27 10

1 1 1.1............................... 1 1.2................................ 2 2 3 2.1......................................... 3 2.2 10 2.............................. 5 2.3 2 16.............................. 6 2.4...................................... 6 2.5....................................... 8 3 11 3.1..................................... 11 3.2......................................... 13 3.3.................................. 14 3.4............................... 14 3.5.......................................... 15 3.6...................................... 17 3.7..................................... 18 3.8....................................... 21 4 23 4.1............................... 23 4.2............................ 24 4.2.1................................. 24 4.2.2.................................. 24 4.3...................................... 25 4.4..................................... 26 4.5..................................... 26 4.6................................. 27 4.7................................. 28 4.8..................................... 30 i

5 33 5.1....................................... 33 5.2............................... 35 5.3......................................... 37 5.4..................................... 38 5.5 2..................................... 39 5.5.1....................................... 39 5.5.2....................................... 39 5.5.3................. 40 5.6.......................................... 41 5.7.......................................... 42 5.8 ALU........................................... 44 6 47 7 49 7.1 RS.................................. 49 7.1.1 RS....................... 49 7.1.2................................... 49 7.1.3................................... 50 7.1.4.................................. 50 7.1.5 RS-......................... 51 7.2 FF FF....................... 51 7.3 D-FF (Delayed flip flop)................................ 52 7.3.1...................................... 52 7.3.2 D-FF............................. 52 7.3.3 D-FF........................... 55 7.4 JK-FF.......................................... 56 7.5 T-FF (Toggle FF)................................... 59 7.6 FF........................................ 59 8 61 8.1...................................... 61 8.2..................................... 62 8.2.1.............................. 62 8.2.2................................ 63 8.2.3.............................. 63 8.2.4 FF............................... 63 8.2.5............................ 64 8.2.6................................. 66 8.3.................................. 67 ii

9 71 9.1.............................. 71 9.2.................................... 71 9.3 N.................................. 73 10 77 10.1......................................... 77 10.2..................................... 77 10.3...................................... 78 11 83 11.1....................................... 83 11.2................................. 83 11.3............................ 85 11.4......................................... 87 11.5......................................... 89 11.6....................................... 89 11.7......................................... 89 A 93 A.1....................................... 93 A.2...................................... 94 A.3................................. 97 A.4 TTL........................................... 98 A.4.1................................. 98 A.4.2................................... 99 A.4.3........................... 100 A.5 CMOS.......................................... 101 iii

1 1.1 (analog) (digital) (1) 1-1 1-2 (1) 0 1 0 1 1

1.2 2

2 2.1 10 10 (9 10 2 2 (1 2 16 16 (15 16 10 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 2 0, 1 16 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F (radix) n n (1) 16 16 0 9 A F A 10 10 F 10 15 a f (2) 1234 16 1234 10 16 1234 10 1234 10 10 2 2 16 16 10 i 10 i 0 1 3

0 n k 0 n-1 2 i 2 i 16 i 16 i. 0 10 1234 1 10 3 + 2 10 2 + 3 10 1 + 4 10 0 10 3, 10 2, 10 1, 10 0 2 1011 1 2 3 + 0 2 2 + 1 2 1 + 1 2 0 2 3, 2 2, 2 1, 2 0 10 2 1011 10 11 2 10 16 52DE 5 16 3 + 2 16 2 + D 16 1 + E 16 0 16 3, 16 2, 16 1, 16 0 5 16 3 + 2 16 2 + 13 16 1 + 14 16 0 10 21214 16 52DE 10 21214 16 10 2-1 (1) 10 5 2 (2) 10 28 16 2-2 (1) 5 2 5 10 (2) 3 16 5 10 2 1 (bit: binary digit ) MSB 2 (Most Significant Bit ) LSB 2 (Least Significant Bit ) 2 8 8 (byte) MSB 2 n 2 b n 1 b n 2...b i...b 0 b i 0 1 b n 1 2 n 1 + b n 2 2 n 2 +... + b i 2 i +... + b 0 2 0 = n 1 i=0 b i2 i MSB n-1 b n 1 LSB 0 b 0 8 2 10101010 MSB 1 LSB 0 2 2 4

2.4 2 2 n 2 10 1K 2 20 1M 2 30 1G 2 40 1T 2 50 1P 1024 1K 1024K 1M 1048576 1GB(1 ) 2 30 CPU 1GHz 1GHz 10 9 Hz 2 2 n 10 10 n 2.2 10 2 2 10 10 2 10 a m 1 a m 2...a 0 2 b n 1 b n 2...b 0 a m 1 a m 2...a 0 = b n 1 2 n 1 + b n 2 2 n 2 +... + b 0 2 0 2 b n 1 2 n 2 + b n 2 2 n 3 +... + b 1 2 0 b 0 1 b 0 2 b 1 b 0 b n 1 26 2 2 )26 2 )13 0 0 2 ) 6 1 1 2 ) 3 0 2 1 1 3 4 11010 1 a m 1 a m 2...a 0 2 5

10 16 2-3 (1) 3 5 10 5 2 2.3 2 16 2 4 16 1 2 16 2 4 16 16 2 16 4 2 1001 1010 0100 0011 9A43 ABCD 1010 1011 1100 1101 2.4 2 0 1-1010 - 0 1 2 2 2 0 1 n 2 n 1 8, 16, 32, 64 n 2 0 1 n-1 8 2 00110011 +51 10011001-25 2 2 6

2.1: 4 2 2 2 10 10 0000 (0) - 0001 (1) 1111 (-1) 0010 (2) 1110 (-2) 0011 (3) 1101 (-3) 0100 (4) 1100 (-4) 0101 (5) 1011 (-5) 0110 (6) 1010 (-6) 0111 (7) 1001 (-7) - 1000 (-8) 2 n 2 b n 1...b 1 b 0 n { }} { 1 00...00 b n 1...b 1 b 0 2 n b n 1...b 1 b 0 (2.1) b n 1...b 1 b 0 2 n+1 b n 1 b 0 0 n 2 n 2 b n 1 0 {}}{ 2 0 1 0...0 2 2.1 B 2 B B + B = 2 n 0 4 2 2 2.1 n 2 n 1 2 n 1 1 0 1 2 2 1. n 2 0 1 1 0 7 n 1

2. 1 3. n + 1 n 4 2 0001 1110 +1 1111 0000 1111 +1 10000 4bits 0000 m 2 A = a m 1...a 1 a 0 n 2 B = b n 1...b 1 b 0 m < n b 0 b m 1 b i = a i b m b n 1 a m 1 A B b m b n 1 0 A A A A 2 A B B 2 B A B B = 2 n B = 2 n A = 2 n (2 m A) = 2 n 2 m + A = (2 n m 1)2 m + A {}}{ A m B n m 1 1 0...0 8 2 2 16 2 2 00110011 0000000000110011 11110000 1111111111110000 2-4 8 2 2 10 (1) 10101010 (2) 00110011 (3) 11000110 (4) 01001100 2-5 8 2 2 2 (1) 11110000 (2) 00111011 2-6 8 2 2 16 (1) 11010011 (2) 00101001 2 2 5.5 2 2-7 2 (1)10101010+101010101 (2) 11011011+10111011 (3) 10001011001+10111011 m 1 2.5 0 1 2 A 1000001 1 0110001 8

