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1.
1.1.
1) X
1.1
1.2 ->-> ( , , , ) [-2;2]
2) g =
.1.1 g(x)
2.1)
3)
3.1) g
3.2)
.1.2 -
.1.3
X
(enter)
3.3)
3.4)
(enter),
3.5) -> ( , )
3.6) -> ,
X , Y ->
3.7) -> ()
4) (.1.4)
.1.4 g(x)
1.2.
1)
.1.5
2) X :
2.1
2.2 ->-> ( , , , ) [-2;2]
3) y=2sin( x) 3cos( x), z = cos²(2 x) 2sin( x).
.1.6 y(x) z(x)
4)
4.1 y z
.1.7 - -
->
X
(enter)
4.2)
4.3)
(enter),
4.4) -> ( , )
4.5) -> ,
X , Y ->
4.6) -> ()
5) (.1.8)
.1.8 y(x) z(x)
2.
.2.1
.2.2
(.2.3)
.2.3
( , , , );
.2.4 -
( 1 1 2, 2 3);
1) 1
(.2.5)
.2.5 1
2) 2.
(.2.6)
.2.6 2
( );
.2.7 -
( , ).
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- () , .
.2.8
3.
(.3.2) (.3.4)
.3.1-
.3.2-
.3.3
.3.4
1) , , 1--1, 1--2, 1--3.
.3.5 1.1
.3.6 1.1
.3.7 1.2
.3.8- 1.2
.3.9 1.3
.3.10 1.3
2) , , , .
.3.11 2.1
.3.12 2.1
.3.13 2.2
.3.14 2.2
3) , , 1--2, - 1--1.
.3.15 3.1
.3.16 3.1
.3.17 3.2
.3.18 3.2
4) , , , , 1--2.
.3.19 5
.3.20 5
5) , , , , () 1--2.
.3.21 8
.3.22 8
6) , , , , , (3) .
.3.23 10
.3.24 10
7) , , , , , (4) : .
.3.25 14
.3.26 14
8) , , , , , (2) : .
.3.27 18
.3.28 18
9) , , , , , (4) .
.3.29 22
.3.30 22
10) , . , .
.3.31
.3.32-
11) , , , , , , , 3,25.
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.3.33 25
.3.34 25
12) , , , , .
.3.35 29
.3.36 29
13) , , , , 3,75.
.3.37 33
.3.38 33
14) , , , , .
.3.39 35
.3.40 35
4.
:
) , . . .
) , . . 0 .
) .
49812,22₁₀ = 1100001010010100,001₂ 49812,22₁₀ = 141224,160₈
0, | |
0, | |
49812,22₁₀ = 294, 385₁₆
0, | |
5.
.
) 10101001,11001₂ = 1*2^7+1*2^5+1*2^3+1*2^0+1*2^(-1)+1*2^(-2)+1*2(-5)= 169,78125₁₀
( ) . . .
5.1
(0-7) | (0-15) | |||
A | ||||
B | ||||
C | ||||
D | ||||
E | ||||
F | ||||
) 674,7₈ = 110111100,111₂=1*2^2+1*2^3+1*2^4+1*2^5+1*2^7+1*2^8+1*2^(-1) +1*2^(-2) +1*2^(-3)= 443,875₁₀
6 7 4. 7
110 111 100. 111₂
) EDF,51₁₆ = 111011011111,01010001₂=1*2^0+1*2^1+1*2^2+1*2^3+1*2^4+1*2^6+ +1*2^7+1*2^9+ +1*2^10+1*2^11+1*2^(-2) 1*2^(-4) 1*2^(-8)= 3807,31640625₁₀
E D F. 5 1
1110 1101 1111. 0101 0001₂
6.
.
|
|
0 + 0 = 0 0 + 1 = 1 1 + 0 = 1 1 + 1 = 10 | ||||||||
. , , , , . .6.1. , '↶'. 6.1 - 8 | ||||||||
+ | ||||||||
↶0 | ||||||||
↶0 | ↶1 | |||||||
↶0 | ↶1 | ↶2 | ||||||
↶0 | ↶1 | ↶2 | ↶3 | |||||
↶0 | ↶1 | ↶2 | ↶3 | ↶4 | ||||
↶0 | ↶1 | ↶2 | ↶3 | ↶4 | ↶5 | |||
↶0 | ↶1 | ↶2 | ↶3 | ↶4 | ↶5 | ↶6 |
, , .6.2. '↶'.
