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36.04.02
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2003
621. 397
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3.
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1. :
568510 = 5×103 + 6×102 + 8×101 + 5×100,
= 10, , 0 = 5, 1 = 8, 2 = 6,
3 = 5, , n = 4, .
2. :
3728 = 3×82 + 7×81 + 2×80 = 25010
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= 8 ( ), A: 0 = 2, 1 = 7, 2 = 3; n = 3, .
3. :
4E16 = 4×161 + 14×160 = 7810
= 16 ( ), 0 = E = 14, 1 = 4 ( 0 9 , , 10, 11, 12, 13, 14, 15 , , , D, , F ); n = 2, .
4. :
11012 = 1×23 + 1×22 + 0×21 + 1×20 = 1310
X = 2, , : 0 = 1, 1 = 0, 2 = 1, 3 = 1, n = 4, .
, : 0 1, "", BIT
BI NARY DIG IT " ". bit .
, , . . , - , . , . .
2 , . . , , . , 5310 :
53: 2 = 26 + 1
26: 2 = 13 + 0
13: 2 = 6 + 1
6: 2 = 3 + 0
3: 2 = 1 +1
1: 2 = 0 +1
1 1 0 1 0 12
.
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, , , . , BYTE. 210 = 1024 "" , 1000.
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BCD ( BINARY CODED DECIMAL, - ), 8421, . , , :
5 2 6
526 10 = 0101 0010 0110 BCD
4- 16 , 10 . 6 , - . . BCD :
23, 22, 21, 20 = 8421.
, :
21, 22, 21, 20 = 2421.
910 , BCD, 1001BCD, , , : 1111 .
, 3 (EXCESS 3 CODE). , . , 9 1100, 8×1 + 4×1 + 2×0 + 1×0 = 12, 3 9.
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10, .. 5 ( 0 4) , 5 ( 5 9); , 0 = 0011EX3 9 = 1100EX3, 1 = 0100EX3 8 = 1011EX3 .. 3 , .
(GRAY CODE). , , , , .. .
B, , G :
Gi = Bi Å Bi+1.
G, , B :
Bi = Gi Å Bi+1.
Å , , , , , , ..:
0 Å 0 = 0
0 Å 1 = 1
1 Å 0 = 1
1 Å 1 = 0
:
1 1 0 1 0 1
Å Å Å Å Å
1 0 1 1 1 1
:
1 0 1 1 1 1
Å Å Å Å Å
1 1 0 1 0 1
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2. = 1, = 1, = 1, F = 1, "×", :
F = A×B×C
3. , . . , :
F
0 0 0 0
0 0 1 0
0 1 0 0
0 1 1 0
1 0 0 0
1 0 1 0
1 1 0 0
1 1 1 1
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F = A & B; F = A ^ B; F = A x B; F = A × B; F = AB.
A B:
2:
F
0 0 0
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1 0 0
1 1 1
() , : |
(AND gate) :
: | |
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: F = A v B; F = A + B.
2:
2: F
0 0 0
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1 0 1
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F = ù A; F = A¢, F =`A.
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4.2. , .
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Ȗ : (Sheffer stroke), NAND ( NOT AND).
Ȗ: F = A ½ B; F = A B.
Ȗ A B:
2Ȗ:
F
0 0 1
0 1 1
1 0 1
1 1 0
() , Ȗ : |
Ȗ :
: | |
: | |
: |
Ȗ : (Pierce arrow), NOR ( NOT OR).
Ȗ:
F = A ¯ B; F = A + B.
2Ȗ:
2Ȗ:
F
0 0 1
0 1 0
1 0 0
1 1 0
() , Ȗ : |
Ȗ :
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4.3. ( ) .
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F = `A`` + ` ` + ` + .
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F = (` + +`) (` + + ) ( +` + ) ( + + ).
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4.4.
, F , , :
F
0 0 0 0 1 0 = ```
1 0 0 1 0
2 0 1 0 1 2 = ` `
3 0 1 1 1 3 = `
4 1 0 0 0
5 1 0 1 0
6 1 1 0 0
7 1 1 1 1 7 =
, F , P0, P2, P3 P7 , . F . , F . 0, 2, 3, 7 , , :
F = 0 + 2 + 3 + 7.