1000001 A 10 65 2 2 2 ASCII 3 ASCII 1960 4 ASCII 7 2.2 2.2 7 3 4 2 6 1111111 http://ja.wikipedia.org/wiki/ascii ASCII ASCII 1960 5 (JIS X 0201) 7 8 JIS X 0201 JIS X 0201 8 0 ASCII ASCII \ ~ JIS X 0201 Y= 6 1 http://ja.wikipedia.org/wiki/jis X 0201 8 2 JIS (ISO) ISO-2022 JIS JIS X 0208 7 8 2 6800 94 x 94 ( 94 x 94 [1] ) 16 1 JIS 1982 2 wiki http://ja.wikipedia.org/wiki/ 3 American Standard Code for Information Interchange 4 C ( C) 7 0 C C 1000011 7 0 0000011 ETX UNIX C emacs I [ ESC 5 [1] 6 ASCII JIS X 0201 9

2.2: ASCII 3 4 000 001 010 011 100 101 110 111 0000 NUL DLE SP 0 @ P p 0001 SOH DC1! 1 A Q a q 0010 STX DC2 2 B R b r 0011 ETX DC3 # 3 C S c s 0100 EOT DC4 $ 4 D T d t 0101 ENQ NAC % 5 E U e u 0110 ACK SYN & 6 F V f v 0111 BEL ETB 7 G W g w 1000 BS CAN ( 8 H X h x 1001 HT EM ) 9 I Y i y 1010 LF/NL SUB : J Z j z 1011 VT ESC + ; K [ k { 1100 FF FS, < L \ l 1101 CR GS - = M ] m } 1110 SO RS. > N ^ n ~ 1111 SI US /? O _ o DEL MULTI16 OS CP/M-86 JIS( ) JIS JIS X 0208 Unicode UTF [2] [ ] [1] Vol. 45, No. 9, pp. 528-535, 2001 [2] Vol. 45, No. 12, pp. 687-694, 2001 [1],[2] http://kanji.zinbun.kyoto-u.ac.jp/ yasuoka/publications/iscie2001.pdf 10

3 3.1 (Boolean algebra) 1850 George Bool 3 1 yes true T on high 0 no false F off low (1) x, y (2) +,, + 12 (3) f, g (1) x,y, + f = x + y (2) X 1, X 2,..., X n, Y Y = f(x 1, X 2,..., X n ) n 11

3.1: (a) (b) x, y z x, y z 0+0 0 0 0 0 0+1 1 0 1 0 1+0 1 1 0 0 1+1 1 1 1 1 (c) x z 0 1 1 0 z = x + y 3.1(a) z = x y 3.1(b) z = x 3.1(c) (1) 1+1=1 1 1 1 (2) 0,1 2 4 2 n 2 n 3 0 1 z = x + y w z = x + (y w) (NOR) (NAND) (XOR, exclusive OR) C = A + B C = A B C = A B 3.2 12

3.2: (a) (b) (c) x, y z x, y z x, y z 0 + 0 1 0 0 1 0 0 0 0 + 1 0 0 1 1 0 1 1 1 + 0 0 1 0 1 1 0 1 1 + 1 0 1 1 0 1 1 0 (C = A + B) (C = A B) (C=Ā) OR A B C 0 0 0 0 1 1 1 0 1 1 1 1 AND A B C 0 0 0 0 1 0 1 0 0 1 1 1 NOT A C 0 1 1 0 16 2 16 16 f i (x, y) x y f 0 f 1 f 2 f 3 f 4 f 5 f 6 f 7 f 8 f 9 f 10 f 11 f 12 f 13 f 14 f 15 0 0 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 1 0 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 2 5 3-1 5 3.2 13

Ā = A A + 0 = A A + 1 = 1 A + Ā = 1 A 0 = 0 A 1 = A A Ā = 0 A + A = A A A = A A + B = B + A A B = B A A + (B + C) = (A + B) + C A (B C) = (A B) C A (B + C) = A B + A C A + B C = (A + B) (A + C) A + A B = A A (A + B) = A A + Ā B = A + B (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17) (18) 3-2 (3), (7), (8), (11), (15),(18) 3.3 A + B = Ā B A B = Ā + B 3-3 3-4 AND OR OR AND (1)A B, (2)A + B + C, (3)A B C 3.4 14

OR A B C 0 0 0 0 1 1 1 0 1 1 1 1 1 0 1 A 0 B 0 0 1 2 3 4 1 2 Ā B, Ā 1 B 1 C 1 3 A B 4 A B C = Ā B + A B + A B C 1 C = Ā B + A B + A B = Ā B + A B + A B + A B = (Ā + A) B + A ( B + B) = B + A = A + B 2 3 4 5 3-5 1 XOR A B C 0 0 0 0 1 1 1 0 1 1 1 0 3.5 n (0 1) 1 3 3.3 n (0 1) 0 3 3.3 15

3.3: x 0 x 1 x 2 x 0 x 1 x 2 0 0 0 x 0 x 1 x 2 0 0 1 x 0 x 1 x 2 0 1 0 x 0 x 1 x 2 0 1 1 x 0 x 1 x 2 1 0 0 x 0 x 1 x 2 1 0 1 x 0 x 1 x 2 1 1 0 x 0 x 1 x 2 1 1 1 x 0 x 1 x 2 0 0 0 x 0 + x 1 + x 2 0 0 1 x 0 + x 1 + x 2 0 1 0 x 0 + x 1 + x 2 0 1 1 x 0 + x 1 + x 2 1 0 0 x 0 + x 1 + x 2 1 0 1 x 0 + x 1 + x 2 1 1 0 x 0 + x 1 + x 2 1 1 1 x 0 + x 1 + x 2 1 1 C = Ā B + A B 0 0 C = (A + B) (A + B) 3-6 A B C D A B C D 0 0 0 1 1 0 0 1 0 0 1 1 1 0 1 0 0 1 0 1 1 1 0 0 0 1 1 1 1 1 1 0 16

3.6 n F (x 1, x 2,..., x i,..., x n ) F (x 1,..., x i,..., x n ) = x i F (x 1,..., 0,..., x n ) + x i F (x 1,..., 1,..., x n ) x i = 0 =F (x 1,..., 0,..., x n ) =0 F (x 1,..., 0,..., x n ) + 0 F (x 1,..., 1,..., x n ) = F (x 1,..., 0,..., x n ) x i = 1 =F (x 1,..., 1,..., x n ) =1 F (x 1,..., 1,..., x n ) + 1 F (x 1,..., 1,..., x n ) = F (x 1,..., 1,..., x n ) x 1 F (x 1, x 2,..., x n ) = x 1 F (0, x 2,..., x n ) + x 1 F (1, x 2,..., x n ) F (0, x 2,..., x n ) F (1, x 2,..., x n ) x 2 F (x 1, x 2,..., x n ) = x 1 x 2 F (0, 0,..., x n ) + x 1 x 2 F (0, 1,..., x n ) + x 1 x 2 F (1, 0,..., x n ) + x 1 x 2 F (1, 1,..., x n ) x 3 F (x 1, x 2,..., x n ) = x 1 x 2... x n F (0, 0,..., 0) + x 1 x 2... x n F (0, 0,..., 1) +... + x 1 x 2... x n F (1, 1,..., 0) + x 1 x 2... x n F (1, 1,..., 1) 1 F (...) 1 F (...) F (...) 3-7 f = x 1 (x 2 + x 3 ) n F (x 1, x 2,..., x i,..., x n ) F (x 1,..., x i,..., x n ) = (x i + F (x 1,..., 1,..., x n )) (x i + F (x 1,..., 0,..., x n )) 3-8 17

