Математика и информатика. Решение логико-познавательных задач. Учебное пособие для студентов вузов

ɦɭ ɥɟɝɤɨ ɧɚɯɨɞɢɬɶ ɫɨɨɬɜɟɬɫɬɜɢɟ ɫ ɞɜɨɢɱɧɵɦɢ ɱɢɫɥɚɦɢ. Ⱦɥɹ ɤɨɞɢɪɨɜɤɢ 3 ɛɢɬɨɜ ɧɟɨɛɯɨɞɢɦɨ 8 ɡɧɚɤɨɜ, ɩɨɷɬɨɦɭ ɜɡɹɥɢ ɰɢɮɪɵ ɨɬ 0 ɞɨ 7 ɞɟɫɹɬɢɱɧɨɣ ɫɢɫɬɟɦɵ.

ɉɪɢ ɤɨɞɢɪɨɜɤɟ ɱɟɬɵɪɟɯ ɛɢɬɨɜ ɬɪɟɛɭɟɬɫɹ 16 ɡɧɚɤɨɜ: 10 ɰɢɮɪ ɞɟɫɹɬɢɱɧɨɣ ɫɢɫɬɟɦɵ ɢ 6 ɛɭɤɜ ɥɚɬɢɧɫɤɨɝɨ ɚɥɮɚɜɢɬɚ: A, B, C, D, E, F. ɉɨɥɭɱɟɧɧɵɟ ɫɢɫɬɟɦɵ, ɢɦɟɸɳɢɟ ɨɫɧɨɜɚɧɢɹ 8 ɢ 16, ɧɚɡɜɚɥɢ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɜɨɫɶɦɟɪɢɱɧɨɣ ɢ ɲɟɫɬɧɚɞɰɚɬɟɪɢɱɧɨɣ.

ȼ ɜɨɫɶɦɟɪɢɱɧɨɣ (octal) ɫɢɫɬɟɦɟ ɫɱɢɫɥɟɧɢɹ ɢɫɩɨɥɶɡɭɸɬɫɹ ɜɨɫɟɦɶ ɰɢɮɪ: 0, 1, 2, 3, 4, 5, 6, 7. ȼ ɲɟɫɬɧɚɞɰɚɬɟɪɢɱɧɨɣ (hexadecimal) ɫɢɫɬɟɦɟ ɫɱɢɫɥɟɧɢɹ ɩɪɢɦɟɧɹɟɬɫɹ ɲɟɫɬɧɚɞɰɚɬɶ ɰɢɮɪ: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A,

B, C, D, E, F (A — ɰɢɮɪɚ «ɚ», B — ɰɢɮɪɚ «ɛɷ» ɢ ɬ.ɩ.).

Ɂɚɦɟɱɚɧɢɟ 3. ȼ ɞɪɭɝɢɯ ɩɨɡɢɰɢɨɧɧɵɯ ɫɢɫɬɟɦɚɯ ɫɱɢɫɥɟɧɢɹ ɫ ɨɫɧɨɜɚɧɢɟɦ ɛɨɥɶɲɟ 16 ɬɚɤɠɟ ɭɞɨɛɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɛɭɤɜɵ ɥɚɬɢɧɫɤɨɝɨ ɚɥɮɚɜɢɬɚ. ɇɚɩɪɢɦɟɪ, ɜ ɞɜɚɞɰɚɬɢɩɹɬɢɪɢɱɧɨɣ ɫɢɫɬɟɦɟ ɫɱɢɫɥɟɧɢɹ ɩɪɢɦɟ-

ɧɹɟɬɫɹ 25 ɰɢɮɪ: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F, G, H, I, J, K, L,

M, N, O.

ɇɢɠɟ ɩɪɟɞɫɬɚɜɥɟɧɚ ɬɚɛɥɢɰɚ ɫɨɨɬɜɟɬɫɬɜɢɹ ɱɢɫɟɥ ɜ ɪɚɡɥɢɱɧɵɯ ɫɢɫɬɟɦɚɯ ɫɱɢɫɥɟɧɢɹ (ɬɚɛɥ. 1.4).

ǺȈȉȓȐȞȈ 1.4

1.4.ǷȍȘȍȊȖȌ ȟȐșȍȓ Ȑȏ ȖȌȕȖȑ șȐșȚȍȔȣ șȟȐșȓȍȕȐȧ

ȊȌȘțȋțȦ

ɉɪɚɜɢɥɨ ɩɟɪɟɜɨɞɚ ɰɟɥɨɝɨ ɞɟɫɹɬɢɱɧɨɝɨ ɱɢɫɥɚ ɜ ɩɨɡɢɰɢɨɧɧɭɸ ɫɢɫɬɟɦɭ ɫɱɢɫɥɟɧɢɹ ɫ ɞɪɭɝɢɦ ɨɫɧɨɜɚɧɢɟɦ (ɫ ɨɫɧɨɜɚɧɢɟɦ q):