+ 6 8 5, 3 2 2 A ₁₆ + 1 0 1 0 1 0 0 1 0, 1 0 ₂ + 4 7 7, 6₈
D A 4 8 5, 4 4 6 0 ₁₆ 1 1 0 0 0 0 1 1 0, 1 1 0 1 0₂6 5 1, 5 6₈
D A B 0 A, 7 6 8 A₁₆ 1 0 1 1 0 1 1 0 0 1, 0 1 0 1 0₂ 1 3 5 1,3 6₈
6.2 - 16-
+ | A | B | C | D | E | F | ||||||||||
A | B | C | D | E | F | |||||||||||
A | B | C | D | E | F | ↶0 | ||||||||||
A | B | C | D | E | F | ↶0 | ↶1 | |||||||||
A | B | C | D | E | F | ↶0 | ↶1 | ↶2 | ||||||||
A | B | C | D | E | F | ↶0 | ↶1 | ↶2 | ↶3 | |||||||
A | B | C | D | E | F | ↶0 | ↶1 | ↶2 | ↶3 | ↶4 | ||||||
A | B | C | D | E | F | ↶0 | ↶1 | ↶2 | ↶3 | ↶4 | ↶5 | |||||
A | B | C | D | E | F | ↶0 | ↶1 | ↶2 | ↶3 | ↶4 | ↶5 | ↶6 | ||||
A | B | C | D | E | F | ↶0 | ↶1 | ↶2 | ↶3 | ↶4 | ↶5 | ↶6 | ↶7 | |||
A | B | C | D | E | F | ↶0 | ↶1 | ↶2 | ↶3 | ↶4 | ↶5 | ↶6 | ↶7 | ↶8 | ||
A | A | B | C | D | E | F | ↶0 | ↶1 | ↶2 | ↶3 | ↶4 | ↶5 | ↶6 | ↶7 | ↶8 | ↶9 |
B | B | C | D | E | F | ↶0 | ↶1 | ↶2 | ↶3 | ↶4 | ↶5 | ↶6 | ↶7 | ↶8 | ↶9 | ↶A |
C | C | D | E | F | ↶0 | ↶1 | ↶2 | ↶3 | ↶4 | ↶5 | ↶6 | ↶7 | ↶8 | ↶9 | ↶A | ↶B |
D | D | E | F | ↶0 | ↶1 | ↶2 | ↶3 | ↶4 | ↶5 | ↶6 | ↶7 | ↶8 | ↶9 | ↶A | ↶B | ↶C |
E | E | F | ↶0 | ↶1 | ↶2 | ↶3 | ↶4 | ↶5 | ↶6 | ↶7 | ↶8 | ↶9 | ↶A | ↶B | ↶C | ↶D |
F | F | ↶0 | ↶1 | ↶2 | ↶3 | ↶4 | ↶5 | ↶6 | ↶7 | ↶8 | ↶9 | ↶A | ↶B | ↶C | ↶D | ↶E |
7.
, . . . 6.1 , , . . .
) _ 2 5 1 5 1 4, 4 0₈
5 4 2 5, 5 5 ₈
2 4 3 0 6 6, 6 3₈
) _1 0 1 1 0 1 1 0 0 0, 1 0 0 0 0₂
1 0 1 0 0 1 0 0 1, 1 0 0 1 1 ₂
1 0 1 1 0 0 1 0 0 1 1, 0 0 0 0 1₂
) _E 3 1 6, 2 5 0₁₆
5 8 8 1, F D C₁₆
8 9 4, 2 7 4
8.
.
0 0 = 0
0 1 = 0
1 0 = 0
1 1 = 1
,
.
, , . , (.8.1) . (. 8.2).
. 8.1. 8-
× | ||||||||
) 1 0 1 0 0 1₂
* 1 1 1 0 1 1 ₂
1 0 1 0 0 1
1 0 1 0 0 1
1 0 1 0 0 1
1 0 1 0 0 1
1 0 1 0 0 1.
1 0 0 1 0 1 1 1 0 0 1 1₂
) 1 0 1 1 1 0 0₂
* 1 1 0 1 1 ₂
1 0 1 1 1 0 0
1 0 1 1 1 0 0
1 0 1 1 1 0 0
1 0 1 1 1 0 0.
