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DIGITAL LOGIC

Engineer S. A. AHSAN RAJON Lecturer Department of Computer Science, Khulna Public College, Khulna. E-mail: ahsan.rajon@gmail.com. DIGITAL LOGIC. TRUE AND FALSE !!!. Rahim will get A+ Karim will get A+ Rahim will not get A+ Karim will not get A+ Rahim Will Get A+

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DIGITAL LOGIC

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  1. Engineer S. A. AHSAN RAJON Lecturer Department of Computer Science, Khulna Public College, Khulna. E-mail: ahsan.rajon@gmail.com DIGITAL LOGIC

  2. TRUE AND FALSE !!! Rahim will get A+ Karim will get A+ Rahim will not get A+ Karim will not get A+ Rahim Will Get A+ Karim will not A+ Rahim will not get A+ Karim will get A+

  3. TRUE AND FALSE => 1 & 0 !!! Rahim will get A+ >> TRUE Karim will get A+ >> TRUE Rahim will get A+ >> FALSE Karim will get A+ >> TRUE Rahim Will Get A+ >> TRUE Karim will get A+ >> FALSE Rahim will get A+ >> FALSE Karim will get A+ >> FALSE

  4. TRUE AND FALSE => 1 & 0 !!! Rahim will get A+  TRUE >> 1 Karim will get A+  TRUE >> 1 Rahim will get A+  FALSE >> 0 Karim will get A+  TRUE >> 1 Rahim Will Get A+  TRUE >> 1 Karim will get A+  FALSE >> 0 Rahim will get A+  FALSE >> 0 Karim will get A+  FALSE >> 0

  5. TRUE AND FALSE => 1 & 0 !!!

  6. TRUE AND FALSE => 1 & 0 !!! • Thus we may define everything with • simply 0 AND 1 • What computer understands is simply TRUE and FALSE. • So, computations based on this binary is sufficient for any computations.

  7. LOGIC GATES • We may also have all the computations based on a couple of operations. • AND • OR • NOT • NAND • NOR

  8. AND • AND • TRUE AND TRUE >> TRUE • TRUE AND FALSE >> FALSE • FALSE AND TRUE >> FALSE • FALSE AND FALSE >> FALSE • It means

  9. OR • OR • TRUE AND TRUE >> TRUE • TRUE AND FALSE >> TRUE • FALSE AND TRUE >> TRUE • FALSE AND FALSE >> FALSE • It means

  10. NOT • NOT • NOT of TRUE >> FALSE • NOT of FALSE >> TRUE • It means

  11. NOT GATE A A

  12. REPRESENTATION AND represented by . Often A^B is also used. OR Represented by A+B NOT Represented by A’

  13. FOR THREE VARIABLES Rahim will get A+ Karim will get A+ Mohim will get A+ Rahim will not get A+ Karim will not get A+ Mohim will get A+ Rahim Will Get A+ Karim will not A+ Mohim will get A+ Rahim will not get A+ Karim will not get A+ Mohim will get A+

  14. FOR THREE VARIABLES Rahim will get A+ Karim will get A+ Mohim will not get A+ Rahim will not get A+ Karim will not get A+ Mohim will not get A+ Rahim Will Get A+ Karim will not A+ Mohim will not get A+ Rahim will not get A+ Karim will not get A+ Mohim will not get A+

  15. FOR THREE VARIABLES Rahim will get A+ >> TRUE >> 1 Karim will get A+ >> TRUE >> 1 Mohim will get A+ >> TRUE >> 1 Rahim will get A+ >> FALSE >> 0 Karim will get A+ >> TRUE >> 1 Mohim will get A+ >> TRUE >> 1 Rahim Will Get A+ >> TRUE >> 1 Karim will get A+ >> FALSE >> 0 Mohim will get A+ >> TRUE >> 1 Rahim will get A+ >> FALSE >> 0 Karim will get A+ >> FALSE >> 0 Mohim will get A+ >> TRUE >> 1

  16. FOR THREE VARIABLES Rahim will get A+ >> TRUE >> 1 Karim will get A+ >> TRUE >> 1 Mohim will get A+ >> FALSE >> 0 Rahim will get A+ >> FALSE >> 0 Karim will get A+ >> TRUE >> 1 Mohim will get A+ >> FALSE >> 0 Rahim Will Get A+ >> TRUE >> 1 Karim will get A+ >> FALSE >> 0 Mohim will get A+ >> FALSE >> 0 Rahim will get A+ >> FALSE >> 0 Karim will get A+ >> FALSE >> 0 Mohim will get A+ >> FALSE >> 0

  17. FOR THREE VARIABLES

  18. OR OF THREE VARIABLES

  19. OR • OR • TRUE AND TRUE >> TRUE • TRUE AND FALSE >> TRUE • FALSE AND TRUE >> TRUE • FALSE AND FALSE >> FALSE • It means

  20. AND OF THREE VARIABLES

  21. NOT • NOT • NOT of TRUE >> FALSE • NOT of FALSE >> TRUE • It means

  22. LOGIC GATES… • THESE ARE CALLED GATES • AND GATE • OR GATE • NOT GATE

  23. TWO INPUT AND GATE A O/P B

  24. THREE INPUT AND GATE A O/P B C

  25. TWO INPUT OR GATE A O/P B

  26. TWO INPUT OR GATE A O/P B c

  27. THREE INPUT AND GATE A O/P B C

  28. OTHER GATES • NAND GATES • NAND = NOT OF AND • NOR GATE • NOT OF OR

  29. THREE INPUT NAND GATE A O/P B C

  30. THREE INPUT NOR GATE A O/P B c

  31. NAND OF THREE VARIABLES

  32. NOR OF THREE VARIABLES

  33. XOR • Exclusive OR Gate • When both the operands are same, the result is 0 • When the operands are different, the result is 1.

  34. XOR Exclusive OR Gate

  35. XNOR Gate… XNOR = NOT of XOR A XNOR B = NOT OF (A XOR B) =

  36. XNOR Gate… XNOR

  37. CODES • ASCII • American Standard Codes for Information Interchange • 128 • Then 256 • English and Latin

  38. CODES • BCD • Binary Coded Decimal • 4 bits • 8421 Code • BCD 1001=(8X1)+(4X0)+(2X0)+(1X1) = DECIMAL 9 • BCD 0010=(8X0)+(4X0)+(2X1)+(1X0) = DECIMAL 2

  39. CODES… • EBCDIC • Extended Binary Coded Decimal Interchange Format. • For example: 00000101=Pound Sign

  40. CODES • UNICODE • Sign/Symbol for all the languages. • Now commonly used. • Unicode Consortium. • 65,535+ codes

  41. Again BOOLEAN ALGEBRA

  42. REVISITING GATES…

  43. LOGIC GATES….

  44. SIMPLE MATH… ___________ __ A+B+ C __ A+B+ C __ C A C B

  45. DE MORGAN’S THEOREM…

  46. BINARY ARITHMETIC…

  47. BOOLEAN ALGEBRA…

  48. BOOLEAN ALGEBRA… Simplification

  49. BOOLEAN ALGEBRA… Slight Change:

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