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

2. Engineer S. A. AHSAN RAJONKHULNA PUBLIC COLLEGE, KHULNA  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. Engineer S. A. AHSAN RAJONKHULNA PUBLIC COLLEGE, KHULNA  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. Engineer S. A. AHSAN RAJONKHULNA PUBLIC COLLEGE, KHULNA  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. Engineer S. A. AHSAN RAJONKHULNA PUBLIC COLLEGE, KHULNA RAHIM will get A+ 11 10 01 00

6. Engineer S. A. AHSAN RAJONKHULNA PUBLIC COLLEGE, KHULNA  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. Engineer S. A. AHSAN RAJONKHULNA PUBLIC COLLEGE, KHULNA  We may also have all the computations based on a couple of operations.  AND  OR  NOT  NAND  NOR

8. Engineer S. A. AHSAN RAJONKHULNA PUBLIC COLLEGE, KHULNA  AND  TRUE AND TRUE >> TRUE  TRUE AND FALSE >> FALSE  FALSE AND TRUE >> FALSE  FALSE AND FALSE >> FALSE  It means ABANDed RESULT 111 100 010 000

9. Engineer S. A. AHSAN RAJONKHULNA PUBLIC COLLEGE, KHULNA  OR  TRUE AND TRUE >> TRUE  TRUE AND FALSE >> TRUE  FALSE AND TRUE >> TRUE  FALSE AND FALSE >> FALSE  It means ABORed RESULT 111 101 011 000

10. Engineer S. A. AHSAN RAJONKHULNA PUBLIC COLLEGE, KHULNA  NOT  NOT of TRUE >> FALSE  NOT of FALSE >> TRUE  It means ANOT 10 01

11. Engineer S. A. AHSAN RAJONKHULNA PUBLIC COLLEGE, KHULNA A A

12. Engineer S. A. AHSAN RAJONKHULNA PUBLIC COLLEGE, KHULNA  AND represented by.  Often A^B is also used.  OR Represented by A+B  NOT Represented by A’

13. Engineer S. A. AHSAN RAJONKHULNA PUBLIC COLLEGE, KHULNA  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. Engineer S. A. AHSAN RAJONKHULNA PUBLIC COLLEGE, KHULNA  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. Engineer S. A. AHSAN RAJONKHULNA PUBLIC COLLEGE, KHULNA  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. Engineer S. A. AHSAN RAJONKHULNA PUBLIC COLLEGE, KHULNA  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. Engineer S. A. AHSAN RAJONKHULNA PUBLIC COLLEGE, KHULNA RAHIM will get A+ Mohim willl get A+ 000 001 010 011 100 101 110 111

18. Engineer S. A. AHSAN RAJONKHULNA PUBLIC COLLEGE, KHULNA XYZ X OR Y OR Z i.e. X+Y+Z 0000 0011 0101 0111 1001 1011 1101 1111

19. Engineer S. A. AHSAN RAJONKHULNA PUBLIC COLLEGE, KHULNA  OR  TRUE AND TRUE >> TRUE  TRUE AND FALSE >> TRUE  FALSE AND TRUE >> TRUE  FALSE AND FALSE >> FALSE  It means ABOR-ed RESULT 111 101 011 000

20. Engineer S. A. AHSAN RAJONKHULNA PUBLIC COLLEGE, KHULNA XYZ X AND Y AND Z i.e. X.Y.Z 0000 0010 0100 0110 1000 1010 1100 1111

21. Engineer S. A. AHSAN RAJONKHULNA PUBLIC COLLEGE, KHULNA  NOT  NOT of TRUE >> FALSE  NOT of FALSE >> TRUE  It means ANOT 10 01

22. Engineer S. A. AHSAN RAJONKHULNA PUBLIC COLLEGE, KHULNA  THESE ARE CALLED GATES  AND GATE  OR GATE  NOT GATE

23. Engineer S. A. AHSAN RAJONKHULNA PUBLIC COLLEGE, KHULNA O/P A B

24. Engineer S. A. AHSAN RAJONKHULNA PUBLIC COLLEGE, KHULNA O/P A C B

25. Engineer S. A. AHSAN RAJONKHULNA PUBLIC COLLEGE, KHULNA O/P A B

26. Engineer S. A. AHSAN RAJONKHULNA PUBLIC COLLEGE, KHULNA O/P A c B

27. Engineer S. A. AHSAN RAJONKHULNA PUBLIC COLLEGE, KHULNA O/P A C B

28. Engineer S. A. AHSAN RAJONKHULNA PUBLIC COLLEGE, KHULNA  NAND GATES  NAND = NOT OF AND  NOR GATE  NOT OF OR

29. Engineer S. A. AHSAN RAJONKHULNA PUBLIC COLLEGE, KHULNA O/P A C B

30. Engineer S. A. AHSAN RAJONKHULNA PUBLIC COLLEGE, KHULNA O/P A c B

31. Engineer S. A. AHSAN RAJONKHULNA PUBLIC COLLEGE, KHULNA XYZ AND OF X Y Z i.e. (X.Y.Z) NOT(AND OF X Y Z) _____ (X.Y.Z) NAND (X,Y,Z) 000011 001011 010011 011011 100011 101011 110011 111100

32. Engineer S. A. AHSAN RAJONKHULNA PUBLIC COLLEGE, KHULNA XYZ X OR Y OR Z NOT OF (X+Y+Z) NOR (A,B,C) 00001 00110 01010 01110 10010 10110 11010 11110