•ɪɚɡɞɟɥɢɬɶ ɞɚɧɧɨɟ ɞɟɫɹɬɢɱɧɨɟ ɱɢɫɥɨ ɧɚ ɧɨɜɨɟ ɨɫɧɨɜɚɧɢɟ q (ɧɚ ɨɫɧɨɜɚɧɢɟ ɬɨɣ ɫɢɫɬɟɦɵ ɫɱɢɫɥɟɧɢɹ, ɜ ɤɨɬɨɪɭɸ ɩɟɪɟɜɨɞɢɦ) ɢ ɡɚɮɢɤɫɢɪɨɜɚɬɶ ɱɚɫɬɧɨɟ ɢ ɨɫɬɚɬɨɤ;

•ɟɫɥɢ ɩɨɥɭɱɟɧɧɨɟ ɱɚɫɬɧɨɟ ɨɤɚɠɟɬɫɹ ɛɨɥɶɲɟ ɧɨɜɨɝɨ ɨɫɧɨɜɚɧɢɹ ɫɢɫɬɟɦɵ ɫɱɢɫɥɟɧɢɹ ɢɥɢ ɪɚɜɧɨ ɟɦɭ, ɬɨ ɧɟɨɛɯɨɞɢɦɨ ɩɪɨɞɨɥɠɚɬɶ ɞɟɥɢɬɶ, ɮɢɤɫɢɪɭɹ ɱɚɫɬɧɨɟ ɢ ɨɫɬɚɬɨɤ;

•ɷɬɢ ɞɟɣɫɬɜɢɹ ɜɵɩɨɥɧɹɬɶ ɞɨ ɬɟɯ ɩɨɪ, ɩɨɤɚ ɩɨɥɭɱɟɧɧɨɟ ɱɚɫɬɧɨɟ ɧɟ ɫɬɚɧɟɬ ɦɟɧɶɲɟ ɧɨɜɨɝɨ ɨɫɧɨɜɚɧɢɹ ɫɢɫɬɟɦɵ ɫɱɢɫɥɟɧɢɹ;

•ɜ ɨɬɜɟɬɟ ɡɚɩɢɫɚɬɶ ɩɨɫɥɟɞɧɟɟ ɱɚɫɬɧɨɟ ɢ ɜɫɟ ɩɨɥɭɱɟɧɧɵɟ ɨɫɬɚɬɤɢ ɜ ɨɛɪɚɬɧɨɣ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɢ.

ɉɪɢɦɟɪ 10. ɉɟɪɟɜɟɞɟɦ ɱɢɫɥɨ 11 ɢɡ ɞɟɫɹɬɢɱɧɨɣ ɫɢɫɬɟɦɵ ɫɱɢɫɥɟɧɢɹ ɜ ɞɜɨɢɱɧɭɸ ɫɢɫɬɟɦɭ (ɪɢɫ. 1.1).

Ɋɚɡɞɟɥɢɦ ɱɢɫɥɨ 1110 ɧɚ ɧɨɜɨɟ ɨɫɧɨɜɚɧɢɟ q 2 . ɉɨɥɭɱɢɦ ɱɚɫɬɧɨɟ,

ɪɚɜɧɨɟ 5, ɢ ɨɫɬɚɬɨɤ, ɪɚɜɧɵɣ 1. ɉɨɫɤɨɥɶɤɭ ɩɨɥɭɱɟɧɧɨɟ ɱɚɫɬɧɨɟ ɛɨɥɶɲɟ ɧɨɜɨɝɨ ɨɫɧɨɜɚɧɢɹ, ɩɪɨɞɨɥɠɚɟɦ ɞɟɥɢɬɶ ɞɨ ɬɟɯ ɩɨɪ, ɩɨɤɚ ɱɚɫɬɧɨɟ ɧɟ ɛɭɞɟɬ ɦɟɧɶɲɟ ɧɨɜɨɝɨ ɨɫɧɨɜɚɧɢɹ ɫɢɫɬɟɦɵ ɫɱɢɫɥɟɧɢɹ q 2 . ȼɨɡɶɦɟɦ ɩɨ-

ɫɥɟɞɧɟɟ ɱɚɫɬɧɨɟ ɢ ɨɫɬɚɬɤɢ ɨɬ ɞɟɥɟɧɢɹ ɢ ɫɨɛɟɪɟɦ ɢɯ ɜ ɧɚɩɪɚɜɥɟɧɢɢ, ɭɤɚɡɚɧɧɨɦ ɫɬɪɟɥɤɨɣ; ɜ ɪɟɡɭɥɶɬɚɬɟ ɩɨɥɭɱɢɬɫɹ ɱɢɫɥɨ ɜ ɞɜɨɢɱɧɨɣ ɫɢɫɬɟɦɟ ɫɱɢɫɥɟɧɢɹ: 1110 10112 .

