Monday 22 October 2012

ARITHMETIC FOR COMPUTER AND DIGITAL LOGIC (Nurul Ain Farhana Binti Che Ab Manan)


ARITHMETIC FOR COMPUTER.

Number System Base .

WHAT IS A BASE FOR NUMBER SYSTEM TYPES ?
Most of the numbering system will have a base .



Ø  DECIMAL NUMBER:

*    Base of 10 .
*    The value of the assigned weight is composed by 10 digits starting from 0 until 9 .
*      The positive and negative values are determined by their position weight structure .


Ø  BINARY NUMBER:

*    Base of 10 .
*    The number consists of  0 and 1 digit only.
*     



*      The least significant bit (LSB) and most significant bits                     (MSB) is depends on the size of binary number. 



Ø  HEXADECIMAL NUMBER : 

           *     Base of 16 .
           *    The value of the assigned weight is composed by 16                                 digits starting from 0 until F .
           *    The number is suitable to present in fours bit number .




Ø  BINARY DIVISION

EXAMPLE 1 :

             1)     1010  /  111 = 











    EXAMPLE 2 :

              2)      110 / 10 =










   digital logic

Combinational Circuits
·  A logic block contains no memory and computes the output given the current inputs .
·       It can be defined by three ways:


TRUTH TABLE 

Ø  Show many possible combinations of input values .
Ø  Between the input values and the result of a specific Boolean operator or combinations on the input variables .



EXAMPLE :
                    F = AB’ + A’B

GRAPHICAL SYMBOLS :

Ø Layout of connected gates that represent the logic circuit .

 F = AB’ + A’B

BOOLEAN EQUATIONS :

Ø Boolean function that consists possible combination of inputs that produce an output signal .


BOOLEAN EQUATION FORMS
*    Combinations of variables and operators . Typically , it has one or more inputs and produces an output in the range of 1 or 0 .
*      It can be represent in two forms :

 Sum-of-products (SOP)
 *  Combination of input values that produce 1 is convert into equivalent variables .
  *     SOP is easier to derive from truth table .
  *     TRUTH TABLE : F = AB’ + A’B

 SOP expression : F = (A’B) + (AB) + (A’B) + (AB)


Product-of-sums (POS)
 *   Input combinations that produce 0 in the sum terms and convert it into equivalent variables .
 *   Usually use if more 1 produce in output function .
 *   TRUTH TABLE : F = AB’ + A’B

POS expression : F = (A’B’) + (AB’) + (A’B’) + ( AB’)







                                   KARNAUGH  MAP ..

  • A grid-like representation of a truth table.
  • The rows and column correspond to the possible values of the    function’s input.
  • Each cell represents the output of the functions for those possible inputs.



        # n input  =  2n



 X = (A’D) + (B’D’) + (AB’CD).








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