DIGITAL LOGIC ( PART II )

hye we meet again today,,, now i want to continue the next part of digital logic
check it out..


4.4 COMBINATIONAL CIRCUITS

• Combinations of different gates in one circuit.
• The output depends only on the levels presents at input.
• Do not use any memory.
• Consists of input variables, logic gates and output variables.
• Can be represented in three ways; truth table, graphical symbols and Boolean equations.

From the figure below draw the truth table and state the Boolean equation.

Answer:

From the truth table above we can conclude that the Boolean expression is

 F = [ (A.B) + (C.D)]'

Another example:

Answer:

From the truth table, the Boolean expression;

F = (A'B) + B'A)

4.5 SUM-OF-PRODUCTS (SOP)

• Automates construction of circuit from truth table
• Identify each row of the output that has a 1 at output
• Convert into equivalent variables, AND together then OR

Example:

From the truth table below construct the SOP expression.

F = (A'B) + B'A)

Step 1: Identify rows with 1

Step 2: Put apostrophe (') over variables that is 0 in its row

Step 3: Make a sum of all product term

SOP expression = A'B + AB'

Step 4: Simplify the SOP expression

SOP = A'B + AB'

* since the expression cannot be simplify just leave the answer like that.

You don't understand???

This is another example to make you understand more..

F = A'B' + ABCD'

SOP = (A'B'C'D') + (A'B'C'D) + (A'B'CD') + (A'B'CD) + (ABC'D)

Lets continue to next subtopic..

4.6 PRODUCT-OF-SUM (POS)

• Identify each row of the output that has 0 at output
• Convert into equivalent variables, OR then AND with other OR forms.
• Usually use if more 1 produce in output function

Example:

Construct the POS expression from the truth table below.

Step 1: Identify row with 0 and put apostrophe over variables that is 1 in its row. Sum the variables as follow.

Step 2: Multiply the product term

POS = (A'+B+C) . (A'+B'+C')

Step 3: Simplify the expression

F = (A'+B+C) . (A'+B'+C')                  ---------------------- Factorize the equation

   = A'A' + A'B' + A'C' + BA' + BB' + CA' + CB' + CC'  --- Use Boolean algebra law: AA' = 0, A'A' = 0 

   = A'B' + A'C' + BA' + BC' + CA' + CB'    ----------- Factorize the same values

   = A'(B' + C' + B + C' + C) + CB'   

   = A'(1 + C') + CB'       -------- Use Boolean algebra law: A+A' = 1

   = A' + CB'

that's all for today,have fun with your study...to be continued

*if you don't understand just give me a hint then i'll upload more example for you

by nadhiah amira nordin

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