12

ˀ̛̭. 1.1

ɉɪɢɦɟɪ 11. ɉɟɪɟɜɟɞɟɦ ɱɢɫɥɨ 2610 ɜ ɞɜɨɢɱɧɭɸ ɢ ɬɪɨɢɱɧɭɸ ɫɢɫɬɟɦɵ ɫɱɢɫɥɟɧɢɹ. Ɉɱɟɜɢɞɧɨ, ɱɬɨ 2610 ο 110102 . Ɂɚɩɢɫɚɬɶ ɩɟɪɟɜɨɞ ɦɨɠɧɨ ɢ ɬɚɤɢɦ ɨɛɪɚɡɨɦ (ɪɢɫ. 1.2):

ǸȐș. 1.2

Ⱥɧɚɥɨɝɢɱɧɨ ɧɚɯɨɞɢɦ, ɱɬɨ 2610 ο 2223 (ɪɢɫ. 1.3):

26 : 3 8 2 (ɨɫɬɚɬɨɤ)

8 : 3 2 2 (ɨɫɬɚɬɨɤ)

ǸȐș. 1.3

ɉɪɢɦɟɪ 12. ɉɟɪɟɜɟɞɟɦ ɱɢɫɥɨ 77 ɢɡ ɞɟɫɹɬɢɱɧɨɣ ɫɢɫɬɟɦɵ ɜ ɜɨɫɶɦɟɪɢɱɧɭɸ ɫɢɫɬɟɦɭ ɫɱɢɫɥɟɧɢɹ (ɪɢɫ. 1.4).

ǸȐș. 1.4

13

ɫɥɟɞɧɟɟ ɱɚɫɬɧɨɟ ɢ ɨɫɬɚɬɤɢ ɨɬ ɞɟɥɟɧɢɹ, ɡɚɬɟɦ ɫɨɛɟɪɟɦ ɜ ɧɚɩɪɚɜɥɟɧɢɢ, ɭɤɚɡɚɧɧɨɦ ɫɬɪɟɥɤɨɣ, ɜ ɪɟɡɭɥɶɬɚɬɟ ɩɨɥɭɱɢɬɫɹ ɱɢɫɥɨ ɜ ɜɨɫɶɦɟɪɢɱɧɨɣ ɫɢɫɬɟɦɟ ɫɱɢɫɥɟɧɢɹ: 7710 1158 .

ɉɪɢɦɟɪ 13. ɉɟɪɟɜɟɞɟɦ ɱɢɫɥɨ 160 ɢɡ ɞɟɫɹɬɢɱɧɨɣ ɫɢɫɬɟɦɵ ɜ ɲɟɫɬɧɚɞɰɚɬɟɪɢɱɧɭɸ ɫɢɫɬɟɦɭ ɫɱɢɫɥɟɧɢɹ (ɪɢɫ. 1.5).

160 : 16 = 10 + 0 (ɨɫɬɚɬɨɤ)

ǸȐș. 1.5

ɉɪɢɦɟɪ 14. ɉɟɪɟɜɟɞɟɦ ɱɢɫɥɨ 478 ɢɡ ɞɟɫɹɬɢɱɧɨɣ ɫɢɫɬɟɦɵ ɜ ɲɟɫɬɧɚɞɰɚɬɟɪɢɱɧɭɸ ɫɢɫɬɟɦɭ ɫɱɢɫɥɟɧɢɹ (ɪɢɫ. 1.6).

ǸȐș. 1.6

Ɍɚɤ ɤɚɤ 13 ɜ ɲɟɫɬɧɚɞɰɚɬɟɪɢɱɧɨɣ ɫɢɫɬɟɦɟ ɫɱɢɫɥɟɧɢɹ ɪɚɜɧɨ D, ɚ 14 ɪɚɜɧɨ E, ɨɤɨɧɱɚɬɟɥɶɧɨ ɩɨɥɭɱɚɟɦ: 47810 1DE .

Ⱦɥɹ ɞɪɨɛɧɵɯ ɱɢɫɟɥ ɩɪɚɜɢɥɨ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɝɨ ɞɟɥɟɧɢɹ ɡɚɦɟɧɹɟɬɫɹ ɩɪɚɜɢɥɨɦ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɝɨ ɭɦɧɨɠɟɧɢɹ.

ɉɪɢɦɟɪ 15. ɉɟɪɟɜɟɞɟɦ ɱɢɫɥɨ 0,37510 ɜ ɞɜɨɢɱɧɭɸ ɫɢɫɬɟɦɭ ɫɱɢɫɥɟɧɢɹ. Ɂɚɩɢɫɚɬɶ ɩɟɪɟɜɨɞ ɦɨɠɧɨ ɬɚɤ, ɤɚɤ ɧɚ ɪɢɫ. 1.7.

0,37510 ο (0,011)2

0,375 • 2 = 0,75

0,75 • 2 = 1,5

0,5 • 2 =1,0

ǸȐș 1.7

14

Ɉɩɟɪɚɰɢɹ ɭɦɧɨɠɟɧɢɹ ɩɪɨɜɨɞɢɬɫɹ ɞɨ ɬɟɯ ɩɨɪ, ɩɨɤɚ ɞɪɨɛɧɚɹ ɱɚɫɬɶ ɧɟ ɨɤɚɠɟɬɫɹ ɪɚɜɧɨɣ ɧɭɥɸ, ɢɥɢ ɧɟ ɛɭɞɟɬ ɞɨɫɬɢɝɧɭɬɚ ɬɪɟɛɭɟɦɚɹ ɬɨɱɧɨɫɬɶ. Ɂɚɬɟɦ ɫɨɛɢɪɚɟɦ ɜɫɟ ɰɟɥɵɟ ɱɚɫɬɢ ɫɜɟɪɯɭ ɜɧɢɡ ɢ ɡɚɩɢɫɵɜɚɟɦ ɪɟɡɭɥɶɬɚɬ:

0,37510 0,0112 .

