chaozhangmail xjtu edu cn 2013 R10 R2 R3
- Slides: 95
数字逻辑电路 任课教师:张超 chaozhang@mail. xjtu. edu. cn 2013
不同进位计数制的数值具有等值关系。参见下表: R=10 R=2 R=3 R=4 R=8 R=16 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 … 0 1 10 11 100 101 110 111 1000 1001 1010 1011 1100 1101 1110 1111 10000 10001 … 0 1 2 10 11 12 20 21 22 100 101 102 110 111 112 120 121 122 … 0 1 2 3 10 11 12 13 20 21 22 23 30 31 32 33 100 101 … 0 1 2 3 4 5 6 7 10 11 12 13 14 15 16 17 20 21 … 0 1 2 3 4 5 6 7 8 9 A B C D E F 10 11 …
⑵ 常用的二进制常数要记住。书P 3 表 1 -2 (R=2) 。 i -7 -6 -5 -4 -3 -2 -1 Ri 0. 0078125 0. 015625 0. 03125 0. 0625 0. 125 0. 5 i 0 1 2 3 4 5 6 Ri 1 2 4 8 16 32 64 ⑶二进制数的单位: 1位二进制数 = 1 b 1 B = 8 b 1 K = 210 1 M = 220 1 G = 230 i 7 8 9 10 11 12 13 Ri 128 256 512 1024 2048 4096 8192
例3 将(1023. 231)4转换成五进制数。 第一步: (1023. 231)4 多项式 替代法 ( ? )10 (1023. 231)4 = (1× 103 +0× 102 +2× 101 +3× 100 +2× 10 -1 +3× 10 -2 +1× 10 -3 )4 = (1× 4 3 + 0× 4 2 + 2× 4 1 + 3× 4 0 + 2× 4 -1 + 3× 4 -2 + 1× 4 -3 )10 = 64 + 0 + 8 + 3 + 0. 5 + 0. 1875 + 0. 015625 = 75. 703125
3. 代码的特点 设:代码表示为 A 3 A 2 A 1 A 0 代码 对应的十进制数值 代码直接按位转换 有权码 (Weighted code) (13)10 = (00010011) BCD 8421码 8 A 3+4 A 2+2 A 1+1 A 0 (1011101010000) BCD = (1750)10 有权码、对 9自补码 (13)10 = (00010011) 2421码 2 A 3+4 A 2+2 A 1+1 A 0 (1110110110000) 2421 = (1750)10 无权码、对 9自补码 (13)10 = (01000110) 余 3码 8 A 3+4 A 2+2 A 1+1 A 0 (100101010000011) 余 3 = (1750)10 -0011
三种十进制数代码的分布图 四位二进制代码 0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011 1100 1101 1110 1111 8421码 0000 0 0001 1 0010 2 0011 3 0100 4 0101 5 0110 6 0111 7 1000 8 1001 9 1010 1011 1100 非 码 1101 区 1110 1111 2421码 0000 0 0001 1 0010 2 0011 3 0100 4 0101 0110 非 0111 码 1000 区 1001 1010 1011 5 1100 6 1101 7 1110 8 1111 9 余 3码 0000 0001 0010 0011 0 0100 1 0101 2 0110 3 0111 4 1000 5 1001 6 1010 7 1011 8 1100 9 1101 1110 1111 非 码 区
但是,当选用典型Gray码设计加 1计数器时,就不会 出现上述情况。如下: 0 1 2 3 4 5 0000 0001 0010 0111 1000 15 6 0101 1001 14 7 0100 1011 1010 1111 1100 13 12 11 10 9 8 Gray码还包括步进码、十进制Gray 码等。参见书 p 15. 表 1-4 。
表 1-4 几种Gray码、步进码和二进制码对照表 十进制数 二进制数 典型Gray 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011 1100 1101 1110 1111 0000 0001 0010 0111 0100 1101 1110 1011 1000 十进制 Gray码⑴ Gray码⑵ 0000 0001 0011 0010 0110 1110 0111 1010 0101 1011 0100 1001 1100 1000 步进码 000001 000111 011110 111000 10000
表 1 -6 “ 8421”海明码 7 6 5 4 3 2 1 B 4 B 3 B 2 P 3 B 1 P 2 P 1 0 0 0 0 1 1 1 2 0 0 1 1 0 0 1 3 0 0 1 1 0 4 0 1 0 1 0 5 0 1 1 0 1 6 0 1 1 0 0 1 1 7 0 1 1 0 0 8 1 0 0 1 1 9 1 0 0 1 1 0 0 位序 N .
低4位代码 (a 4 a 3 a 2 a 1) 高 3位代码(a 7 a 6 a 5) 000 001 010 011 100 101 110 111 0000 NUL DEL SP 0 0001 SOH DC 1 ! 1 A Q a q 0010 STX DC 2 " 2 B R b 0011 ETX DC 3 # 3 C S c s EOT DC 4 $ 4 D T d 0100 0101 0110 0111 @ P E U e ACK SYN & 6 F V f G W BS CAN ( 8 H X HT EM ) 9 I Y 1011 LF SUB * : J 1100 VT ESC + ; K [ 1010 t % 5 , 7 1001 r ENQ NAK BEL ETB 1000 、 p Z g v w h i u x y j z k {
第一章 习题 1. 1 ⑴、⑶、⑸、⑺ 1. 2 (10110111 )B = ( ) 10 (101. 1 )O = ( ) 10 (15 C 38)H = ( (101. 1)H = ( ) 10 1. 3 (1032)H = ( 1. 4 ⑴、⑶、⑸ 1. 5 (57190) 10 = ( )16 (13705. 207) 8 = ( (82. 02) 10 = ( )16 (1234. 56) 8 = ( )B (1234)10 = ( 1. 6 ⑴ 、⑵ 、⑶ 、⑷ 1. 16 1. 17 1. 23 1. 24 1. 25 )B 1. 26 (4321)8 = ( )16 1. 27 )B
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