F (x 1, x 2,..., x n ) = (x 1 + x 2 +... + x n + F (1, 1,..., 1)) (x 1 + x 2 +... + x n + F (1, 1,..., 0))... (x 1 + x 2 +... + x n + F (0, 0,..., 1)) (x 1 + x 2 +... + x n + F (0, 0,..., 0)) F (...) 3-9 f = x 1 (x 2 + x 3 ) 3.7 2 2 1 AND 2 2 1 OR 1 1 NOT C = A + B OR D = A + B C E = B C AND D = A + E OR A B C AND E OR D C = Ā B + A B + A B 3 1 3 1 C = A + B 1 2 6 A (B + B) A B + B = 1 B + B = 1 1 3.2 18

2 A, B 0 1 B 0 1 A 0 1 A B A B + A B 1 (A, B) 2 A = 1, B = 1 A = 1, B = 0 1 1 0 1 0 A B 0 1 A B 0 1 0 1 1 1 0 1 0 1 0 1 1 A 1 B 0 1 1 A (B + B) A Ā B + A B + A B Ā B + A B + A B B 0 1 A 0 1 0 1 1 1 1 B 0 1 A 0 1 0 1 1 1 A B 1 A + B 2 (A, B) (0,0), (0,1), (1,0), (1,1) 19

1 L B A L A = 0, B = 0 1 2 2 1 A, B 1 1 1 1 1 2 2 1 2 2 1 1 3 A, B, C 3 A, B 3 3 A B C 0 1 0 1 1 0 0 0 1 1 A, B A + Ā 1 2 A B A + Ā 1 1 B A B C D 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 1 1 0 0 0 1 0 1 1 1 1 0 1 1 1 1 1 1 AB + BC + CA 3 20

A B C 0 1 0 1 1 0 0 0 1 1 0 0 1 0 0 1 1 1 A B C 0 1 0 1 1 0 0 0 1 1 0 0 1 0 0 1 1 1 3 1 4 A, B 2 2 1 2 3 1 2 3 2 1 2 2 4 4 5 4 5 E=0 E=1 A B C D 0 0 1 0 1 1 0 1 0 1 1 0 0 0 1 1 A B C D 0 0 1 0 1 1 0 1 0 1 1 0 0 0 1 1 A B C D 0 0 1 0 1 1 0 1 0 1 1 0 0 0 1 1 5 2 2 3 1 6 3-10 1. f = Ā B C + ĀB C + A BC + ABC 2. f = (A + D)B C + (Ā + C)BD + ( C + D)ĀB 3. f = B C D + ABC + ĀBC + BC D + Ā BC 3.8 BCD BCD 4 2 10 10 10 1 4 2 4 BCD Binary Coded Decimal 21

BCD 10 BCD 10 BCD 0 0000 5 0101 1 0001 6 0110 2 0010 7 0111 3 0011 8 1000 4 0100 9 1001 BCD 1010 1111 (don t care) BCD 1 0 ϕ (BCD ) (BCD ) a 3 a 2 a 1 a 0 a 3 a 2 a 1 a 0 0000 1 1000 1 0001 0 1001 0 0010 1 1010 ϕ 0011 0 1011 ϕ 0100 1 1100 ϕ 0101 0 1101 ϕ 0110 1 1110 ϕ 0111 0 1111 ϕ ϕ ϕ a 0 a 1 0 0 1 1 0 1 1 0 0 0 0 1 1 0 a 3 a 2 0 1 1 1 0 0 1 1 φφ X X 1 0 1 φ X 0 ϕ 0 1 ϕ 0 f = ā 0 ā 3 + ā 0 ā 1 ā 2 0 ϕ 1 f = ā 0 22

4 4.1 A, B C C=A+B A B C 0 0 0 0 1 1 1 0 1 1 1 1 C=A B A B C 0 0 0 0 1 0 1 0 0 1 1 1 C=Ā A C 0 1 1 0 MOSFET CMOSFET TTL CMOSFET CMOS CMOSFET BiCMOS Passive element Active element FET 23

4.2 4.2.1 4.1 抵 抗 抵 抗 電 池 5V V 電 池 5V V?V?V 4.1: 4.2.2 3 4.2 (B) (C) (E) - - 1 0V 5V 4.3 0V 0 5V 1 抵 抗 トランジスタ 電 池 5V B C E V ここに, 適 切 な 電 流 を 流 すと,このトランジス タはスイッチの 働 きをする.( 電 流 を 流 すとス イッチが 閉 じ, 流 さないとスイッチが 開 く.) 4.2: 1 24

抵 抗 抵 抗 電 池 5V B C E V 電 池 5V B C E V スイッチなら 人 間 の 手 で 操 作 し,トランジスタでは, 電 子 回 路 で 制 御 ( 操 作 )する. 4.3: 4.3 4.4 0(=0V) 1(=5V) 1 0 1 0 0 1 0を 入 力 するとスイッチが 開 く 1を 入 力 するとスイッチが 閉 じる 4.4: 4.5 A C C = Ā A C NOT 4.5: 25

4.4 4.6 A, B 2 0 C 0 1 C A B この 図 は,0,0を 入 力 したときのスイッチの 状 態 を 表 している.( 他 の 入 力 の 組 合 せについては 各 自 で 確 認 してください.) 4.6: 4.7 A, B C A B C OR 4.7: 4-1 4.5 4.8 A, B 2 1 C 1 0 この 図 は,1, 1を 入 力 した 時 の スイッチの 状 態 を 表 している. 4.8: 4.9 A, B C 26

A B C AND 4.9: 4-2 MOSFET CMOSFET 4.6 NOR, NAND, XOR 2 C = A + B A B C 0 0 1 0 1 0 1 0 0 1 1 0 C = A B A B C 0 0 1 0 1 1 1 0 1 1 1 0 C = A B A B C 0 0 0 0 1 1 1 0 1 1 1 0 4.10 4.6 C A B 4.10: 4-3 C = A B + Ā B 2 XOR, EOR,EXOR 27

4-4 4.11 A B C A B C A B C NOR NAND XOR 4.11: 3 3 4-5 3 4.7 OR AND NOT, AND, OR, NAND, NOR, XOR NOT 1 1 2 1 XOR 1 1. 2. (a) NOT (b) AND (c) OR A B + Ā B A B Step (a) Step (b) Step (c) 28

NAND NOR A B NAND Ā + B NAND 1 NOT 2 OR 1 1. 2. 2.1 NOT 2.2 2.3 XOR 2.4 2.2, 2.3 A B + C + D A B C D Step 2.1 Step 2.2 Step 2.4 4-6 A B C D 0 0 0 1 0 0 1 0 0 1 0 1 0 1 1 1 1 0 0 0 1 0 1 0 1 1 0 1 1 1 1 1 29

4.8 C = A B C = Ā + B + 3 1 0 Ā, B, C A B C 0 0 0 0 1 0 1 0 0 1 1 1 Ā B C 1 1 1 1 0 1 0 1 1 0 0 0 4.12 0V 0 5V 1 4.5 0V 0 5V 1 1 0 C = A B 4 C = Ā + B 2 この 図 は,1, 1を 入 力 した 時 の スイッチの 状 態 を 表 している. 4.12: ( ) 3 + 4 Ā B C 30

C = A + B C = Ā B 4-7 (NOT) 5 C = A C = Ā (NAND) NAND A B C 0 0 1 0 1 1 1 0 1 1 1 0 (C = A B) NAND 6 C = A B C = F, F = A B NAND NAND Ā B C 1 1 0 1 0 0 0 1 0 0 0 1 C = Ā + B (C = Ā+ B) (NOR) C = A + B C = Ā B 5 6 31

4-8 C = A B + Ā B 2 XOR Ā B C 1 1 1 1 0 0 0 1 0 0 0 1 C = Ā B + Ā B 32

5 (Combinatorial circuit) (Sequential circuit) 5.1 (Encoder) 5.1 0 9 2 0000 1001 2 5.2 10 2 4 5.1 10 1 1 5V 5.1: O 0 5V. encoder O 1 O 2... O 3 Ten Key 5.2: 33

