, . , .
k, , m .
. . .
( ) d A B , 2. V .
, A=100111001 B=011011100. : V(A)=5, V(B)=5. C=A+B=111100101, V(C)=6. , A B d(A,B)=V(C)=6.
1. , , 2t. , , t .
, , , .
2. / .
, . 1 0 , 2 0 1 . / . , .
1. :
1 |
/ . , n . k, :
, , .
, . , , , . , 0 1.
, , , .
|
|
. n , .
, :
,
;
;
.
n, :
2.1.a
n | ||||||||||||||||
1110=10112. . 2.2.a : , .
. k , i k. 7- :
2.1.c
k1 | k2 | 4 | k3 | 3 | 2 | 1 | |
ki ( ); i ( ).
: , 0, 1.
2.1.d
1, 3, 5, 7, 9, 11, 13 | |
2, 3, 6, 7, 10, 11, 14 | |
4, 5, 6, 7, 12, 13, 14 | |
8, 9, 10, 11, 12, 13, 14 |
, 2.2.d ki:
k1 = 1 + 0 + 1 = 0;
k2 = 1 + 1 + 1 = 1;
k3 = 0 + 1 +1 = 0.
0110011 1110.
, . 01100 0 1. , . , 2.2.d:
k1 = 0 + 1 + 0 + 1 = 0 ;
k2 = 1 + 1 + 0+ 1 = 1 ;
k3 = 0 + 0 +0 + 1 = 1 .
, .. 2 + 4 = 6. 6- .
. .
A = 30710 = 1001100112
2.2.a : , .
k1 | k2 | 9 | k3 | 8 | 7 | 6 | k4 | 5 | 4 | 3 | 2 | 1 | |
|
|
k1 = 1 + 0 + 1 + 1 + 0 + 1 = 0;
k2 = 1 + 0 + 1 + 0 + 0 = 0;
k3 = 0 + 0 +1 + 1 + 1 = 1;
k4 = 1 + 0 + 0 + 1 + 1 = 1.
0011001110011.
, 0011001110 1 11. :
k1 = 0 + 1 + 0 + 1 + 1 + 1 + 1 = 1; ;
k2 = 0 + 1 + 0 + 1 + 0 + 1 = 1; ;
k3 = 1 + 0 + 0 +1 + 1 + 1 = 0; ;
k4 = 1 + 1 + 0 + 1 + 1 + 1 = 1 .
1 + 2 + 8 = 11, 11- .
, . . .
. , 160 6. 160 6, 4.
, . , 160 6. 160 7, 6. 1, , 160 6, .
: , , , .
i- (i+x) . , / .
: , , . :
KA = A mod P, KB = B mod P,
KA+B = (A + B) mod P = (KA + KB) mod P,
KA*B = (A * B) mod P = (KA * KB) mod P.
, A, B , :
A | B | A + B | A B | A * B | |
9 |
:
|
KAB = (8 3) mod 9 = 5
KA*B = (8 * 3) mod 9 = 6 .
. A C P, A + C A C.
= 307 mod 9 = 1;
KC = 91 mod 9 = 1;
KA+C = (307+91) mod 9 = 398 mod 9 = 2; ;
KA+C = (1 + 1) mod 9 = 2 mod 9 = 2; ;
KAC = (30791) mod 9 = 216 mod 9 = 0; ;
KAC = (1 1) mod 9 = 0 mod 9 = 0; .
: , , , , .
. A C P, A + C A C.
= (3+0+7) mod 9 = 1;
KC = (9+1) mod 9 = 1;
KA+C = (3+0+7+9+1) mod 9 = 20 mod 9 = 2; ;
KA+C = (1 + 1) mod 9 = 2 mod 9 = 2; ;
KAC = (3+0+791) mod 9 = 0 mod 9 = 0; ;
KAC = (1 1) mod 9 = 0 mod 9 = 0; .
, , .
.. [A] = [A] = [A].
, :
|
|
, , ;
.. [A] = 1 + [A].
() () , , .
. , , , , , .
= 30710 = 1001100112 = 9110 = 10110112
[A] = [A] = [A] = 0|000000100110011
[A]. = 00|00000100110011
[A]. = 00|00000100110011
[A] = 1|000000100110011
[A] = 1|111111011001100
[A]. = 11|11111011001100
[A] = 1|111111011001100+1 = 1|111111011001101
[A]. = 11|11111011001100+1 = 11|11111011001101
[C] = [C] = [C] = 0|000000001011011
[C]. = 00|00000001011011
[C]. = 00|00000001011011
[C] = 1|000000001011011
[C] = 1|111111110100100
[C]. = 11|11111110100100
[C] = 1|111111110100100+1 = 1|111111110100101