ɉɪɚɜɢɥɨ ɩɟɪɟɜɨɞɚ ɱɢɫɟɥ ɢɡ ɥɸɛɨɣ ɩɨɡɢɰɢɨɧɧɨɣ ɫɢɫɬɟɦɵ ɫɱɢɫɥɟɧɢɹ (ɫ ɨɫɧɨɜɚɧɢɟɦ q) ɜ ɞɟɫɹɬɢɱɧɭɸ ɫɢɫɬɟɦɭ:

•ɩɪɨɧɭɦɟɪɨɜɚɬɶ ɪɚɡɪɹɞɵ ɱɢɫɥɚ;

•ɡɚɩɢɫɚɬɶ ɞɚɧɧɨɟ ɱɢɫɥɨ ɜ ɜɢɞɟ ɦɧɨɝɨɱɥɟɧɚ ɩɨ ɫɬɟɩɟɧɹɦ ɨɫɧɨɜɚɧɢɹ q;

•ɩɨɫɱɢɬɚɬɶ ɪɟɡɭɥɶɬɚɬ ɩɨ ɩɪɚɜɢɥɚɦ ɞɟɫɹɬɢɱɧɨɣ ɚɪɢɮɦɟɬɢɤɢ.

ɉɪɢɦɟɪ 16. ɉɟɪɟɜɟɞɟɦ ɱɢɫɥɨ 101101 ɢɡ ɞɜɨɢɱɧɨɣ ɜ ɞɟɫɹɬɢɱɧɭɸ ɫɢɫɬɟɦɭ ɫɱɢɫɥɟɧɢɹ.

Ɂɚɩɢɲɟɦ ɞɚɧɧɨɟ ɱɢɫɥɨ ɜ ɜɢɞɟ ɦɧɨɝɨɱɥɟɧɚ, ɩɪɟɞɜɚɪɢɬɟɥɶɧɨ ɩɪɨɧɭɦɟɪɨɜɚɜ ɪɚɡɪɹɞɵ ɫɩɪɚɜɚ ɧɚɥɟɜɨ, ɧɚɱɢɧɚɹ ɫ ɧɭɥɟɜɨɝɨ ɢ ɩɨɫɱɢɬɚɟɦ ɪɟɡɭɥɶɬɚɬ:

101101 1 25 0 24 1 23 1 22 0 21 1 20 32 0 8 4 0 1 45.

5 4 3 2 1 0

Ɉɤɨɧɱɚɬɟɥɶɧɨ ɩɨɥɭɱɚɟɦ: 1011012 4510 .

ɉɪɢɦɟɪ 17. ɉɟɪɟɜɟɞɟɦ ɱɢɫɥɨ 4035 ɢɡ ɲɟɫɬɟɪɢɱɧɨɣ ɜ ɞɟɫɹɬɢɱɧɭɸ ɫɢɫɬɟɦɭ ɫɱɢɫɥɟɧɢɹ.

ɉɪɢɦɟɧɹɹ ɩɪɚɜɢɥɨ ɩɟɪɟɜɨɞɚ, ɩɨɥɭɱɚɟɦ:

ɉɪɢɦɟɪ 19. ɉɟɪɟɜɟɞɟɦ ɱɢɫɥɨ 11100111,11012 ɜ ɞɟɫɹɬɢɱɧɭɸ ɫɢɫɬɟ-

ɦɭ ɫɱɢɫɥɟɧɢɹ.

ɉɪɢɦɟɧɹɹ ɩɪɚɜɢɥɨ ɩɟɪɟɜɨɞɚ, ɩɨɥɭɱɚɟɦ:

1 1 1 0 0111, 1 1 0 1 1 27 1 26 1 25 0 24 0 23 1 22

7 6 5 4 3 2 1 0 1 2 3 4

1 21 1 20 1 2 1 1 2 2 0 2 3 1 2 4 231,812510.

ɉɪɢɦɟɪ 20. Ɂɚɩɢɲɟɦ ɞɟɫɹɬɢɱɧɨɟ ɡɧɚɱɟɧɢɟ ɦɚɤɫɢɦɚɥɶɧɨɝɨ ɲɟɫɬɢɪɚɡɪɹɞɧɨɝɨ ɬɪɨɢɱɧɨɝɨ ɱɢɫɥɚ.

