Code conversion

CODE CONVERSION IS A VERY USEFUL TOPIC IN DIGITAL ELECTRONIC. THIS PRESENTATION WILL HELP TO CLEAR THE CONCEPT OF ALL TYPES OF CODE CONVERSIONS.

1. CODE CONVERSION BY :- ALAPAN RANJAN BANERJEE

2. INTRODUCTION The electronics signals are continuous and can have any value over a given range, are called analog signal . The electrical signal which have only two discreet value or level (high and low), is called digital signal . Actual values of the signal are unimportant.

3. BRIEF DESCRIBTION OF DIGITAL SYSTEM In this system, if 0 and 1 refer to the low and high values respectively, the system is termed a positive logic system . On the contrary, if 1 and 0 refer to the low and high values respectively, the system is termed a negative logic system . The signal between 0 and 1 volt can be recognized as binary 0, between 3 and 5 volt can be taken as binary 1. In digital system functions only in two state, i.e. in a binary manner. The voltage is only leveled low or high; its exact value is immaterial.

4. BINARY CODE A binary code r epresents text, computer processor instructions, or any other data using a two-symbol system. The two-symbol system used is often the binary number system's 0 and 1. The binary code assigns a pattern of binary digits, also known as bits, to each character, instruction, etc. For example, a binary string of eight bits can represent any of 256 possible values and can therefore represent a wide variety of different items.

5. CLASSIFICATION OF BINARY CODE

6. THE NUMERIC CODES

7. BCD OR 8421 CODE The Binary-coded Decimal uses the binary number system to specify the decimal numbers 0 to 9. It has four bits. The weights of the first position is 2 (1), the second 2 1 (2), the third 2 2 (4), and the fourth 2 3 (8). Reading from left to right, the weights 8-4-2-1, hence it is called 8421 code. Valid BCD code are : 0000 to 1001 Invalid BCD code are :1010 to 1111

8. EXCESS-3 CODE As the name indicates, the excess-3 represents a decimal number, in binary form, as a number greater than 3. An excess-3 code is obtained by adding 3 to a decimal number. Valid excess-3 code : 0011 to 1100 Invalid excess-3 code :[0000 to 0010] and [1101 to 1111]

9. GRAY CODE The Gray Code belongs to a class of code called minimum-change code, in which only one bit in the code group changes when moving from one step to another step. The Gray Code is a non-weighted code. Therefore it is not suitable arithmetic operations but finds applications in input/output devices and in some types of analog to digital converters.

10. CODE CONVERTERS A code converters is a logic circuits whose bit patterns representing numbers (or characters) in one code and whose outputs are the corresponding representations in another code. Code converters are usually multiple output circuits.

11. The Karnaugh Map The K-map method of solving the logical expressions is referred to as the graphical technique of simplifying Boolean expressions. K-maps are also referred to as 2D truth tables as each K-map is nothing but a different format of representing the values present in a one-dimensional truth table. In K-maps, the rows and the columns of the table use Gray code-labeling which in turn represent the values of the corresponding input variables. This means that each K-map cell can be addressed using a unique Gray Code-Word

12. K-MAP SIMPLIFICATION TECHNIQUE ( using one example )

13. STEP 1: Truth Table / Canonical Expression Leading to Min- or Max-Terms Minterm expansion will be  ∑ m (4,5,7,8,10,11,13,14) + ∑ d  (0,1,2) Maxterm expansion will be ∏ M (3,6,9,12,15)  ·  ∏ D  (0,1,2)

14. STEP 2: Select and Populate K-Map we have to fill the K-map cells with one for each minterm , zero for each maxterm , and X   for Don't Care terms. The procedure is to be repeated for every single output variable.

15. STEP 3: Form the Groups The process has to be initiated by grouping the bits which lie in adjacent cells such that the group formed contains the maximum number of selected bits. This means that for an  n -variable K-map with 2 n cells, The procedure must be applied for all adjacent cells of the K-map, even when they appear to be not adjacent—the top row is considered to be adjacent to the bottom row and the rightmost column is considered to be adjacent to the leftmost column A bit appearing in one group can be repeated in another group provided that this leads to the increase in the resulting group-size. Don’t Care conditions are to be considered for the grouping activity if and only if they help in obtaining a larger group. Otherwise, they are to be neglected. 