5.1: i 0 i 1 i 2 i 3 i 4 i 5 i 6 i 7 i 8 i 9 o 3 o 2 o 1 o 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 10 o 3 1. o 3 1 i 8 = 1 i 0 = 0... i 7 = 0, i 9 = 0 i 9 = 1 i 0 = 0... i 8 = 0 2 i 0 i 1...i 7 i 8 i 9 i 0 i 1...i 8 i 9 2. o 3 = i 0 i 1...i 7 i 8 i 9 + i 0 i 1...i 8 i 9 i 8 1 1 i 8 = 1 i 8 1 i 9 o 3 o 3 = i 8 + i 9 o 3 = i 8 + i 9 o 2 = i 7 + i 6 + i 5 + i 4 o 1 = i 2 + i 3 + i 6 + i 7 o 0 = i 1 + i 3 + i 5 + i 7 + i 9 5-1 4 34

5.2 2 0 3 5.2 5.2: i 0 i 1 i 2 i 3 o 1 o 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 1 0 1 0 1 1 1 1 0 i 0 i 1 i 2 i 3 o 1 o 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 1 0 0 1 0 1 0 0 1 1 0 1 0 1 0 1 0 1 0 1 1 1 0 1 0 i 0 i 1 i 2 i 3 o 1 o 0 0 0 0 1 1 1 0 0 1 1 1 1 0 1 0 1 1 1 0 1 1 1 1 1 1 0 0 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 o 0 o 1 o 1 = i 3 + i 2 o 0 = i 3 + i 2 i 1 5-2 o 0, o 1 5.2 1. i 3 1 i 2, i 1, i 0 o 1 o 0 1 35

5.3: 10 i 0 i 1 i 2 i 3 i 4 i 5 i 6 i 7 i 8 i 9 o 3 o 2 o 1 o 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 1 0 1 1 0 0 0 0 1 1 0 1 0 0 0 1 1 1 1 0 1 0 0 0 1 1 0 0 1 2. i 2 1 i 1, i 0 o 1 1 3. i 2 0 i 1 1 i 0 o 0 1 1 2 o 1 = i 3 + i 2 1 3 o 0 = i 3 + i 2 i 1 10 10 5.3 5.3 1. i 9 = 1 i 8 = 1 o 3 1 2. i 9 = 0 i 8 = 0 i 7 = 1 i 6 = 1 i 5 = 1 i 4 = 1 o 2 1 3. i 9 = 0 i 8 = 0 i 7 = 1 i 6 = 1 i 9 = 0 i 8 = 0 i 5 = 0 i 4 = 0 i 3 = 1 i 2 = 1 o 1 1 4. i 9 = 1 i 9 = 0 i 8 = 0 i 7 = 1 i 9 = 0 i 8 = 0 i 6 = 0 i 5 = 1 i 9 = 0 i 8 = 0 i 6 = 0 i 4 = 0 i 3 = 1 i 9 = 0 i 8 = 0 i 6 = 0 i 4 = 0 i 2 = 0 i 1 = 1 o 0 1 o 0 = i 9 + i 9 i 8 i 7 + i 9 i 8 i 6 i 5 + i 9 i 8 i 6 i 4 i 3 + i 9 i 8 i 6 i 4 i 2 i 1 36

= i 9 + i 8 i 7 + i 8 i 6 i 5 + i 8 i 6 i 4 i 3 + i 8 i 6 i 4 i 2 i 1 o 1 = i 9 i 8 (i 7 + i 6 ) + i 9 i 8 i 5 i 4 (i 3 + i 2 ) o 2 = i 9 i 8 (i 7 + i 6 + i 5 + i 4 ) o 3 = i 9 + i 8 o 0 a + āb = a + b 5.3 (Decoder) 3 2 1 0 n 2 n 2 10 2 10 4 10 3 5.4 3-to-8 3 8 5.4: 3-to-8 i 2 i 1 i 0 o 0 o 1 o 2 o 3 o 4 o 5 o 6 o 7 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 1 0 0 0 0 0 1 0 0 1 1 0 0 0 0 0 0 0 1 0 1 1 1 0 0 0 0 0 0 0 1 5.4 o 0 = i 2 i 1 i 0 o 1 = i 2 i 1 i 0 o 2 = i 2 i 1 i 0 o 3 = i 2 i 1 i 0 o 4 = i 2 i 1 i 0 o 5 = i 2 i 1 i 0 o 6 = i 2 i 1 i 0 37

i 0 i 1 i 2 i 3 multiplexer (selector) o c 0 c 1 5.3: o 7 = i 2 i 1 i 0 5-3 3-to-8 5.4 4 (i 0...i 3 ) 1 2 n 1 log n n 2 4 c i c 1 c 0 o 0 0 i 0 0 1 i 1 1 0 i 2 1 1 i 3 5.3 00 i 0 o = c 0 c 1 i 0 + c 0 c 1 i 1 + c 0 c 1 i 2 + c 0 c 1 i 3 38

5.5 2 2 5.5.1 2 2 10 4 0101+0110=1011 (5+6=11) 2 2 + + + A B B 2 B B B = 2 n B A+B A B A B A < B A B A < B A B 2 n +A B 2 n +A B = 2 n +A (2 n B) = A+B A B A B A B A B = A (2 n B) = A + B 2 n 0 A + B 2 n A + B n + 1 2 n n n + 1 A B n + A B A 2 B 2 2 A B A B 2 n (A + B ) = 2 n (2 n A + 2 n B) = A + B 2 n A + B n + 1 2 n A B n 2 2 2 5.5.2 2 2 2 2 A B A B = A + ( B) 2 B 2 B A + B 39

A,B A B A B = A + 2 n B 2 n = A + (2 n B) 2 n A B 0 A + (2 n B) 2 n A + (2 n B) n + 1 B 2 2 A < B A + (2 n B) < 2 n A B 2 5.5.3 n n + 1 5.5.2 2 4 2 2 10 8 7 0100 2 0101 2 0100 2 + 0101 2 = 1001 2 4 + 5 = 9 4 + 5 = 7 A B A + B < max( A, B ) 5.5 A B = A + ( B) A B 5.5 5-4 40

5.5: 5.6 2 1 2 1 0 + 0 = 00, 0 + 1 = 01, 1 + 0 = 01, 1 + 1 = 10 2 2 10 1 2 2 1 1 (1) 0 (0) s c 0 s 0 = 0, 0 s 1 = 1, 1 s 0 = 1, 1 s 1 = 0 0 c 0 = 0, 0 c 1 = 0, 1 c 0 = 0, 1 c 1 = 1 a b s c 0 0 0 0 0 1 1 0 1 0 1 0 1 1 0 1 a b s c 1 a = 0 b = 1 a = 1 b = 0 a = 0 ā = 1 a = 0 b = 1 ā b = 1 s = ā b + a b = a b c = a b 41

