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).