16. STEP 4: Simplified Logical Expression   For each of the resulting groups, we have to obtain the corresponding logical expression in terms of the input-variables. This can be done by expressing the bits which are common amongst the Gray code-words which represent the cells contained within the considered group. Thus, Y =  B̅D̅ + A̅C̅ + A̅BD + BC̅D + AB̅C + ACD̅ OR Y = (A+B) (B+C+D̅) (A+C̅+D) (A̅+B̅+C+D) (A̅+B̅+C̅+D̅)

17. STEP 5: System Design

18. BINARY TO GRAY CODE CONVERTER

19. CONVERSION TABLE 4-BIT BINARY 4-BIT GRAY B4 B3 B2 B1 G4 G3 G2 G1 0 0 0 1 1 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1 1 0 0 1 0 1 1 1 0 1 1 1 1 1 0 0 1 1 0 1 1 1 1 0 1 1 1 1 0 0 0 1 1 1 1 0 1 1 0 1 1 1 1 0 1 1 0 0 1 1 0 0 1 1 0 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 0 1 1 0 0

20. K-MAP For G4 (G4=B4) FOR G3 (G3= B4.B3+B3.B4 B4⊕B3) B2B1 B4B3 00 01 11 10 00 01 11 1 1 1 1 10 1 1 1 1 B2B1 B4B3 00 01 11 10 00 01 1 1 1 1 11 10 1 1 1 1

21. K-MAP FOR G2 (G2=B2.B3+B3.B2 B2 ⊕B3) FOR G1 (G1= B2.B3+B3.B2 B2 ⊕B1) B2B1 B4B3 00 01 11 10 00 1 1 01 1 1 11 1 1 10 1 1 B2B1 B4B3 00 01 11 10 00 1 1 01 1 1 11 1 1 10 1 1

22. We can also do this simplification only by observing the conversion table for G1,G2,G3,G4 as follows:- G4=∑m(8,9,10,11,12,13,14,15) G3=∑m(4,5,6,7,8,9,10,11) G2=∑m(4,5,6,7,8,9,10,11,12,13) G1=∑m(1,2,5,6,9,10,13,14)

23. CIRCUIT DIAGRAM

24. GRAY TO BINARY CODE CONVERTER

25. CONVERSION TABLE 4 BIT GRAY 4 BIT BINARY G4 G3 G2 G1 B4 B3 B2 B1 0 0 0 1 1 1 1 1 0 0 1 0 1 1 1 0 1 1 1 1 0 0 1 0 1 1 1 0 1 1 1 1 1 0 0 1 1 0 1 1 1 1 0 1 1 1 1 0 0 0 1 1 1 1 0 1 1 1 1 1 0 1 0 0 1 0 1 1 1 1 1 1 1 1 0 1 1 0 0 1 1 0 1 1 0 0 1 0 1 1 1 1 1 1 0

26. K-MAP FOR B4 =G4 FOR B3= G4.G3+G3.G4 =G4⊕G3 G 2G1 G4G3 00 01 11 10 00 01 11 1 1 1 1 10 1 1 1 1 G2G1 G4G3 00 01 11 10 00 01 1 1 1 1 11 10 1 1 1 1

27. K-MAP FOR B2= G2⊕G3⊕G4 FOR B1=G1⊕G2⊕G3⊕G4 G2G1 G4G3 00 01 11 10 00 1 1 01 1 1 11 1 1 10 1 1 1 1 G2G1 G4G3 00 01 11 10 00 1 1 01 1 1 11 1 1 10 1 1

28. We can also do this simplification only by observing the conversion table for B1,B2,B3,B4 as follows:- B4=∑m(8,9,10,11,12,13,14,15) B3=∑m(4,5,6,7,8,9,10,11) B2=∑m(2,3,4,5,8,9,14,15) B1=∑m(1,2,4,7,8,11,13,14)