Ɇɚɤɫɢɦɚɥɶɧɵɦ ɲɟɫɬɢɪɚɡɪɹɞɧɵɦ ɬɪɨɢɱɧɵɦ ɱɢɫɥɨɦ ɹɜɥɹɟɬɫɹ 2222223 , ɬɚɤ ɤɚɤ ɜ ɬɪɨɢɱɧɨɣ ɫɢɫɬɟɦɟ ɫɱɢɫɥɟɧɢɹ ɢɫɩɨɥɶɡɭɸɬɫɹ ɬɨɥɶɤɨ ɰɢɮɪɵ 0, 1, 2. ɉɪɢɦɟɧɹɹ ɩɪɚɜɢɥɨ ɩɟɪɟɜɨɞɚ, ɧɚɯɨɞɢɦ ɞɟɫɹɬɢɱɧɨɟ ɡɧɚɱɟɧɢɟ ɞɚɧɧɨɝɨ ɱɢɫɥɚ:

2 2 2 2 2 2 2 35 2 34 2 33 2 32 2 31 2 30 72810 .

5 4 3 2 1 0

Ɉɤɨɧɱɚɬɟɥɶɧɨ ɩɨɥɭɱɚɟɦ: 2222223 72810 .

ɉɪɢɦɟɪ 21. ȼɨ ɫɤɨɥɶɤɨ ɪɚɡ ɭɜɟɥɢɱɢɬɫɹ ɱɢɫɥɨ 324 , ɟɫɥɢ ɩɪɢɩɢɫɚɬɶ ɤ ɧɟɦɭ ɫɩɪɚɜɚ ɬɪɢ ɧɭɥɹ?

ȿɫɥɢ ɩɪɢɩɢɫɚɬɶ ɤ ɱɢɫɥɭ 324 ɫɩɪɚɜɚ ɬɪɢ ɧɭɥɹ, ɬɨ ɩɨɥɭɱɢɦ ɱɢɫɥɨ

ɇɚɢɛɨɥɟɟ ɩɪɨɫɬɨ ɩɟɪɟɜɟɫɬɢ ɱɢɫɥɚ ɜ ɪɨɞɫɬɜɟɧɧɵɟ ɫɢɫɬɟɦɵ ɫɱɢɫɥɟɧɢɹ ɢ ɨɛɪɚɬɧɨ (ɧɚɩɪɢɦɟɪ, ɢɡ ɞɜɨɢɱɧɨɣ ɫɢɫɬɟɦɵ ɫɱɢɫɥɟɧɢɹ ɜ ɱɟɬɜɟɪɢɱɧɭɸ, ɜɨɫɶɦɟɪɢɱɧɭɸ ɢ ɲɟɫɬɧɚɞɰɚɬɟɪɢɱɧɭɸ ɫɢɫɬɟɦɵ ɫɱɢɫɥɟɧɢɹ, ɨɫɧɨ-

ɜɚɧɢɟ ɤɨɬɨɪɵɯ ɦɨɠɟɬ ɛɵɬɶ ɩɪɟɞɫɬɚɜɥɟɧɨ ɜ ɜɢɞɟ 2n ).

ɋɢɫɬɟɦɚɦɢ ɫɱɢɫɥɟɧɢɹ, ɪɨɞɫɬɜɟɧɧɵɦɢ ɞɜɨɢɱɧɨɣ, ɫɱɢɬɚɸɬɫɹ ɬɚɤɢɟ ɫɢɫɬɟɦɵ, ɨɫɧɨɜɚɧɢɹ ɤɨɬɨɪɵɯ ɹɜɥɹɸɬɫɹ ɡɧɚɱɟɧɢɟɦ ɫɬɟɩɟɧɢ ɱɢɫɥɚ 2.

Ⱦɥɹ ɡɚɩɢɫɢ ɰɟɥɨɝɨ ɞɜɨɢɱɧɨɝɨ ɱɢɫɥɚ ɜ ɫɢɫɬɟɦɟ ɫɱɢɫɥɟɧɢɹ ɫ ɨɫɧɨɜɚɧɢɟɦ 2n ɧɟɨɛɯɨɞɢɦɨ:

16

•ɪɚɡɞɟɥɢɬɶ ɷɬɨ ɱɢɫɥɨ ɫɩɪɚɜɚ ɧɚɥɟɜɨ ɧɚ ɝɪɭɩɩɵ ɩɨ n ɰɢɮɪ ɜ ɤɚɠɞɨɣ;

•ɜ ɫɥɭɱɚɟ, ɟɫɥɢ ɜ ɩɨɫɥɟɞɧɟɣ ɥɟɜɨɣ ɝɪɭɩɩɟ ɛɭɞɟɬ ɦɟɧɶɲɟ n ɰɢɮɪ, ɧɟɨɛɯɨɞɢɦɨ ɞɨɩɨɥɧɢɬɶ ɟɟ ɧɭɥɹɦɢ ɞɨ ɧɭɠɧɨɝɨ ɱɢɫɥɚ;

•ɤɚɠɞɭɸ ɝɪɭɩɩɭ ɨɩɪɟɞɟɥɢɬɶ ɤɚɤ n-ɪɚɡɪɹɞɧɨɟ ɞɜɨɢɱɧɨɟ ɱɢɫɥɨ ɢ ɡɚɦɟɧɢɬɶ ɟɟ ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɣ ɰɢɮɪɨɣ ɜ ɫɢɫɬɟɦɟ ɫɱɢɫɥɟɧɢɹ ɫ ɨɫɧɨɜɚɧɢɟɦ 2n .