(Half Adder) c in c out a b c in s c out Full Adder a b c in s c out 0 0 0 0 0 0 0 1 1 0 0 1 0 1 0 0 1 1 0 1 1 0 0 1 0 1 0 1 0 1 1 1 0 0 1 1 1 1 1 1 a = 1 b = 1 c in = 1 1+1+1=11 1 1 s c in 1 4 s = ā b c in + ā b c in + a b c in + a b c in = a b c in (5.1) c out = ā b c in + a b c in + a b c in + a b c in = a b + b c in + c in a (5.2) 5.4 Full Adder n 2 n 2 5.5 c in 0 n 2 5-5 5.7 2 5.5.2 2 1 42

a b c in s a s c out b c in FA c out (a) 論 理 回 路 (b) ブロック 図 5.4: s 0 s 1 s n-1 s s s FA 0 FA 0 1 FA n-1 c c in c out c in c out c in c n out a b a b a b a 0 b 0 a 1 b 1 a n-1 b n-1 5.5: 2 n 43

s 0 s 1 s n-1 add/sub c in ADDER c out a 0 b 0 a 1 b 1 a n-1 b n-1 5.6: 2 n 1 XOR 5.6 ADDER 5.5 b XOR XOR b i add/sub add/sub 0 1 ADDER c in XOR b i b i ADDER 5.8 ALU ALU Arithmetic Logic Unit 4 ALU 5.7 5.8 5.7 1 5.8 n n ALU 1 ctl 1 ctl 0 0 0 0 1 1 0 1 1 5.7 (00 11 5.8(a) c in 5.8(b) \ n n 1 ALU SN74181 SN74 ALU 48 6 44

c in ctl 1 ctl 0 a b ctl 1 ctl 0 00 c in ctl 1 ctl 0 01 out s a b ALU s 10 a c in FA b c out s 11 c out multiplexer c out (a) 論 理 回 路 (b) ブロック 図 5.7: 1 ALU ctl 0 ctl 1 s 0 s 1 s n-1 c0 s c 0 s c 0 s c 1 ALU c 1 0 ALU c 1 1 ALU n-1 c in c out c in c out c in c out a b a b a b c n a b n n ctl 2 ALU n s a 0 b 0 a 1 b 1 a n-1 b n-1 c out (a) ALU 構 成 図 (b) ブロック 図 5.8: n ALU 45

n NOR 2 c n 2 5.5 ALU 46

6 6.1 100 1 金 額 表 示 投 入 口 りんご オレンジ 取 出 口 6.1: 47

, b, b, 2 6 6, 2, 2 6.2: 6.2 6-1 6.2 6-2( ) 30 2 20 48

7 7.1 RS 7.1.1 RS RS-FF(set reset flip flop): RS-FF 7.1 R S Q Q Q Q Q, Q Q R S Q R S Q Q Q Q n, Q n+1 7.1 Q n R S Q n+1 Q n+1 X Q n Q n+1 7-1 7.1 7.1 Q Q 7-2(RS-FF ) 7.1 RS-FF 4 4 7.1: RS 49

S R Q n Q n+1 comment 0 0 0 0 0 0 1 1 0 1 0 0 0 1 1 0 1 0 0 1 1 0 1 1 1 1 0 x 1 1 1 x = S R Q n+1 0 0 Q n 0 1 0 1 0 1 1 1 x 7.1: RS-FF 7.1.2 RS-FF R = 1, S = 1 R S 0 RS = 0 RS-FF RS = 0 7-3 RS-FF 7.1.3 7.1 Q n+1 S R Q n Q n+1 Q n+1 = S RQ n + S R = S RQ n + S R + SR = S RQ n + S = RQ n + S SR = 0 Q n+1 RS-FF 7.1.4 7.2 low T 7.2: 0 high 5 low high high low 50

T f f = 1/T Hz 1 1 1GHz 1 1 nsec 1 1 7.1.5 RS- RS-FF ( ) RS-FF CLK S R Q n+1 0 any any Q n 1 0 0 Q n 1 0 1 0 1 1 0 1 1 1 1 X any (0,1) X RS-FF CLK 1 RS-FF CLK 0 1 CLK high 1 7.3 7.3 CLK 1 S R 2 1 FF RS-FF RS-FF &/. 4 4 7.3: RS-FF 7-4 7.3 1 0 0 1 2 low 51

7.2 FF FF SR-FF high ( ) high low FF 3 FF FF FF FF high low FF FF FF FF 4 setup time hold time 7.4 VHWXSWLPH &/. KROGWLPH 56 1F2I{)2 -L-î 7.4: setup time hold time FF FF FF 7.3 D-FF (Delayed flip flop) 7.3.1 D-FF RS-FF R R = S 7.5 D-FF 3 (trigger) 4 0 0 52

' 4 4 &/. 7.5: D-FF CLK D Q n+1 0 any Q n 1 0 0 1 1 1 any (0,1) D-FF Q n+1 = D 7-5 7.5 7.3.2 D-FF D-FF 7.6 D-FF &/. 4 4 ' 7.6: D-FF CLK D Q n+1 0,1, any Q n 0 0 1 1 any (0,1) 53

CLK setup time hold time Q n+1 = D [ ] 7.7 (a) Q = 1, D = 0, CLK = 0 (b) CLK : 0 1 (c) (b) D CLK : 1 0, D : 0 (d) (b) high D 1 D : 0 1, CLK : 1 (e) (b) D 1 D : 0 1, CLK : 1 0 (f) (d) CLK : 1 0 FF (i)q = 1, D = 1, CLK = 0, (ii)q = 0, D = 0, CLK = 0, (iii)q = 0, D = 1, CLK = 0 7.3.3 D-FF D-FF 7.8 FF 7.8 high low D-FF high RS-FF I 1 low 5 low high low 6 (Q, Q) Q n+1 = D 7-6 7.9 (a) Q = 1, D = 0, CLK = 0 (b) high CLK : 0 1 (c) CLK : 1 0 (d) (c) D 1 D : 0 1 5 (0,1) (1,0) 6 54

4 4 ' &/. 4 4 ' &/. 4 4 ' &/. 4 4 ' &/. 4 4 ' &/. 4 4 ' &/. D E F G H I 7.7: D-FF 55

', tz t 4 4 &/., 7.8: D-FF FF (i)q = 1, D = 1, CLK = 0, (ii)q = 0, D = 0, CLK = 0, (iii)q = 0, D = 1, CLK = 0 7.4 JK-FF JK-FF RS-FF R = 1, S = 1 FF JK-FF S, R J, K CLK J K Q n+1 0 any any Q n 1 0 0 Q n 1 0 1 0 1 1 0 1 1 1 1 Q n any (0,1) FF 7.10 (Q, Q) (G3, G4) CLK = 0, J = 1, K = 1, Q = 1, Q = 0 CLK 0 1 G4 1 G4 0 G3 ( Q 0 )1 Q 1 Q 0 G4 1 G3 0 Q 1 Q 0 G4 0 G3 1... Q 1010... 7.11 56

4 4 ' &/. tz t,, 4 4 ' &/. tz t,, 4 4 ' &/. tz t,, 4 4 ' &/. tz t,, D E F G 7.9: D-FF 57

- 4 &/.. 4 7.10: JK-FF tz t - 4. 4 &/., 7.11: JK-FF 7-7 7.11 JK-FF JK-FF J K Q n Q n+1 0 0 0 0 0 0 1 1 0 1 0 0 0 1 1 0 1 0 0 1 1 0 1 1 1 1 0 1 1 1 1 0 Q n+1 = J KQ n + J KQ n + J KQ n + JKQ n = ( J K + J K)Q n + (J K + JK)Q n = KQ n + JQ n 58

7.5 T-FF (Toggle FF) T-FF JK-FF J=K Q n+1 = T Q n + T Q n 7-8T-FF (i) (ii) (iii) 7.6 FF FF 7.12 FF IC SN74LS74 S CLK R Q Q D CLK Q Q (a) 同 期 式 SR-FF (b)d-ff J CLK K Q Q T CLK Q Q (C)JK-FF (d)t-ff 7.12: FF 59