29. CIRCUIT DIAGRAM

30. BINARY TO BCD CODE CONVERSION

31. CONVERSION TABLE 4-BIT BINARY 4-BIT BCD B4 B3 B2 B1 Y4 Y3 Y2 Y1 0 0 0 1 1 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1 1 0 0 1 0 1 1 1 0 1 1 1 1 1 0 0 1 1 0 1 1 1 1 0 1 1 1 1 0 0 0 1 1 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1 1 0 0 1 0 1 X X X X X X X X X X X X X X X X X X X X X X X X

32. K-MAP FOR Y4=B4 FOR Y3=B3 B2B1 B4B3 00 01 11 10 00 01 11 X X X X 10 1 1 X X B2B1 B4B3 00 01 11 10 00 1 1 01 1 1 1 1 11 X X X X 10 X X

33. K-MAP FOR Y2=B2 FOR Y1=B1 B2B1 B4B3 00 01 11 10 00 1 1 01 1 1 11 X X X X 10 X X B2B1 B4B3 00 01 11 10 00 1 1 01 1 1 11 X X X X 10 1 X X

34. CIRCUIT DIAGRAM

35. BCD TO EXCESS-3 CODE CONVERSION

36. CONVERSION TABLE 4-BIT BCD 4-BIT EXCESS-3 B4 B3 B2 B1 Y4 Y3 Y2 Y1 0 0 0 1 1 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1 1 0 0 1 0 1 1 1 1 0 0 1 1 1 1 0 1 1 1 1 0 0 1 0 1 1 1 0 1 1 1 1 1 0 0

37. K-MAP FOR Y4= B4+B3.B1+B3.B2 FOR Y3=B3.B1+B3.B2+B3.B2.B1 B2B1 B4B3 00 01 11 10 00 01 1 1 1 11 X X X X 10 1 1 X X B2B1 B4B3 00 01 11 10 00 1 1 1 01 1 11 X X X X 10 1 X X

38. K-MAP FOR Y2= B2.B1+B2.B1 FOR Y1=B2.B1+B2.B1 =B1 B2B1 B4B3 00 01 11 10 00 1 1 01 1 1 11 X X X X 10 1 X X B2B1 B4B3 00 01 11 10 00 1 1 01 1 11 X X X X 10 1 X X

39. CIRCUIT DIAGRAM

40. EXCESS-3 TO BCD CODE CONVERSION

41. CONVERSION TABLE 4-BIT EXCESS-3 4-BIT BCD Y4 Y3 Y2 Y1 B4 B3 B2 B1 1 1 1 0 0 1 1 1 1 0 1 1 1 1 0 0 1 0 1 1 1 0 1 1 1 1 1 0 0 0 0 0 1 1 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1 1 0 0 1 0 1

42. K-MAP FOR B4=Y4(Y3+Y2.Y1) FOR B3=Y3.Y1+Y3.Y2+Y3.Y2.Y1 =Y3 ⊕Y2.Y1 Y2Y1 Y4Y3 00 01 11 10 00 X X X 01 11 1 X X X 10 1 Y2Y1 Y4Y3 00 01 11 10 00 X X X 01 1 11 X X X 10 1 1 1

43. K-MAP FOR B2=Y2 ⊕Y1 FOR B1=Y2.Y1+Y2.Y1 =Y1 Y2Y1 Y4Y3 00 01 11 10 00 X X X 01 1 1 11 X X X X 10 1 1 Y2Y1 Y4Y3 00 01 11 10 00 X X X 01 1 1 11 1 X X X 10 1 X 1

44. CIRCUIT DIAGRAM

45. DEFINETION OF VERIOUS NUMERIC CODE

46. WEIGHTED AND NON-WEIGHTED CODE SEQUEMTIAL CODE SELF COMPLEMENTING CODE CYCLIC CODE REFLECTIVE CODE

47. THE ALPHA NUMERIC CODE

48. ASCII CODE EBCDIC CODE The ASCII code- American Standards Code For Information Interchange is used in most microcomputers by its manufacturers. This code is represented by 7 bit binary combination EBDIC or Extended Binary Coded Decimal Interchange Code is used in IB equipment. It differs from ASCII code only in its grouping for the different alphanumeric characters. It uses 8 bits for each characters.

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