2015下数字逻辑设计第二章

1、Digital DesignDigital Design Principles and Principles and PracticesPracticesDigital DesignDigital Design Principles and Principles and PracticesPracticesBinary Codes for DecimalMost people are accustomed to using Decimal. BCD (Binary-Coded Decimal, 8421 Code)It has 10 valid code words and 6 invalid

2、 code words. Natural code (just like 4-bit binary numbers)Each digit is weighted.DecimalBCD(8421)00000100012001030011401005010160110701118100091001Unused Code Words101010111100110111101111Addition of BCD DigitsBinary Codes for Decimal01100100+11000100000008816+101100110+1010001011001459+100110010010

3、9918+101101000+1100111105914+0101修正修正+6修正修正+6修正修正+69, 无效码字无效码字9, 无效码字无效码字进位进位-10+4进位进位-10+69, 有效码字有效码字9, 无效码字无效码字进位进位-10+8Subtraction of BCD DigitsBinary Codes for Decimal修正修正-6-6MSB有借位，结果无效有借位，结果无效正确正确10011000192- - -0001 01100010- - MSB无借位，结果有效无借位，结果有效01010011853- - -1000 Binary Codes for Decimal

4、2421 CodeDecimal242100000100012001030011401005101161100711018111091111Unused Code Words010101100111100010011010Each digit is weighted.Self-complementingMSB indicates higher/lower part.It has 10 valid code words and 6 invalid code words. Easy to obtain 9s complement.Binary Codes for Decimal Excess-3

5、CodeDecimalExcess-300011101002010130110401115100061001710108101191100Unused Code Words000000010010110111101111Digits isnt weighted.Self-complementing8421 code + 0011It has 10 valid code words and 6 invalid code words. Easy to obtain 9s complement.A wider rang of underflow/overflowMSB indicates highe

6、r/lower part.Use BCD code for a decimal number: A = 1946 8421 code : A = 0001 1001 0100 0110 2421 code : A = 0001 1111 0100 1100 Excess-3 code: A = 0100 1100 0111 1001 Examples: Binary Codes for DecimalBinary Codes for Decimal Biquinary Code (二五混合二五混合码码)DecimalBiquinary001000011010001020100100301010

7、00401100005100000161000010710001008100100091010000Unused Code Words00000000000001000001000000110000101.7-bits Two hot codeFirst 2 bits are one hot code for higher/lower partLast 5 bits are one hot code in the range. Error- detecting property !Binary Codes for Decimal 1-out-of-10 CodeDecimal1-out-of-

8、10010000000001 2 3 4 5 6 7 8 9 Unused Code Words.10-bits One hot codeIt is very useful in control systems.Gray CodeMechanical Encoding1101011000110001110010100 ? ?Four possible values: 000, 001, 010, 0111101011000110001110010100 0 1Gray CodeGray Mechanical Encoding1011111100100001000010110 ? 1Two po

9、ssible values: 001, 011. Both are valid.Property : In each pair of successive code words, only one bit changes.Target: Code for continues changed numbers (in binary system) to prevent wrong code happened in transition time.最高位的最高位的0和和1只改变一次只改变一次!最大数回到最大数回到0也只有一位码元不同也只有一位码元不同!Gray CodeTable 2-10 A co

10、mparison of 3-bit binary code and Gray codeReflected Gray CodeGray Code ConstructingMethod 1：Recursive Constructing01001011The first 2n code words The last 2n code words 0000011110001111The first 2n code words The last 2n code words n+1 bits Gray code, n=0n+1 bits Gray code, n=1n+1 bits Gray code, n

11、=2Gray CodeGray Code ConstructingMethod 2：Direct ConstructingFrom binary number to Gray code The width is same, the MSB is same; From left to right, if a bit in binary number is same as its left bit, the gray bit is 0. If it is different, the gray bit is 1. Examples: Binary number: 1001 0010 Gray co

12、des: 1101 1011Gray CodeTranslation between Gray Code and Binary CodeBinary code: bn-1 bn-2 bn-1 b1 b0Gray code: gn-1 gn-2 gn-1 g1 g0gn-1 = bn-1 0 = bn-1gi = bi+1 bi A = BCA = BCC = A BB = A Cbn-1 = gn-1 0 = gn-1 bi = bi = bi+1gi bi+1gi Character CodesASCII Code128 Keyboard signs , 7-bitCharacter CodesHow are you! 1001000 1101111 1110111 0100000 1100001 1110010 1100101 0100000 1111001 1101111 1110101 0100001 12 characters Transmitting WayParallel way Us