

23) 0 (5) 0 (6) 1 (7) 0 (8) --- [0 0 1 0]

24) 0 (5) 1 (7) 0 (9) 1 (11) --- [0 1 0 1]

25) 0 (5) 0 (8) 1 (11) 0 (14) --- [0 0 1 0]

26) 0 (5) 0 (9) 1 (13) 1 (17) --- [0 0 1 1]

27) 0 (5) 1 (10) 0 (15) 0 (20) --- [0 1 0 0]

28) 0 (6) 1 (7) 0 (8) 0 (9) --- [0 1 0 0]

29) 0 (6) 0 (8) 1 (10) 1 (12) --- [0 0 1 1]

30) 0 (6) 0 (9) 1 (12) 0 (15) --- [0 0 1 0]

31) 0 (6) 1 (10) 0 (14) 1 (18) --- [0 1 0 1]

32) 1 (7) 0 (8) 0 (9) 1 (10) --- [1 0 0 1]

33) 1 (7) 0 (9) 1 (11) 1 (13) --- [1 0 1 1]

34) 1 (7) 1 (10) 1 (13) 0 (16) --- [1 1 1 0]

35) 1 (7) 1 (11) 0 (15) 1 (19) --- [1 1 0 1]

36) 0 (8) 0 (9) 1 (10) 1 (11) --- [0 0 1 1]

37) 0 (8) 1 (10) 1 (12) 0 (14) --- [0 1 1 0]

38) 0 (8) 1 (11) 0 (14) 1 (17) --- [0 1 0 1]

39) 0 (8) 1 (12) 0 (16) 0 (20) --- [0 1 0 0]

40) 0 (9) 1 (10) 1 (11) 1 (12) --- [0 1 1 1]

41) 0 (9) 1 (11) 1 (13) 0 (15) --- [0 1 1 0]

42) 0 (9) 1 (12) 0 (15) 1 (18) --- [0 1 0 1]

43) 1 (10) 1 (11) 1 (12) 1 (13) --- [1 1 1 1]

44) 1 (10) 1 (12) 0 (14) 0 (16) --- [1 1 0 0]

45) 1 (10) 1 (13) 0 (16) 1 (19) --- [1 1 0 1]

46) 1 (11) 1 (12) 1 (13) 0 (14) --- [1 1 1 0]

47) 1 (11) 1 (13) 0 (15) 1 (17) --- [1 1 0 1]

48) 1 (11) 0 (14) 1 (17) 0 (20) --- [1 0 1 0]

49) 1 (12) 1 (13) 0 (14) 0 (15) --- [1 1 0 0]

50) 1 (12) 0 (14) 0 (16) 1 (18) --- [1 0 0 1]

51) 1 (13) 0 (14) 0 (15) 0 (16) --- [1 0 0 0]

52) 1 (13) 0 (15) 1 (17) 1 (19) --- [1 0 1 1]

53) 0 (14) 0 (15) 0 (16) 1 (17) --- [0 0 0 1]

54) 0 (14) 0 (16) 1 (18) 0 (20) --- [0 0 1 0]

55) 0 (15) 0 (16) 1 (17) 1 (18) --- [0 0 1 1]

56) 0 (16) 1 (17) 1 (18) 1 (19) --- [0 1 1 1]

57) 1 (17) 1 (18) 1 (19) 0 (20) --- [1 1 1 0]

And I've also calculated the relative frequency of these substrings

0 0 0 0------ 0,0175438596491228

0 0 0 1------ 0,0350877192982456

0 0 1 0------ 0,0877192982456140

0 0 1 1------ 0,0701754385964912

0 1 0 0------ 0,0701754385964912

0 1 0 1------ 0,0701754385964912

0 1 1 0------ 0,0526315789473684

0 1 1 1------ 0,0526315789473684

1 0 0 0------ 0,0175438596491228

1 0 0 1 0,122807017543860

1 0 1 0 0,0701754385964912

1 0 1 1 0,0701754385964912

1 1 0 0 0,0526315789473684

1 1 0 1 0,0701754385964912

1 1 1 0 0,0701754385964912

1 1 1 1 0,0701754385964912

Now let's say I want to know if the number 21 of the succession will be "0" or "1". To do this do the following:

s= 1(1) 0(2) 1(3) 1(4) 0(5) 0(6) 1(7) 0(8) 0(9) 1(10) 1(11) 1(12) 1(13) 0(14) 0(15) 0(16) 1(17) 1(18) 1(19) 0(20) X(21)

and now build substrings that have to do with X:

1: 1 (18), 1 (19), 0 (20), X (21) --- [1,1,0, X]

2: 0 (15), 1 (17), 1 (19), X (21) --- [0,1,1, X]

3: 1 (12), 0 (15), 1 (18), X (21) --- [1,0,1, X]

4: 0 (9), 1 (13), 1 (17), X (21) --- [0,1,1, X]

5: 0 (6), 1 (11), 0 (16), X (21) --- [0,1,0, X]

6: 1 (3), 0 (9), 0 (15), X (21) --- [1,0,0, X]

And replacing the X I have:

 X = 1, 
1: 1 (18), 1 (19), 0 (20), X (21) --- [1,1,0, 1 ]

2: 0 (15), 1 (17), 1 (19), X (21) --- [0,1,1, 1 ]

3: 1 (12), 0 (15), 1 (18), X (21) --- [1,0,1, 1 ]

4: 0 (9), 1 (13), 1 (17), X (21) --- [0,1,1, 1 ]

5: 0 (6), 1 (11), 0 (16), X (21) --- [0,1,0, 1 ]

6: 1 (3), 0 (9), 0 (15), X (21) --- [1,0,0, 1 ]

 X = 0, 
1: 1 (18), 1 (19), 0 (20), X (21) --- [1,1,0, 0 ]

2: 0 (15), 1 (17), 1 (19), X (21) --- [0,1,1, 0 ]

3: 1 (12), 0 (15), 1 (18), X (21) --- [1,0,1, 0 ]

4: 0 (9), 1 (13), 1 (17), X (21) --- [0,1,1, 0 ]

5: 0 (6), 1 (11), 0 (16), X (21) --- [0,1,0, 0 ]

6: 1 (3), 0 (9), 0 (15), X (21) --- [1,0,0, 0 ]

Okay, from here someone could tell me how I can study the probability to predict the next number in the string?

[Walter Roberson]

Duplicates http://www.mathworks.co.uk/matlabcentral/answers/85666-problem-with-binary-code