8 8.1 8.1 f : X Z X Z [ I [ P µ' Á ] Q ««««%XÁ 8.1: 61

S = s 1, s 2,, s l X = x 1, x 2,, x m Z = z 1, z 2,, z n f : X S S g : X S Z M = (S, X, Z, f, g) 8.2 8.2.1 1. 2. [3] 3. FF FF 4. FF 5. [ ]0 1 1 4 1 0 62

V V V V 8.2: 8.1: z x = 0 x = 1 x = 0 x = 1 s0 s0 s1 0 0 s1 s0 s2 0 0 s2 s0 s3 0 0 s3 s0 s3 0 1 11011111001111111 00000011000001111 8.2.2 0 (s0) 1 1 (s1) 1 2 (s2) 1 3 (s3) 8.2 8.1 8.2.3 8.2.4 FF 1 FF 2 m FF 2 m n m log 2 n m FF 4 2 FF 63

I8 : µ'á )) )) &/. 8.3: 8.2: FF FF1 FF2 (Q1) (Q2) s0 0 0 s1 0 1 s2 1 0 s3 1 1 8.3 FF s i 8.2 8.1 8.2 FF 8.3 8.2.5 8.3 FF FF x 8.3: z x = 0 x = 1 (Q 1, Q 2 ) (Q 1, Q 2) (Q 1, Q 2) x = 0 x = 1 s0: (0, 0) (0, 0) (0, 1) 0 0 s1: (0, 1) (0, 0) (1, 0) 0 0 s2: (1, 0) (0, 0) (1, 1) 0 0 s3: (1, 1) (0, 0) (1, 1) 0 1 64

Q = f 1 Q + f 2 Q Q ( )FF Q ( )FF f 1, f 2 Q, Q f 1, f 2 FF 8.3 Q 1 Q 2 8.3 Q 1 = x Q 1 Q 2 + xq 1 Q2 + xq 1 Q 2 = x(q 2 + Q 2 )Q 1 + xq 2 Q1 = xq 1 + xq 2 Q1 Q 2 = x Q 1 Q2 + xq 1 Q2 + xq 1 Q 2 = xq 1 Q 2 + x( Q 1 + Q 1 ) Q 2 = xq 1 Q 2 + x Q 2 FF1 f 1 = x, f 2 = xq 2 FF2 f 1 = xq 1, f 2 = x FF FF RS-FF Q = RQ + S, RS = 0, Q = f 1 Q + f 2 Q S = f(f 1, f 2, Q), R = g(f 1, f 2, Q) 1 Q = RQ+S Q = f 1 Q+f 2 Q R = f1, S = f 2 Q Q = f 1 Q + f 2 Q = f1 Q + f 2 Q + Q Q = (f1 + Q)Q + f 2 Q = f1 QQ + f 2 Q R = f 1 Q, S = f 2 Q RS = f 1 f 2 Q Q = 0 FF D-FF Q = D Q = f 1 Q + f 2 Q D = f 1 Q + f 2 Q JK-FF Q = KQ + J Q Q = f 1 Q + f 2 Q J = f 2, K = f 1 T-FF Q = T Q + T Q Q = f 1 Q + f 2 Q Q = T Q + T Q = T Q + Q T QQ QQ QQ = T Q QQ = T Q QQ + QQ = T Q + T Q = T ( Q + Q) = T Q T = f 1 Q + f 2 Q 1,p.113,,1996 65

8.4: FF FF RS-FF Q = RQ + S, RS = 0 Q = f 1 Q + f 2 Q R = f1 Q, S = f 2 Q D-FF Q = D Q = f 1 Q + f 2 Q D = f1 Q + f 2 Q JK-FF Q = KQ + J Q Q = f 1 Q + f 2 Q J = f2, K = f 1 T-FF Q = T Q + T Q Q = f 1 Q + f 2 Q T = f1 Q + f 2 Q ] [ &/. )) 4 6 &/. 4 5 )) 4 6 &/. 4 5 8.4: 8-1 T-FF 8.4 8.2.6 8.3 FF1 f 1 = x, f 2 = xq 2 FF2 f 1 = xq 1, f 2 = x RS-FF R = f 1 Q, S = f 2 Q F F 1 : S 1 = xq 2 Q1, R 1 = xq 1 F F 2 : S 2 = x Q 2, R 2 = xq 1 Q 2 z = xq 1 Q 2 8.4 8.4 8-2D-FF 8.3 8-3JK-FF 8.3 66

&/. ; 5 6 4 5 6 4 = 8.5: 8-4T-FF 8.3 8.3 2 3 CLK, x, z, S 1, R 1, Q 1, S 2, R 2, Q 2 8.5 x = 11011111 Q 1, Q 2 Q 0 FF X 0 FF 1. FF FF FF 2. FF 8.5 1. R 1 = 0, S 1 = 0 Q 1 0 Q 2 2. 8.4 x 1 S 2 = x Q 2 S 2 = 1 2 timing chart 3 67

LQSXW FORFN ' 4 &. 4 [ 8.6: 8-5 8-2 8-4 FF 10nsec 5nsec FF Q 20nsec 20nsec Q X 8.6 D-FF FF D-FF Q 20nsec 8.5 x R S 20nsec 1 100nsec 20nsec R S 10nsec R S 5nsec Q 0 FF FF max(hold time, Q ) + set up time + 20 + 10 + α = 30 + α nsec α SN74LS74A D-FF (Texas Instruments FF http://focus.ti.com/lit/ds/ symlink/sn74ls74a.pdf SN74LS74A IC 68

8.5: SN74LS74 set up time hold time 20 nsec 5 nsec tplh from clk to Q 13 nsec tplh 0 1 tphl from clk to Q 25 nsec tphl 1 0 69

9 9.1 T 6.2 CLK T-FF 0 9.2 Q 1, Q 2, Q 3 CLK 9.1 Q 1, Q 2, Q 3 3 2 0,1,2,...,7,0,... FF 3 0 7 FF n 0 2 n 1 &/. 7 4 &. 4 7 4 &. 4 7 4 &. 4 )) )) )) 9.1: T-FF FF 9.1: CLK Q 1 0 1 0 1 0 1 0 1 0 Q 2 0 0 1 1 0 0 1 1 0 Q 3 0 0 0 0 1 1 1 1 0 9-1 D-FF 9-2 JK-FF 9-3 RS-FF 9.2 FF 9.3 n FF 71

&/. 4 4 4 4 4 4 4 4 9.2: 9.1 P PP P &/. 4 4 4 4 4 4 4 4 Šq 9.3: FF n CLK FF FF Q 1 Q 2 9.2 9.3 Q 1 Q 2 9.3 JK-FF 9.4 n n + 1 1 n 1 n + 1 JK-FF 1 72

&/. -&. 4. 4 -&. 4. 4 -&. 4. 4 )) )) )) «-&. 4. 4 ))Q 9.4: n JK-FF and FF FF FF FF FF and and 9.3 N N N N FF m log 2 N m 6 0,1,2,...,5,0,... 1 JK-FF FF 3 9.2 9.2: 6 s i : (Q 3, Q 2, Q 1 ) s i : (Q 3, Q 2, Q 1) s 0 : (0, 0, 0) s 1 : (0, 0, 1) s 1 : (0, 0, 1) s 2 : (0, 1, 0) s 2 : (0, 1, 0) s 3 : (0, 1, 1) s 3 : (0, 1, 1) s 4 : (1, 0, 0) s 4 : (1, 0, 0) s 5 : (1, 0, 1) s 5 : (1, 0, 1) s 0 : (0, 0, 0) 9.2 Q 1 = Q 1 Q2 Q3 + Q 1 Q 2 Q3 + Q 1 Q2 Q 3 = Q 1 Q3 + Q 1 Q2 = Q 1 ( Q 3 + Q 2 ) = Q 1 = 0 Q 1 + Q 1 Q 2 = Q 1 Q3 Q 2 + Q 1 Q3 Q2 1 5,4,3,2,1,0,... 73

