Engineer S. A. AHSAN RAJON Lecturer Department of Computer Science, Khulna Public College, Khulna.

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Presentation transcript:

Engineer S. A. AHSAN RAJON Lecturer Department of Computer Science, Khulna Public College, Khulna.

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+

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

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

Engineer S. A. AHSAN RAJONKHULNA PUBLIC COLLEGE, KHULNA RAHIM will get A

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.

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

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

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

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

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

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’

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+

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+

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

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

Engineer S. A. AHSAN RAJONKHULNA PUBLIC COLLEGE, KHULNA RAHIM will get A+ Mohim willl get A

Engineer S. A. AHSAN RAJONKHULNA PUBLIC COLLEGE, KHULNA XYZ X OR Y OR Z i.e. X+Y+Z

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

Engineer S. A. AHSAN RAJONKHULNA PUBLIC COLLEGE, KHULNA XYZ X AND Y AND Z i.e. X.Y.Z

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

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

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

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

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

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

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

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

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

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

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)

Engineer S. A. AHSAN RAJONKHULNA PUBLIC COLLEGE, KHULNA XYZ X OR Y OR Z NOT OF (X+Y+Z) NOR (A,B,C)

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

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

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

Engineer S. A. AHSAN RAJONKHULNA PUBLIC COLLEGE, KHULNA  XNOR ABXORXNOR

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

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

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

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

Engineer S. A. AHSAN RAJONKHULNA PUBLIC COLLEGE, KHULNA

Engineer S. A. AHSAN RAJONKHULNA PUBLIC COLLEGE, KHULNA

Engineer S. A. AHSAN RAJONKHULNA PUBLIC COLLEGE, KHULNA

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

Engineer S. A. AHSAN RAJONKHULNA PUBLIC COLLEGE, KHULNA

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

Engineer S. A. AHSAN RAJONKHULNA PUBLIC COLLEGE, KHULNA

Engineer S. A. AHSAN RAJONKHULNA PUBLIC COLLEGE, KHULNA

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

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

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.

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

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

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

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

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

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

Engineer S. A. AHSAN RAJONKHULNA PUBLIC COLLEGE, KHULNA    ___________________ 

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

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

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

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

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