補充資料：關於布林代數與邏輯閘physexp.thu.edu.tw/~mengwen/exp-electronics/about_boolean.pdf ·...
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關於布林代數與邏輯閘 - 1 - 補充資料：關於布林代數與邏輯閘 數字系統：十進位（Decimal） 二進位（Binary） 八進位（Octal） 十六進位（Hexadecimal） 十進位 （Decimal） 二進位 （Binary） 二進位轉換成十進位的方法 0 0 0 0 2 × 1 1 0 1 2 × 2 10 1 0 2 2 1 0 × + × 3 11 1 0 2 2 1 1 × +× 4 100 2 1 0 2 2 2 1 0 0 × + × + × 5 101 2 1 0 2 2 2 1 0 1 × + × +× 6 110 2 1 0 2 2 2 1 1 0 × +× + × 7 111 2 1 0 2 2 2 1 1 1 × +× +× 8 1000 3 2 1 0 2 2 1 0 0 0 2 2 × + × + × + × 9 1001 3 2 1 0 2 2 1 0 0 1 2 2 × + × + × +× 10 1010 3 2 1 0 2 2 1 0 1 0 2 2 × + × +× + × 11 1011 3 2 1 0 2 2 1 0 1 1 2 2 × + × +× +× 12 1100 3 2 1 0 2 2 1 1 0 0 2 2 × +× + × + × 13 1101 3 2 1 0 2 2 1 1 0 1 2 2 × +× + × +× 14 1110 3 2 1 0 2 2 1 1 1 0 2 2 × +× +× + × 15 1111 3 2 1 0 2 2 1 1 1 1 2 2 × +× +× +× 16 10000 4 3 2 1 0 2 2 2 2 2 1 0 0 0 0 × + × + × + × + × 32 64 128 二進位數字換成十進位數字：（足碼表示代表的數字系統） 3 2 1 0 8 4 2 1 2 10 1010 1 0 1 0 10 2 2 2 2 = = = = =× + × +× + × =
Transcript of 補充資料：關於布林代數與邏輯閘physexp.thu.edu.tw/~mengwen/exp-electronics/about_boolean.pdf ·...
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Decimal
Binary Octal Hexadecimal
Decimal
Binary
0 0 00 21 1 01 22 10 1 02 21 0 + 3 11 1 02 21 1 + 4 100 2 1 02 2 21 0 0 + + 5 101 2 1 02 2 21 0 1 + + 6 110 2 1 02 2 21 1 0 + + 7 111 2 1 02 2 21 1 1 + + 8 1000 3 2 1 02 21 0 0 02 2 + + + 9 1001 3 2 1 02 21 0 0 12 2 + + + 10 1010 3 2 1 02 21 0 1 02 2 + + + 11 1011 3 2 1 02 21 0 1 12 2 + + + 12 1100 3 2 1 02 21 1 0 02 2 + + + 13 1101 3 2 1 02 21 1 0 12 2 + + + 14 1110 3 2 1 02 21 1 1 02 2 + + + 15 1111 3 2 1 02 21 1 1 12 2 + + + 16 10000 4 3 2 1 02 2 2 2 21 0 0 0 0 + + + + 32 64 128
3 2 1 0
8 4 2 12
10
1010 1 0 1 0
10
2 2 2 2= = = =
= + + +
=
-
- 2 -
3 2 1 0
8 4 2 12
10
1111 1 1 1 1
15
2 2 2 2= = = =
= + + +
=
4 3 2 1 0
16 8 4 2
1
12
0
10000 1 0 0 0 0
2 2 2
6
2 2
1= = = = =
= + + + +
=
10 230 ?=
30 2 15 ...... 015 2 7 ...... 17 2 3 ...... 13 2 1 ...... 11 2 0 ...... 1
= = = = =
10 230 11110= 10 225 ?=
25 2 12 ...... 112 2 6 ...... 06 2 3 ...... 03 2 1 ...... 11 2 0 ...... 1
= = = = =
10 225 11001=
Decimal
Binary
Octal
Hexadecimal 0 0 0 0 1 1 1 1 2 10 2 2 3 11 3 3 4 100 4 4 5 101 5 5 6 110 6 6 7 111 7 7 8 1000 10 8 9 1001 11 9 10 1010 12 A 11 1011 13 B
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Decimal
Binary
Octal
Hexadecimal
12 1100 14 C 13 1101 15 D 14 1110 16 E 15 1111 17 F 16 10000 20 10 32 64 128
Boolean Algrbra 1800 George Boolean
+ A B+ OR A B AND A NOT
1 1A 0A = 0A 1A = 2 0 0 0+ = 0 0 0 = 31 1 1+ = 1 1 1 = 4 0 1 1+ = 0 1 0 =
5 0 1= 1 0=
1 0A A+ = 0 0A = 2 1 1A+ = 1A A = 3 A A A+ = A A A =
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4 1A A+ = 0A A =
5 A A=
1
A B B A+ = + A B B A =
2 ( ) ( )A B C A B C A B C+ + = + + = + + ( ) ( )A B C A B C A B C+ + = + + = + +