&/. -&. 4. 4 -&. 4. 4 -&. 4. 4 )) )) )) 9.5: 6 Q 3 = Q 1 Q2 Q 3 + Q 1 Q 2 Q3 9.2 Q 2 Q 3 1 Q 2 + Q 3 = 1 Q 1 JK-FF J = f 2, K = f 1 J 1 = 1, K 1 = 1 J 2 = Q 1 Q3, K 2 = Q 1 Q3 = Q 1 + Q 3 J 3 = Q 1 Q 2, K 3 = Q 1 Q2 = Q 1 + Q 2 9.5 9-4 60 60 = 6 10 6 10 FF 1)10 2)60 3)7 segment LED 7 (led1 led7) 9.6 7 segment LED ( l1 led1 l1 = 1 led1 l1 = 0 ) In In0, In1, In2, In3 l1 74

OHG OHG OHG OHG OHG OHG OHG,QOHGOHGOHGOHGOHGOHGOHG 9.6: 7 LED 75

10 10.1 10.1 D-FF D-FF 10.2 A 0 A n B 0 B n $ $ $ $Q &/. ' 4 &. ' 4 &. ' 4 &. «' 4 &. % % % %Q 10.1: CLK A 0 -A n A B C B 0 -B n A B 10.2: 10-1 JK-FF 6.1 (5M) CK 10.1 10.2 10.3 D-FF D-FF 77

r ƒi r ƒœ t % % % %Q )) )) )) ))Q ' 4 ' 4 ' 4 «' 4 &. &. &. &. 10.3: &/. r ƒi % % % 10.4: 10.4 FF 10-2JK-FF (5M) 10.5 R/L = 1 R/L = 0 10-3 10.5 (10M) 10.3 r ƒœ t 5/ r ƒi % % % % ' 4 ' 4 ' 4 ' 4 &. &. &. &. )) )) )) )) Àr ƒi 10.5: 78

[ ] 1 7 segment LED 16 LED 10-4LED 16 16 0 9, A F A F 10.6 (10M) 10.6: A F led 8 ( x ) x FF s 0 s 1 g (s 1 = 0) x 1 (g = 1) s 1 = 1 x = 1 g = 0 1 79

[ &/. ' 4 4 &. J 10.7: Q g Q x = 0 x = 1 x = 0 x = 1 s 0 : 0 0 1 0 1 s 1 : 1 0 1 0 0 x Q = xq + x Q = x g = x Q D-FF 10.7 (x) 10.8 10.9 10.10 9 &/. ' 4 4 &. [ 10.8: 7 segment LED 10.10 10-5 2 1 1 2 1 2 8 (20M) 80

9 îîîîî 9 LLL 5( LLL J 10.9: 9 îîî 9 $ 5( LLL $ % % % % LLL LLL /('ŸG Á /('ŸG Á 9 ' 4 4 &. [ ' 4 4 &. J &/. 10.10: 81

11 1 11.1 16 Clear 4 10 32 7 segment LED 1. 2. 11.1 2 11.2 11.2 x 0,..., x 9, x a,..., x f 4 (z 3,...,z 0 ) (F ) 1 2 83

H I FOU «HQFRGHU FRQWURO ] ] ] ] ) UHJ FOU UHJ FOU J FO DOXF J FO GLVS GLVS /(' /(' 11.1: 9 &/. ' 4 4 &. [ 11.2: 11.1 z 0 = x 1 + x 3 +... + x f z 1 = x 2 + x 3 +... + x f z 2 = x 4 + x 5 +... + x f z 3 = x 8 + x 9 +... + x f F = x 0 + x 1 +... + x f F 11.3 FF 11.3 F 11.4 11-116 10 10 2 10 84

11.1: x 0 x 1 x 2... x f z 3 z 2 z 1 z 0 F 1 0 0... 0 0 0 0 0 1 0 1 0... 0 0 0 0 1 1 0 0 1... 0 0 0 1 0 1...... 0 0 0... 1 1 1 1 1 1 0 0 0... 0 0 0 0 0 0 H I «] ] ] ] ) HQFRGHU ] ] ] ] ) UHJ h õüo"î 1M s tz.v~ƒonî 11.3: 10 2 2 BCD (Binary Coded Decimal) 11.3 11.1 85

KM ' ' ' ' ' ] ] ] ] ««UHJ ««' ' ' ' ' ' ' ' ' ï- À 1+û,1 >.'-N ) 11.4: ( ) ( ) clr ( ) 86

clr ( ) - a + b + c +... a + b = clr ( ) 3 clr 11.4 11.2 s 0, s 1, s 2, s 3, s 4 1 1 (ϕ ) opff ḡ 1, ḡ 2 : ḡ 3 : opff 3 87

11.2: (action) clr clr s 0 s 1 s 0 s 0 s 0 s 0 s 0 (1) ϕ ϕ ϕ ϕ s 1 s 1 s 2 s 2 s 4 s 0 s 1 (1) (3) (4) (5) (2) s 2 s 3 s 2 s 2 s 4 s 0 s 2 (1) (6) (7) (10) (2) s 3 s 3 s 2 s 2 s 4 s 0 s 3 (1) (8) (9) (10) (2) s 4 s 1 s 2 s 2 s 4 s 0 s 4 (11) (6) (7) ϕ (2) (1) ḡ 1 = 0 (2) cl 1 = 0, cl 2 = 0 (3) opc = 0, aluc = 0, cl 1 = 0, ḡ 2 = 0, ḡ 3 = 0 (4) opc = 1, aluc = 0, cl 1 = 0, ḡ 2 = 0, ḡ 3 = 0 (5) aluc = 0, cl 1 = 0, ḡ 2 = 0 (6) opc = 0, ḡ 3 = 0 (7) opc = 1, ḡ 3 = 0 (8) opc = 0, aluc = opff, cl 1 = 0, ḡ 2 = 0, ḡ 3 = 0 (9) opc = 1, aluc = opff, cl 1 = 0, ḡ 2 = 0, ḡ 3 = 0 (10) aluc = opff, cl 1 = 0, ḡ 2 = 0 (10) aluc = opff, cl 1 = 0, ḡ 2 = 0 (11) ḡ 1 = 0, cl 2 = 0 11.3: Q 3, Q 2, Q 1 F p m e c n s 0 :000 s 1 :100 s 0 :000 s 0 :000 s 0 :000 s 0 :000 s 0 :000 s 1 :100 s 1 :100 s 2 :101 s 2 :101 s 4 :111 s 0 :000 s 1 :100 s 2 :101 s 3 :110 s 2 :101 s 2 :101 s 4 :111 s 0 :000 s 2 :101 s 3 :110 s 3 :110 s 2 :101 s 2 :101 s 4 :111 s 0 :000 s 3 :110 s 4 :111 s 1 :100 s 2 :101 s 2 :101 s 4 :111 s 0 :000 s 4 :111 F p m e c cl 2 g 1 o a cl 1 g 2 g 3 o a cl 1 g 2 g 3 a cl 1 g 2 cl 1 cl 2 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 1 0 1 1 1 0 1 1 1 1 0 1 0 0 0 0 1 1 0 0 0 1 f 1 1 1 1 0 1 0 f 1 1 1 1 f 1 1 1 f 1 1 1 1 1 1 0 0 0 0 1 1 0 0 0 1 0 0 0 1 1 88

cl 1, cl 2 : opc : opff aluc : alu (aluc = 1 aluc = 0 ) 11-2 11.2 11.5 5 3 FF 2 FF 3 clr F, p, m, e, c, n opc, aluc o, a f opff Q 11.3 (F, p, m, e, c, n) 1 0 1 0 0 0 11.6 Q 1 = Q 3 (p + m + e) + Q 3 Q 1 n Q 2 = Q 3 ( Q 2 Q 1 + Q 2 Q1 )F + Q 3 e + Q 3 Q 2 n Q 3 = F + Q 3 (p + m + e + n) g 1 = F g 2 = Q 3 Q1 (p + m) + Q 3 Q 1 Q 2 e g 3 = Q 3 (p + m) opc = Q 3 m aluc = Q 3 Q 2 Q1 f(p + m + e) + Q 3 Q 2 Q 1 fe cl 1 = Q 1 c + Q 3 Q1 (p + m) + Q 3 Q 1 Q 2 e cl 2 = Q 1 c + Q 1 Q 2 Q 3 F 1.1 g 1, g 2, g 3, cl 1, cl 2 11.7 11.5 11.1 control D-FF n n = p + m + e + c 89

