Question

How many strings consisting of 7 bits have at minimum 3 consecutive 1's? And how many have exactly 3 consecutive 1's?

Answer 1

ANSWERS

Exactly 3 consecutive 1s = 27

Minimum 3 consecutive 1s = 47

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EXPLANATION

Total = 2^7 = 128

Minimum 3 consecutive 1s

1. 0000111
2. 0001110
3. 0001111
4. 0010111
5. 0011100
6. 0011101
7. 0011110
8. 0011111
9. 0100111
10. 0101110
11. 0101111
12. 0110111
13. 0111000
14. 0111001
15. 0111010
16. 0111011
17. 0111100
18. 0111101
19. 0111110
20. 0111111
21. 1000111
22. 1001110
23. 1001111
24. 1010111
25. 1011100
26. 1011101
27. 1011110
28. 1011111
29. 1100111
30. 1101110
31. 1101111
32. 1110000
33. 1110001
34. 1110010
35. 1110011
36. 1110100
37. 1110101
38. 1110110
39. 1110111
40. 1111000
41. 1111001
42. 1111010
43. 1111011
44. 1111100
45. 1111101
46. 1111110
47. 1111111

Exactly 3 consecutive 1s

1. 0000111
2. 0001110
3. 0010111
4. 0011100
5. 0011101
6. 0100111
7. 0101110
8. 0110111
9. 0111000
10. 0111001
11. 0111010
12. 0111011
13. 1000111
14. 1001110
15. 1010111
16. 1011100
17. 1011101
18. 1100111
19. 1101110
20. 1110000
21. 1110001
22. 1110010
23. 1110011
24. 1110100
25. 1110101
26. 1110110
27. 1110111