ɉɪɢɦɟɪ 22. ɉɟɪɟɜɟɞɟɦ ɱɢɫɥɨ 1011000010 ɢɡ ɞɜɨɢɱɧɨɣ ɫɢɫɬɟɦɵ ɜ ɱɟɬɜɟɪɢɱɧɭɸ, ɜɨɫɶɦɟɪɢɱɧɭɸ ɢ ɲɟɫɬɧɚɞɰɚɬɟɪɢɱɧɭɸ ɫɢɫɬɟɦɵ ɫɱɢɫɥɟɧɢɹ.

Ⱦɥɹ ɩɟɪɟɜɨɞɚ 10110000102 ɜ ɱɟɬɜɟɪɢɱɧɭɸ ɫɢɫɬɟɦɭ ɫɱɢɫɥɟɧɢɹ ɩɪɟɞɜɚɪɢɬɟɥɶɧɨ ɫɨɫɬɚɜɢɦ ɬɚɛɥɢɰɭ ɫɨɨɬɜɟɬɫɬɜɢɹ ɞɜɨɢɱɧɵɯ ɱɢɫɟɥ ɱɟɬ-

ɜɟɪɢɱɧɵɦ. Ɍɚɤ ɤɚɤ ɨɫɧɨɜɚɧɢɟ ɱɟɬɜɟɪɢɱɧɨɣ ɫɢɫɬɟɦɵ ɪɚɜɧɨ 2n 22 4 , ɬɨ ɤɚɠɞɨɦɭ ɱɟɬɜɟɪɢɱɧɨɦɭ ɱɢɫɥɭ ɧɟɨɛɯɨɞɢɦɨ ɩɨɫɬɚɜɢɬɶ ɜ ɫɨɨɬɜɟɬɫɬɜɢɟ ɞɜɭɯɪɚɡɪɹɞɧɨɟ ɞɜɨɢɱɧɨɟ ɱɢɫɥɨ. ȿɫɥɢ ɜ ɡɚɩɢɫɢ ɞɜɨɢɱɧɨɝɨ ɱɢɫɥɚ ɧɟ ɯɜɚɬɚɟɬ ɪɚɡɪɹɞɚ, ɬɨ ɜɩɟɪɟɞɢ ɞɨɩɢɫɵɜɚɟɦ ɧɨɥɶ (ɬɚɛɥ. 1.5).

ǺȈȉȓȐȞȈ 1.5

Ɍɟɩɟɪɶ ɪɚɡɨɛɶɟɦ ɢɫɯɨɞɧɨɟ ɞɜɨɢɱɧɨɟ ɱɢɫɥɨ ɧɚ ɝɪɭɩɩɵ ɩɨ 2 ɰɢɮɪɵ (ɞɢɚɞɵ) ɢ ɡɚɦɟɧɢɦ ɢɯ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɦɢ ɱɟɬɜɟɪɢɱɧɵɦɢ ɰɢɮɪɚɦɢ

(ɬɚɛɥ. 1.6).

Ɉɤɨɧɱɚɬɟɥɶɧɨ ɩɨɥɭɱɚɟɦ: 10110000102 230024 .

Ⱦɥɹ ɩɟɪɟɜɨɞɚ 10110000102 ɜ ɜɨɫɶɦɟɪɢɱɧɭɸ ɫɢɫɬɟɦɭ ɫɱɢɫɥɟɧɢɹ ɩɪɟɞɜɚɪɢɬɟɥɶɧɨ ɫɨɫɬɚɜɢɦ ɬɚɛɥɢɰɭ ɫɨɨɬɜɟɬɫɬɜɢɹ ɞɜɨɢɱɧɵɯ ɱɢɫɟɥ ɜɨɫɶɦɟɪɢɱɧɵɦ. Ɍɚɤ ɤɚɤ ɨɫɧɨɜɚɧɢɟ ɜɨɫɶɦɟɪɢɱɧɨɣ ɫɢɫɬɟɦɵ ɪɚɜɧɨ 2n 23 8 , ɬɨ ɤɚɠɞɨɦɭ ɜɨɫɶɦɟɪɢɱɧɨɦɭ ɱɢɫɥɭ ɧɟɨɛɯɨɞɢɦɨ ɩɨɫɬɚɜɢɬɶ

17

ɜ ɫɨɨɬɜɟɬɫɬɜɢɟ ɬɪɟɯɪɚɡɪɹɞɧɨɟ ɞɜɨɢɱɧɨɟ ɱɢɫɥɨ. ȿɫɥɢ ɜ ɡɚɩɢɫɢ ɞɜɨɢɱɧɨɝɨ ɱɢɫɥɚ ɧɟ ɯɜɚɬɚɟɬ ɪɚɡɪɹɞɨɜ, ɬɨ ɜɩɟɪɟɞɢ ɞɨɩɢɫɵɜɚɟɦ ɧɭɥɢ (ɬɚɛɥ. 1.7).