0, 2, 3, 7 , .
, , , :
0 = ```; 2 = ` `; 3 = ` ; 7 = .
, :
F = ``` + ` ` +` + .
, .
4.5. .
, ().
+ = + =
( + ) + = ( + ) + () = ()
( + ) = + + () = ( + )( +)
+ = ` ×` × = ` +`
+ = =
= +` = +
+ = ×( + ) =
+` = 1 ×` = 0
+ 0 = × 0 = 0
+ 1 = 1 × 1 =
, , , , .
4.6.
. , , :
1. , , , :
+ +...= ; + +...=;
... = ; ... = .
2. +` = 1, ×` = 0.
3. , .
:
F = ` + ` + ` + =
= ` + ` + ` + + + =
= ` + + ` + + ` + =
= ( +`) + ( +`) + ( +`) =
= + + .
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16 , , 16 , .4.10.1.
`` ` `
``D 1 1
`C D 1 1
C D 1 1
C`D
.4.10.1. 4 .
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4 :
1. F1 = ` ``D1 + A B`C`D2 +`A B`C D3 + A B`C D4 +
+ `A`B C`D5 + `A B C`D6.
`` ` `
``D 11 12 B`C 1,2,3,4
`C D 13 14 `A C`D 5,6
C D
C`D 15 16
F1 = B C + `A C`D
.4.10.2. F1 4 .
F1 15 16 , , B `B. `A C`D. 11, 12, 13 14, A `A, D `D, B C.
.F2 =````D1 +`A B`C`D2 + A B`C`D3 +`A`B C`D4 +`AB C`D5
`` ` `
``D 11 12 13 B`C`D 2,3
`C D `A`D 1,2,4,5
C D
C`D 14 15
F2 =`A`D + B`C`D
.4.10.3. F2 4 .
F2 12 13 , , `. B`C`D. 11, 12, 14 15, , `, `, `A`D. , .
, ( ).
32 , , 32 , .4.10.4. 64 , .4.10.5.
5 :
3. F3 = ````D E1 +`A`B`C D E2 +
+`A`B C`D`E4 +`A B C`D`E5 +`A B C D E6 +
+` D`E7 +`A B`C D E8 +`A B`C D`E9 +
+ A B`C D E10 + A B`C D`E11 + A B C D E12 +
+ D`E13 + A`B`C`D E14 + A`B`C D E15.
```C `` C ` C ` `C `C C ` C ``C
```C `` C ` C ` `C `C C ` C ``C
`D`E 14 15
`D E 11 114
D E 12 16 18 110 112 115
D`E 17 19 111 113
`A C`D E 4,5 B D 6,7,8,9,10,11,12,13
`B`C E 1,2,14,15
F3 = `B`C E 1,2,14,15 +``A C`D E 4,5 + B D 6,7,8,9,10,11,12,13
.4.10.4. F3 5 .
6 :
4. F4 = ````D E`G 1 +`A`B`C D E`G 2 +`A`B C`D E`G 3 +
+`A`B C D E`G 4 +`A B C`D E G 5 +`A B C`D`E G 6 +
+` ``D`E`G 7 +`A B`C`D E`G 8 +`A B`C D E`G 9 +
+`A B`C D`E`G 10 +`A B`C D`E G 11 +`A B`C D E G 12 +
+` ``D E G 13 +`A B`C`D`E G 14 + A B`C`D`E`G 15 +
+ A B`C`D E`G 16 + A B`C D E`G 17 + A B`C D`E`G 18 +
+ ` D`E G 19 + A B`C D E G 20 + A B`C`D E G 21 +
+ A B`C`D`E G 22 + A B C`D E G 23 + A B C`D`E G 24 +
+ ` `D E`G 25 + A`B C D E`G 26 + A`B C`D E`G 27 +
+ A`B`C D E`G 28 + A`B`C D`E G 29.
```C `` C ` C ` `C `C C ` C ``C
`D`E`G 17 115
`D E`G 11 13 18 116 125 127
D E`G 12 14 19 117 126 128
D`E`G 110 118
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: 2016-10-06; !; : 457 |
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==> ...
: 0.485 .