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Implementing Combinational networks

Babylon University

The college of science for girls

Logic Design

Experiment (3)

                                    Implementing Combinational

                                                 networks

object:-  To implementing the combinational networks.

Theory:- in this experiment , we will start with an equation that describes a logic

               function and from it determine the circuit required to implement the

               function . As before several experiments will be used to illustrate a general

               procedure.

First:- Let us review two basic conversions regarding Logic equations.

1)whenever a + appears between two or more  terms , such as X+Y+X

               This means these terms are ORed

           2)whenever two or more terms appears XYZ this means that they are ORed

Consider the following example:

       X= AB + CDE

A brief  inspection reveals  that this function is composed of two terms, AB and CDE

With a dodged of five variables the first term is formed by ANDing A with b and the second term is formed by ANDing C,D,and E

These two terms are then ORed to form the function X

These operations are indicated in the structure of the equation (3-1) as follows:-

                                                                           AND (second-level operation)

                             X= AB + CDE   

                                                                              OR (first-level operation)

In should be noted that, in this particular equation, the AND operation forming the two indivitual terms, AB and CDE, musst be formed before the terms can be ORed.

Figure (3-1) illusrate the resulting logic circuit.

Another example consider the following equation

   X= AB` + A`B………………(3-2)

This equation requires three levels to implement it

     NOT

    (third level)                                                    AND (second-level operation)

                                 X=AB` + A`B

                                                                                  OR (first-level operation)

                            Ahmed M. Shhaab

Figure (3-2) a shows a combinational logic circuit that realize equation (3-2) this circuit is known as an exclusive–OR it is widely used because of special arithmetic properties which will be discussed in a later chapter .Because of its wide application it has a special symbol shown in figure (3-2)b , A special  exclusive-OR  operation  symbol      , is often used so that the expression .

   Y= AB` + A`B  can be written as Y=A    B stated as Y="A exclusive-OR B"

PROCEDURE:-

A/   1)connect the circuit as shown in the figure (3-2)a

        2)stat the Truth Table .

       What can you conclude from this Truth Table?

B/  implement the following expression

       X=ACD` + A`B(CD +BC)

      1)state the levels of this expression

      2)implement the circuit knowing the standard logic gates.

      3)state the Truth Table .

     4)minimize the expression ,and then implement it

     5)state the Truth Table of the minimized expression

        What can you conclude from the minimized expression?

Discussion:-

1)state the levels of the following expression and implement it

      X= AB + (CD +EF)

2)implement exclusive-NOR using combinational gates (standard gates)

                                                 second-level

                                                                                  X=AB + CDE(first-level)

                                      Fig (3-1)

Ahmed M. Shhaab

      (third level)           (second-level)                     (first-level)

                               (A)

                                                                             Y=A     B=AB` + A`B

                                 (B)

                               Fig (3-2) A&b

Ahmed M. Shhaab