33. Engineer S. A. AHSAN RAJONKHULNA PUBLIC COLLEGE, KHULNA  Exclusive OR Gate  When both the operands are same, the result is 0  When the operands are different, the result is 1. ABXORed RESULT 000 011 101 110

34. Engineer S. A. AHSAN RAJONKHULNA PUBLIC COLLEGE, KHULNA  Exclusive OR Gate

35. Engineer S. A. AHSAN RAJONKHULNA PUBLIC COLLEGE, KHULNA  XNOR = NOT of XOR  A XNOR B = NOT OF (A XOR B)  =

36. Engineer S. A. AHSAN RAJONKHULNA PUBLIC COLLEGE, KHULNA  XNOR ABXORXNOR 0001 0110 1010 1101

37. Engineer S. A. AHSAN RAJONKHULNA PUBLIC COLLEGE, KHULNA  ASCII  American Standard Codes for Information Interchange  128  Then 256  English and Latin

38. Engineer S. A. AHSAN RAJONKHULNA PUBLIC COLLEGE, KHULNA  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. Engineer S. A. AHSAN RAJONKHULNA PUBLIC COLLEGE, KHULNA  EBCDIC  Extended Binary Coded Decimal Interchange Format.  For example: 00000101=Pound Sign

40. Engineer S. A. AHSAN RAJONKHULNA PUBLIC COLLEGE, KHULNA  UNICODE  Sign/Symbol for all the languages.  Now commonly used.  Unicode Consortium.  65,535+ codes

41. Engineer S. A. AHSAN RAJONKHULNA PUBLIC COLLEGE, KHULNA

42. Engineer S. A. AHSAN RAJONKHULNA PUBLIC COLLEGE, KHULNA

43. Engineer S. A. AHSAN RAJONKHULNA PUBLIC COLLEGE, KHULNA

44. Engineer S. A. AHSAN RAJONKHULNA PUBLIC COLLEGE, KHULNA C __ C __ A+B+ C ___________ __ A+B+ C A B

45. Engineer S. A. AHSAN RAJONKHULNA PUBLIC COLLEGE, KHULNA

46. Engineer S. A. AHSAN RAJONKHULNA PUBLIC COLLEGE, KHULNA XYZ __ X __ Y _Z_Z X+Y+Z _____ X+Y+Z X.Y.Z ____ X.Y.Z _ _ _ X+Y+Z _ _ _ X.Y. Z 000111010111 001110100110 010101100110 011100100110 100011100110 101010100110 110001100110 111000101000

47. Engineer S. A. AHSAN RAJONKHULNA PUBLIC COLLEGE, KHULNA

48. Engineer S. A. AHSAN RAJONKHULNA PUBLIC COLLEGE, KHULNA

49. Engineer S. A. AHSAN RAJONKHULNA PUBLIC COLLEGE, KHULNA  Simplification

50. Engineer S. A. AHSAN RAJONKHULNA PUBLIC COLLEGE, KHULNA  Slight Change:

51. Engineer S. A. AHSAN RAJONKHULNA PUBLIC COLLEGE, KHULNA  We have already proved the above…  The equivalent logic circuit has also been designed.  Since, those two are same, it is the same to draw the simplified circuit.

52. Engineer S. A. AHSAN RAJONKHULNA PUBLIC COLLEGE, KHULNA __ A A LOGIC CIRCUIT OF __ A. B. C __ B B C __ A. B. C

53. Engineer S. A. AHSAN RAJONKHULNA PUBLIC COLLEGE, KHULNA  (123.445) 10 = (?) 2 

54. Engineer S. A. AHSAN RAJONKHULNA PUBLIC COLLEGE, KHULNA  (1001011.1100111) 2 =(?) 10

55. Engineer S. A. AHSAN RAJONKHULNA PUBLIC COLLEGE, KHULNA  BINARY SUMMATION  1+1=0 (SUM)  1+1=1 (CARRY)  0+0=0  0+1=1  1+0=1

56. Engineer S. A. AHSAN RAJONKHULNA PUBLIC COLLEGE, KHULNA  BINARY subtraction  1-1=0 (SUM)  1+1=1 (CARRY)  0-0=0  0-1=1

57. Engineer S. A. AHSAN RAJONKHULNA PUBLIC COLLEGE, KHULNA  1100  1000  ______________________  10100

58. Engineer S. A. AHSAN RAJONKHULNA PUBLIC COLLEGE, KHULNA  10100.01  11000.11  ___________________  101101.00

59. Engineer S. A. AHSAN RAJONKHULNA PUBLIC COLLEGE, KHULNA  11001  1001  _______________  10000

60. Engineer S. A. AHSAN RAJONKHULNA PUBLIC COLLEGE, KHULNA  101001.00  11001.11  __________________  1111.01  0-1=1;  Have a borrow from the left of next digit.  This borrow will be added with the left of next.

61. Engineer S. A. AHSAN RAJONKHULNA PUBLIC COLLEGE, KHULNA  COMPLEMENT OF 0 is 1  COMPLEMENT OF 1 is 0

62. Engineer S. A. AHSAN RAJONKHULNA PUBLIC COLLEGE, KHULNA  9-4=5  WITHOUT COMPLEMENT  9 = 1001  -4 = -0100  __________________  101

63. Engineer S. A. AHSAN RAJONKHULNA PUBLIC COLLEGE, KHULNA 9-4=5 WITH COMPLEMENTS 9 = 1001 -4 = 1011 [4= 0100; So, 1’s complement of 4 is 1011 ] __________________ 1 0100 Since, there is carry, there should have 1 plus with the main result. Thus, The result is 0100 +1 ____________ 0101 Since 5=0101, it is proved.