11-3 cl 1, cl 2 D-FF FF 4 5 9 16 7 segment LED 8 32 disp1 disp2 4 low low 5 90

S P H F ) Q 4 4 4 4 4 4 4 ) )) ' 4 4 &. 4 4 )) ' 4 4 &. 4 4 )) ' 4 4 &. 4 ' 4 4 &. ' 4 4 &. J J FO FO FON RSII RSF ' 4 J &. 4 I DOXF 11.5: 11.1 91

A A.1 p n A.1 A.1: A.2 0.6V Vz 1 v = V 0 sin(ωt) A.3 R A.4 v R 0 電 圧 が 変 え られる + - A V I 0.6V V I 電 圧 が 変 え られる - + A V Vz V A.2: 1 A.2 R V V/R Vz 93

D v ~ R V V t A.3: A.4: R A.3 R A.2 2 p n 2 n p A.5 1mm pnp npn B C B C n p n p n p E pnp 形 トランジスタ E npn 形 トランジスタ A.5: A.6: A.6 C B E A.7 npn 2 A.7: A.7 n p n 2 pnp 94

3 α 1 α α 0.99 0.95 I B = (1 α)i E, I C = αi E I E I B I C α 1 α 99 19 4 (i c = βi b β ) 5 A.8 V CE I C A 2 V BE I B A 1 V CE A.8: V BE I B A 1 A.9 A.2 V CE A 2 I C I C I B I B7 I B6 I B5 I B4 I B3 I B 大 V BE I B2 I B1 V BES V CE A.9: A.10: I B 3 4 5 95

I C V i R i V BE V CE R C V CC Q S P I B7 I B6 I B5 I B4 I B3 I B2 I B1 I B 大 V CES V CC V CE A.11: A.12: V BE I C A.10 V CE I C I B1 I B7 I B1 = 20µA, I B2 = 40µA, I B3 = 60µA,... A.11 A.10 V CC R C V CE V CE = V CC R C I C V CE 0 I C I C = V CC /R C I C 0 V CE = V CC 2 (V CE = 0, I C = V CC /R C ) (V CE = V CC, I C = 0) A.10 A.12 I B1 S V CE I C Q V CE V CE V CES I B = (V i V BE )/R i V i 6 V i 0V 5V (V CE, I C ) A.12 P Q V i 5V Q I b R i V CC = 5V V i V CE V i 0V 5V V CE 5V V CES V CES = 0 6 µa R i R i 96

A.13: MOSFET G G S (a) n-channel MOS D S D (b) p-channel MOS A.14: MOSFET A.3 (MOSFET) MOSFET Metal-Oxide-Semiconductor Field Effect Transister MOS- FET A.13 7 (source) (gate) (drain) n p n p n 8 n MOSFET n MOS A.14(a) A.15 MOSFET A.13 p n p MOSFET p MOSFET 0V p MOSFET A.14(b) p n 7 A.13 A.17 http://www.jeea.or.jp/course/contents/02107/ 8 97

V Vo Vi A.15: MOSFET A.16: MOSFET A.17: CMOSFET A.16 0V/5V FET A.15 MOSFET n 0V A.17(a) p n MOSFET (b) 5V 0V V CC CMOS(Complementary MOS MOS) A.4 TTL A.4.1 TTL Transistor Transistor Logic NAND NOR NOT IC 2 NAND A.18 98

T1 T4 T2 T3 A.18: NAND IC7400 9 T1 T2 Vcc 0, 0 Vcc T3 T4 T1 0V pn T1 T1 T1 T2 T2 A.11 A.12 T1 Vces 0V T2 T2 (Vc2) 0V T3 T4 V 0 T1 Vcc T1 T2 T2 T2 R3 T3 T3 T2 T3 (Vbes) T2 Vces T4 T4 T3 Vces Vd T4 V 0 0V NAND 9 http://focus.tij.co.jp/jp/lit/ds/symlink/sn7400.pdf T1 T4 99

A.4.2 0V 0.8V 2.0V 5V 0V 0.4V 2.4V 5V A.4.3 A.18 5 5.4 a 1 EXOR 3 AND A.18 T3 T3 T3 T3 T3 Vce T3 1.6mA T3 n T 3 1.6mA 1.6n ma n Vce 0.4V 10 ma Vce 0.4V TTL 16mA 10 1.6mA 1 ma 1.6mA 16mA 10 10 1 T3 T4 TTL T4 400 A 40 A 10 1 T4 10 10 1.6mA 10 r o 1.6n r i mv 100

A.5 CMOS CMOS A.3 CMOS A.3 CMOS 0V 1.5V 3.5V 5V 0V 0.05V 4.95V 5V TTL TTL CMOS TTL CMOS TTL CMOS TTL CMOS CMOS TTL CMOS 101

1. 2. 3. New Text 9 102

10, 3 16, 3 2 10, 21 2, 3 2, 7 2, 7 2, 6 ALU, 44 ASCII, 9 BiCMOS, 23 CMOS, 98 CMOS, 23 D, 52, 52, 52, 65 hold time, 52 JIS X 0201, 9 JIS X 0208, 9 JK, 56, 56, 58, 65 LSB, 4 MOSFET, 97 MSB, 4 npn, 94 N, 73 pnp, 94 RS, 49, 50, 50, 65 setup time, 52 SR, 49 TTL, 99 TTL, 23 T, 59, 59, 65 unicode, 10, 1, 1, 99, 47, 52 D-FF, 53, 24, 94, 33, 64, 89, 40, 3, 39, 41, 16 103

, 18, 3, 14, 49, 33, 22, 50, 67, 18, 97, 14, 39, 42, 14, 24, 94, 96, 15, 15, 100, 44, 47 JIS, 9, 77, 77, 17, 51, 51, 48, 48, 23, 61, 62, 47, 87, 48 FF, 63, 89, 16, 13, 9, 9, 30, 16, 52, 38, 42, 30, 78 MOS, 98, 97, 93, 67, 84, 50, 50, 79, 97, 78, 37, 1, 1, 97, 83, 86, 71, 93, 14, 24, 80 RS, 51, 72, 50, 50, 24, 94 104

, 24, 96, 95, 97, 22, 14, 47, 47, 50, 65, 23, 12, 4, 42, 4, 12, 25, 100, 100, 12, 96, 6, 6, 35, 49, 30, 14, 22, 12, 71, 42, 77, 52, 11, 90, 11, 12, 26, 12, 11, 11, 12, 26, 12, 27, 16, 18, 24, 94, 96, 14, 96, 52 D-FF, 55, 99, 38 105