3 ( )A B A C A B C + = + ( ) ( )A B A C A B C+ + = + 4 ( )A A B A + = A A B A+ = 5Demorgans theroem
A B A B+ = A B A B = +
1 NOT A
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2 AND A B
3 NAND A B
4 OR A B+
5 NOR A B+
6 XOR AB AB
A B+
=
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7
XNOR
AB ABA B+
=
IC74LS00 74LS00 4 NAND IC
NAND 1
3 4 5 A B
( ) ( )F A B A B A B A B A B A B A B= = + = + =
AND
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A B FV F 0 0 0 0 1 0 1 0 0 1 1 1
2
3 9 A A
6 10 B B
( ) ( )F A A B B A B A B A B= = = + = +
OR
A B FV F 0 0 0 0 1 1 1 0 1 1 1 1
3
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F A A A= = NOT
A B= FV F
0 1 1 0
4
3 9 A A
6 10 B B
8 12 13 ( ) ( )F A A B B=
F A A B B A A B B A B A B A B A B A B A B
A B A B
= = = + = +
= = +
NOR
A B FV F 0 0 1 0 1 0 1 0 0 1 1 0
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5
AND
A B C 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
6
NAND
A B C F 0 0 0 1 0 0 1 1 0 1 0 1 0 1 1 1 1 0 0 1 1 0 1 1 1 1 0 1 1 1 1 0
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7
XOR
A B F 0 0 0 0 1 1 1 0 1 1 1 0
1567 2 NAND XNOR
ICTC4011 TC4011 4 NAND IC
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NAND GateIC74LC00 5V
A B F
0 0 1
0 1 1
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1 0 1
1 1 0
68000 TTL
Transistor-Transistor Logic TTLTTL
74 TTL CMOS TTL CMOS
TTL CMOS TTL
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CMOS TTL TTL
7400 TTL N
CE CC 0 1 74 54
7400
74 0 70 C TTL
54 -55 125 C 74 TTL IC
7400
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1) Low Power L
74L00 2) High Speed H
74H00 S H LS L H L H
Schottky
Intel 8051 LS TTL 1) Schottky LogicS74S00 2) Advanced Schottky LogicAS
74AS00 3) Low Power Schottky Logic
LS74LS00 4) Advanced Low Power Schottky
LogicALS74ALS00 FastF
TTL74F00 CMOSComplementary Metal Oxide Semiconductor TTL CMOS TTL CMOS RCA 40 45 CMOS IC C CMOS 1) CMOSC74C00 2) CMOS Advanced CMOS LogicAC
74AC00 3) CMOS High Speed CMOS LogicHC
74HC00 4) CMOS Advanced High Speed CMOS Logic
AHC74AHC00 TTL
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(mW/Gate) tpd(nsec)
TTL 74 1962 10 10
TTL 74L
1 35
TTL 74H TTL
20 6
TTL 74S
TTL 20 3
TTL 74LS 1970 80 TTL
2 10
(Advanced)LS-TTL 74ALS
1980 LS-TTL
1 4
(Advanced)S-TTL 74AS
1980 S-TTL
20 1.5
FAST 74F 1980 Fairchild TTL
4 2.5
Totem-pole Output 74 IC
Open Collector O.C.
Wired-AND
Tri-state 3-state 0 1 (bus)
Schmitt Trigger 0/1
RC
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IC NAND74007410741274207430 NOR74027427 NOT74047414 AND740874117421 OR7432 XOR7486 XNOR74266 Buffer740774244 BCD()74477448 Full Adders748374283 D D-type Latches74373 Asynchronous Counter7490 Decade7492
TTL 5V TTL
o Hi 2.0V o Low 0.8V
o Hi 2.4V o Low 0.4V
0.4V
1. IC 2. TTL 5V 4.75V 5.25V 3. HI 4. 5.
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