Chapter 11 CODES, CONVERTERS, COMPARATORS, AND LOGIC OPERATION PROCESSING CIRCUITS

Transcription

1 Chapter 11 CODES, CONVERTERS, COMPARATORS, AND LOGIC OPERATION PROCESSING CIRCUITS

2 Lesson 2 Unit Distance Code and Gray Code Converters, and ASCII (American Code for Information Interchange) for the alphanumeric characters

3 Outline Unit Distance Code Gray code Gray code generation ASCII Code

4 Number of places where bit changes on increment of decrement of a number When 3 increments to 4, then 8421 B code changes from 0011 to The digits are changing at three places p = 0, 1 as well as 3. [0 to 1, 1 to 0 and 0 to 1] On conversion of analog signal to digital bits, it is more reliable if for each increment or decrement step, the bit change is only at one place. Effect of some misalignment in the sensors can be detected from the signals received from the rotating shaft and is accounted for

5 Outline Unit distance code Gray code Gray code generation ASCII Code

6 Gray Code, Cell number in Karnaugh Map and Miniterm Y3Y2Y1Y0 Corresponding Cell number 0000 gray gray gray gray 2 Miniterm number

7 Gray Code, Cell number in Karnaugh Map and Miniterm Y3Y2Y1Y0 Corresponding Cell number 0110 gray gray gray gray 4 Miniterm number

8 Gray Code, Cell number in Karnaugh Map and Miniterm Y3Y2Y1Y0 Corresponding Cell number Miniterm number 1100 gray gray gray gray 14

9 Gray Code, Cell number in Karnaugh Map and Miniterm Y3Y2Y1Y0 Corresponding Cell number Miniterm number 1010 gray gray gray gray 8

10 Number of places where bit changes on increment of decrement of a number Gray code is unit distance code, when 3 increments to 4, then Gray code changes from 0010 to The digits are changing only at one place p = 3. [0 to 1]

11 Outline Unit distance code Gray code Gray code generation ASCII Code

12 Y3 (msb) of Gray code Y3: 4-bit Gray code Y3 and A in binary number are equal in the truth table. Karnaugh map for the output Y3 shows an octet, and simplifies to Y3 and A

13 Map for Y3 = Σ m(8, 9, 10,11,12, 13, 14, 15) C AB AB 00 AB 01 AB AB

14 Y2 (msb but 1) of Gray code Y2: 4-bit Gray code Y2 and A, B in binary number interrelated by Boolean function: Y2 = A. B + A. B = A XOR B Karnaugh map for the output Y2 shows two quads with offset adjacency. [Refer Gray code table 5 th to 8 th and 13 th to 16 th row. y2 = 1 in all of them.]

15 Map for Y2 = Σ m(8, 9, 10, 11,4, 5, 6, 7 ) C AB AB 00 AB AB 11 AB

16 Y1 (lsb but 1) of Gray code Y1: 4-bit Gray code Y1 and B, C in binary number interrelated by Boolean function: Y1 = B. C+ C. B = B XOR C Karnaugh map for the output Y1 shows two quads, and simplifies to B XOR C

17 Map for Y1 = Σ m(2, 3, 10,11,4, 5, 12, 13 ) C AB AB AB AB AB

18 Y0 (lsb) of Gray code Y0: 4-bit Gray code Y- and D, C in binary number interrelated by Boolean function: Y1 = D. C+ C. D = D XOR C Karnaugh map for the output Y0 shows two quads, and simplifies to D XOR C

19 Map for Y1 = Σ m(1, 5, 13,9,2, 6, 14, 10 ) C AB AB 00 AB AB 11 1 AB

20 Outline Unit distance code Gray code Gray code generation ASCII Code

21 ASCII Code American Code for Information Interchange Computer keyboard Alphanumeric characters a to z, A to Z, 0 to 9 and signs #, $, % and so on. Telephone keypad. Alphanumeric characters are 0 to 9 and signs * and #. ASCII codes now universally used for English characters

22 ASCII Code Maximum significant bit (msb) Bit 7 used as parity bit to check transmission error at the receiver when an ASCII code transfers as a byte on a line or network

23 Unicode For International characters representation, an extension of ASCII code Called 16-bit Unicode

24 ASCII Code Examples Y6Y5Y4Y3Y2Y1Y ascii Corresponding Character SP (space) ! ascii A ascii B ascii

25 ASCII Code Examples Y6Y5Y4Y3Y2Y1Y0 Corresponding Character a ascii ascii Q T ascii [ ascii

26 Summary

27 Unit distance code shows one place bitchange only on increment or decrement of the number Gray code is a unit distance code. MSB is same as 4-bit binary number. Other three bits of Gray code are obtained by XORs of two binary numbers ASCII code represent alphanymeric characters for information interchange and for dispaly devices

28 End of Lesson 2 Unit Distance Code and Gray Code Converters, and ASCII (American Code for Information Interchange) for the alphanumeric characters

29 THANK YOU