1 0 0 1 1 0 1 1 0 1 0 0₂
) B C D, 5₁₆
* D5A ₁₆
9 D 9 3 3 E 2₁₆
.8.2 16-
× | A | B | C | D | E | F | ||||||||||
A | B | C | D | E | F | |||||||||||
A | C | E | 1A | 1C | 1E | |||||||||||
C | F | 1B | 1E | 2A | 2D | |||||||||||
C | 1C | 2C | 3C | |||||||||||||
A | F | 1E | 2D | 3C | 4B | |||||||||||
C | 1E | 2A | 3C | 4E | 5A | |||||||||||
E | 1C | 2A | 3F | 4D | 5B | |||||||||||
1B | 2D | 3F | 5A | 6C | 7E | |||||||||||
A | A | 1E | 3C | 5A | 6E | 8C | ||||||||||
B | B | 2C | 4D | 6E | 8F | 9A | A5 | |||||||||
C | C | 3C | 6C | 9C | A8 | B4 | ||||||||||
D | D | 1A | 4E | 5B | 8F | 9C | A9 | B6 | C3 | |||||||
E | E | 1C | 2A | 7E | 8C | 9A | A8 | B6 | C4 | D2 | ||||||
F | F | 1E | 2D | 3C | 4B | 5A | A5 | B4 | C3 | D2 | E1 |
9.
. . 0 , 1 .
, , . , , .
(. twos complement, twos-complement) . , . , 1.
1 , .
. . 1.
A)X =10111
Y=-11110
:
X=0,10111 1,11110
Y=1,11110 0,10111
1,00111
:
X=0,10111 0,10111
Y=1,00001 1,00001
1,11000 1,00111
:
X=0,10111 0,10111
Y=1,00010 1,00010
1,11001 1,00110
1
1,00111
)X=110110
Y=101110
:
X=0,110110
Y=0,101110
:
X=0,110110 0,0110110
Y=0,101110 0,0101110
0,1100100
:
X=0,110110 0,0110110
Y=0,101110 0,0101110
0,1100100
10.
1. . . () 0, 1. . , .
X Y
2. . . , .
X
Z
Y
3. . , .
X
Z
Y
F=(A v B) ʌ (C v D)
10.1
A | B | C | D | A | B | C | D | (A v B) | (C vD) | F=(A v B) ʌ (C v D) |
A
B
C
D
11.
, . , .
1. : () =
.
2. () :
: A V B = B V A
: A&B = B&A
, .
3. () :
: (A v B) v C = A v (Bv C);
: (A&B)&C = A&(B&C).
.
4. () :
: (A v B)&C = (A&C)v(B&C);
: (A&B) v C = (A v C)&(B v C).
.
5. ( ):
: (Av B) = A & B;
: (A& B) = A v B;
6.
: A v A = A;
: A&A = A.
.
7. :
: A v 1 = 1, A v 0 = A;
: A&1 = A, A&0 = 0.
8. : A& A = 0.
, .
9. : A v A = 1.
10. :
: A v (A&B) = A;
: A&(A v B) = A.
11. ():
: (A&B) v (A &B) = B;
: (A v B)&(A v B) = B.
12. ( ):
(A v B) = (Bv A).
(→) = &
&(v)= &
v &=v
, , , , .
F= B ʌ ((B A) ʌ ((BʌA) (BʌA))) = B ʌ ((BvA) ʌ ((BʌA) v (BʌA))) = B ʌ ((B v A) ʌ (B v A v B ʌ A)= B ʌ (((B v A) ʌ B) v ((B v A) ʌ A) v ((B v A) ʌ (B v A)))= B ʌ (⌐B v (A ʌ ⌐B) v(⌐A ʌ ⌐B) v(A ʌ ⌐A)v(⌐BʌA))= B ʌ (⌐B v(A ʌ ⌐B) v(⌐A ʌ ⌐B)) = B ʌ(⌐B v ⌐B ʌ (A v⌐A))= B ʌ⌐B = 0
11.1
A | B | B | (B A) | (BʌA) | (BʌA) | (B ʌ A) (BʌA) | ((B A) ʌ ((BʌA) (BʌA))) | F |
1. .., .. . . .: : -, 2004.