ǺȈȉȓȐȞȈ 1.7

Ɍɟɩɟɪɶ ɪɚɡɨɛɶɟɦ ɢɫɯɨɞɧɨɟ ɞɜɨɢɱɧɨɟ ɱɢɫɥɨ ɧɚ ɝɪɭɩɩɵ ɩɨ 3 ɰɢɮɪɵ (ɬɪɢɚɞɵ) ɢ ɡɚɦɟɧɢɦ ɢɯ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɦɢ ɜɨɫɶɦɟɪɢɱɧɵɦɢ ɰɢɮɪɚɦɢ. Ɋɚɡɛɢɟɧɢɟ ɞɜɨɢɱɧɨɝɨ ɱɢɫɥɚ ɧɚɱɢɧɚɟɦ ɫɩɪɚɜɚ ɧɚɥɟɜɨ. ɋɥɟɞɭɟɬ ɡɚɦɟɬɢɬɶ, ɱɬɨ ɜ ɩɨɫɥɟɞɧɟɣ ɬɪɢɚɞɟ (ɤɪɚɣɧɟɣ ɥɟɜɨɣ ɝɪɭɩɩɟ) ɨɤɚɡɚɥɨɫɶ ɦɟɧɶɲɟ ɬɪɟɯ ɰɢɮɪ, ɩɨɷɬɨɦɭ ɦɵ ɞɨɩɨɥɧɢɥɢ ɟɟ ɧɭɥɹɦɢ (ɬɚɛɥ. 1.8).

ǺȈȉȓȐȞȈ 1.8

ɦɭ ɫɱɢɫɥɟɧɢɹ. Ɍɚɤ ɤɚɤ ɨɫɧɨɜɚɧɢɟ ɲɟɫɬɧɚɞɰɚɬɟɪɢɱɧɨɣ ɫɢɫɬɟɦɵ ɪɚɜɧɨ 2n 24 16 , ɬɨ ɤɚɠɞɨɦɭ ɲɟɫɬɧɚɞɰɚɬɟɪɢɱɧɨɦɭ ɱɢɫɥɭ ɧɟɨɛɯɨɞɢɦɨ ɩɨɫɬɚɜɢɬɶ ɜ ɫɨɨɬɜɟɬɫɬɜɢɟ ɱɟɬɵɪɟɯɪɚɡɪɹɞɧɨɟ ɞɜɨɢɱɧɨɟ ɱɢɫɥɨ. ȿɫɥɢ ɜ ɡɚɩɢɫɢ ɞɜɨɢɱɧɨɝɨ ɱɢɫɥɚ ɧɟ ɯɜɚɬɚɟɬ ɪɚɡɪɹɞɨɜ, ɬɨ ɜɩɟɪɟɞɢ ɞɨɩɢɫɵɜɚɟɦ ɧɭɥɢ (ɬɚɛɥ. 1.9).

ǺȈȉȓȐȞȈ 1.9

Ɍɟɩɟɪɶ ɪɚɡɨɛɶɟɦ ɢɫɯɨɞɧɨɟ ɞɜɨɢɱɧɨɟ ɱɢɫɥɨ ɧɚ ɝɪɭɩɩɵ ɩɨ 4 ɰɢɮɪɵ (ɬɟɬɪɚɞɵ) ɢ ɡɚɦɟɧɢɦ ɢɯ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɦɢ ɲɟɫɬɧɚɞɰɚɬɟɪɢɱɧɵɦɢ ɰɢɮɪɚɦɢ. ȼ ɩɨɫɥɟɞɧɟɣ ɬɟɬɪɚɞɟ (ɤɪɚɣɧɟɣ ɥɟɜɨɣ ɝɪɭɩɩɟ) ɨɤɚɡɚɥɨɫɶ ɦɟɧɶɲɟ ɱɟɬɵɪɟɯ ɰɢɮɪ, ɩɨɷɬɨɦɭ ɦɵ ɞɨɩɨɥɧɢɥɢ ɟɟ ɧɭɥɹɦɢ (ɬɚɛɥ. 1.10).

Ɉɤɨɧɱɚɬɟɥɶɧɨ ɩɨɥɭɱɚɟɦ: 10110000102 2C216 .

ɉɪɢɦɟɪ 23. ɉɟɪɟɜɟɞɟɦ ɱɢɫɥɨ AF8516 ɜ ɞɜɨɢɱɧɭɸ ɫɢɫɬɟɦɭ ɫɱɢɫɥɟɧɢɹ.

Ⱦɥɹ ɩɟɪɟɜɨɞɚ ɱɢɫɥɚ AF8516 ɜ ɞɜɨɢɱɧɭɸ ɫɢɫɬɟɦɭ ɫɱɢɫɥɟɧɢɹ ɜɨɫɩɨɥɶɡɭɟɦɫɹ ɬɚɛɥɢɰɟɣ ɫɨɨɬɜɟɬɫɬɜɢɹ ɞɜɨɢɱɧɵɯ ɢ ɲɟɫɬɧɚɞɰɚɬɟɪɢɱɧɵɯ ɱɢɫɟɥ. Ʉɚɠɞɭɸ ɰɢɮɪɭ ɞɚɧɧɨɝɨ ɲɟɫɬɧɚɞɰɚɬɟɪɢɱɧɨɝɨ ɱɢɫɥɚ AF85B16 ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨ ɡɚɦɟɧɹɟɦ ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɣ ɞɜɨɢɱɧɨɣ ɬɟɬɪɚɞɨɣ ɢɡ ɬɚɛɥɢɰɵ 9. ȼ ɪɟɡɭɥɶɬɚɬɟ ɩɨɥɭɱɚɟɦ ɬɚɛɥ. 1.11:

ǺȈȉȓȐȞȈ 1.11

19

ɉɪɢɦɟɪ 24. ɉɟɪɟɜɟɞɟɦ ɱɢɫɥɨ 11100111,11012 ɜ ɲɟɫɬɧɚɞɰɚɬɟɪɢɱ-

ɧɭɸ ɫɢɫɬɟɦɭ ɫɱɢɫɥɟɧɢɹ.

Ɋɚɡɨɛɶɟɦ ɢɫɯɨɞɧɨɟ ɞɜɨɢɱɧɨɟ ɱɢɫɥɨ ɧɚ ɬɟɬɪɚɞɵ ɫɩɪɚɜɚ ɧɚɥɟɜɨ ɨɬ ɞɟɫɹɬɢɱɧɨɣ ɡɚɩɹɬɨɣ — ɞɥɹ ɰɟɥɨɣ ɱɚɫɬɢ ɱɢɫɥɚ, ɢ ɫɥɟɜɚ ɧɚɩɪɚɜɨ — ɞɥɹ ɞɪɨɛɧɨɣ. Ⱦɚɥɟɟ ɡɚɦɟɧɢɦ ɜɵɞɟɥɟɧɧɵɟ ɬɟɬɪɚɞɵ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɦɢ ɲɟɫɬɧɚɞɰɚɬɟɪɢɱɧɵɦɢ ɰɢɮɪɚɦɢ. Ɉɤɨɧɱɚɬɟɥɶɧɨ ɩɨɥɭɱɚɟɦ:

11100111,11012 E7, D16 .

Ⱥɧɚɥɨɝɢɱɧɨ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɩɟɪɟɜɨɞ ɱɢɫɟɥ ɜ ɞɪɭɝɢɯ ɪɨɞɫɬɜɟɧɧɵɯ ɫɢɫɬɟɦɚɯ ɫɱɢɫɥɟɧɢɹ.

ɉɪɢɦɟɪ 25. ɉɟɪɟɜɟɞɟɦ ɱɢɫɥɨ 11200210112012113 ɜ ɞɟɜɹɬɟɪɢɱɧɭɸ ɫɢɫɬɟɦɭ ɫɱɢɫɥɟɧɢɹ.

Ɍɪɨɢɱɧɚɹ ɢ ɞɟɜɹɬɟɪɢɱɧɚɹ ɫɢɫɬɟɦɵ ɹɜɥɹɸɬɫɹ ɪɨɞɫɬɜɟɧɧɵɦɢ, ɬɚɤ ɤɚɤ ɨɫɧɨɜɚɧɢɹ ɷɬɢɯ ɫɢɫɬɟɦ ɫɱɢɫɥɟɧɢɹ ɪɚɜɧɵ ɡɧɚɱɟɧɢɹɦ ɫɬɟɩɟɧɢ ɱɢɫɥɚ 3.

Ⱦɥɹ ɩɟɪɟɜɨɞɚ 11200210112012113 ɜ ɞɟɜɹɬɟɪɢɱɧɭɸ ɫɢɫɬɟɦɭ ɫɱɢɫɥɟɧɢɹ ɩɪɟɞɜɚɪɢɬɟɥɶɧɨ ɫɨɫɬɚɜɢɦ ɬɚɛɥɢɰɭ ɫɨɨɬɜɟɬɫɬɜɢɹ ɬɪɨɢɱɧɵɯ ɱɢɫɟɥ ɞɟɜɹɬɟɪɢɱɧɵɦ. Ɍɚɤ ɤɚɤ ɨɫɧɨɜɚɧɢɟ ɞɟɜɹɬɟɪɢɱɧɨɣ ɫɢɫɬɟɦɵ ɪɚɜɧɨ 3n 32 9 , ɬɨ ɤɚɠɞɨɦɭ ɞɟɜɹɬɟɪɢɱɧɨɦɭ ɱɢɫɥɭ ɧɟɨɛɯɨɞɢɦɨ ɩɨɫɬɚɜɢɬɶ ɜ ɫɨɨɬɜɟɬɫɬɜɢɟ ɞɜɭɯɪɚɡɪɹɞɧɨɟ ɬɪɨɢɱɧɨɟ ɱɢɫɥɨ (ɬɚɛɥ. 1.12).

Ɍɟɩɟɪɶ ɪɚɡɨɛɶɟɦ ɢɫɯɨɞɧɨɟ ɬɪɨɢɱɧɨɟ ɱɢɫɥɨ ɧɚ ɞɢɚɞɵ ɢ ɡɚɦɟɧɢɦ ɢɯ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɦɢ ɞɟɜɹɬɟɪɢɱɧɵɦɢ ɰɢɮɪɚɦɢ (ɬɚɛɥ. 1.13).

20