Post on 03-Apr-2018
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TWO-LEVEL IMPLEMENTATION
EXPERIMENT TITLE
EXPERIMENT 4
EXPERIMENT NO.
TAGUBA, KRISTOFFER NINO R.
NAME
ENGR. ERWIN B. DACULAN
PROFESSOR
OCT 22 2011
DATE OF EXPERIMENT
OCT 29, 2011
DATE OF SUBMISSION
GRADE
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TAGUBA, KRISTOFFER NINO R.NAME
ENGR. ERWIN B. DACULANPROFESSOR
OCT 22, 2011DATE OF EXPERIMENT
OCT 29, 2011DATE OF SUBMISSION
GRADE
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I. OBJECTIVE
1. To simplify the given function into their minimum SOP and POS forms
2. To construct AND-OR and OR-AND networks.
3. To verify the theoretical truth tables of AND-OR and OR-AND networks.
II. DATA /ANALYSIS
Q(C, O , D, E ) = I (0, 1,2,3,7,8,10) + d(5,6,11,15)
1. AND OR Network
a. K-Map: SOP (encircle 1s)
1 0 0 1
1 x 0 0
1 1 x x
1 x 0 1
b. Simplified function: ()+(E)
c. Theoretical Truth Table
00 01 11
00
01
11
10
ABCD
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C O E Q E
0 0 0 1 1 1 1 1 0
0 0 1 1 1 1 0 0 1
0 1 0 0 1 0 1 0 0
0 1 1 1 1 0 0 0 1
1 0 0 1 0 1 1 1 0
1 0 1 0 0 1 0 0 0
1 1 0 0 0 0 1 0 0
1 1 1 0 0 0 0 0 0
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d. Design circuit
e. Experimental truth Table
C O E Q
0 0 0 1
0 0 1 1
0 1 0 0
0 1 1 1
1 0 0 1
1 0 1 0
1 1 0 0
1 1 1 0
E
O
C
+
Figure 4-2 AND OR Network
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2. OR - AND Network
a. K-Map: POS (encircle 0 s)
1 0 0 1
1 x 0 0
1 1 x x
1 x 0 1
b. Simplified function: (+)(+E)
c. Theoretical Truth Table
C O E Q + +E
0 0 0 1 1 1 1 1 1
0 0 1 1 1 1 0 1 1
0 1 0 0 1 0 1 0 1
0 1 1 1 1 0 0 1 11 0 0 1 0 1 1 1 1
1 0 1 0 0 1 0 1 0
1 1 0 0 0 0 1 0 1
1 1 1 0 0 0 0 1 0
00 01 11
00
01
11
10
ABCD
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d. Design circuit
e. Experimental truth Table
C O E Q
0 0 0 1
0 0 1 1
0 1 0 0
0 1 1 1
1 0 0 1
1 0 1 0
1 1 0 0
1 1 1 0
C
O
E
+
E+
(+)(E+)
Figure 4-2 AND OR Network
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This are the tables that are in the experiment, from the first part which is the AND
OR network, and the second is the OR AND network connection. Each data and results are
express to obtain more convenient connections of logic gates using AND-OR network and OR-
AND network.
In the first part which is the AND-OR network, firstly we must determine the values
that are minterms using k-map: SOP which are the all 1 outputs which means that those are the
values that are easy to determine which connections or combinations that are able to minimize
the logic diagram, by using AND and OR gates.
Next part of AND-OR network is the obtaining the minimized value of the diagramequation, and obtain on the next table the theoretical truth table that to determine the given
output by using the simplified function or the circuit design in the data result.
Second part of the experiment is the OR-AND network, first we must determines the
output of the table by using k-map: POS which means we must encircle all the 0 (zero) terms int
the table but to determine we use the given guide that all 1 values are from 0,1,2,3,7,8 and 10
those are the give outputs with 1 value and the dont-care functions are 5,6,11 and 15 which
means the rest are zeroes.
Now we can determine the valued output of the theoretical table, but first we must
determine the simplified function by grouping the 0 zeros and determine the equivalent value.
Then determine the output value, next design the simplified function and determine the
experimental truth table and its output.
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QUESTIONS AND ANSWER
1. State the procedure in implementing a Boolean function using AND-OR and OR-
AND networks.
Procedure for implementing a Boolean function using AND-OR Network:
First we must construct a truth table based on AND and OR gates, using 4 inputs, using
the truth table we must obtain the output, which the k-map are going to be useful in
determining the outputs, but first we must number up each implied inputs and assign the
numbers on each numbers on every box of the k-map, next determine the canonical
values of the k-map and when it determine, use the Boolean algebra to make it more
easier or shorter canonical simplified value. Now design the canonical functions and use
an experimental truth table to determine if the diagram is correct and also to prove that
the simplified function is equally base also on a AND or OR gates.
Procedure for implementing a Boolean function using OR-AND network
First construct a truth table with 4 input values, then create a k-map:POS which
determine that is product of sums. Next is to the encircle zero values or the max terms to
determine which designated canonical value are used and verify the simplified function
of the canonical value using Boolean algebra, and construct a circuit design using OR-
AND network and prove to the experimental truth table if the canonical function is true.
2. Do the actual truth tables of the network agree with the theoretical truth tables?
Explain discrepancies, if any
1 0 0 1
1 x 0 01 1 x x
1 x 0 1
00 01 11
00
01
11
10
ABCD
(+)(+E)
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C O E Q + +E
0 0 0 1 1 1 1 1 1
0 0 1 1 1 1 0 1 1
0 1 0 0 1 0 1 0 1
0 1 1 1 1 0 0 1 1
1 0 0 1 0 1 1 1 1
1 0 1 0 0 1 0 1 0
1 1 0 0 0 0 1 0 1
1 1 1 0 0 0 0 1 0
C
O
E
1
1
1 1
1
1
0
0
0
0
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C O E Q
0 0 0 1
0 0 1 1
0 1 0 0
0 1 1 1
1 0 0 1
1 0 1 0
1 1 0 0
1 1 1 0
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In the experimental truth table showed that the diagram showed the exact output on the table
which means there no discrepancies and proved that minimizing the canonical function is easier
to determine the correct output.
3. Define DONT CARE CONDITIONS in your own words
Don't cares in a Karnaugh map, or truth table, may be either1s or0s, as long as we
don't care what the output is for an input condition we never expect to see. We plot these cells
with an X among the normal 1s and 0s. When forming groups of cells, treat the don't care cell as
either a 1 or a 0, or ignore the don't cares. This is helpful if it allows us to form a larger group
than would otherwise be possible without the don't cares. There is no requirement to group all or
any of the don't cares. Only use them in a group if it simplifies the logic.
4. Why is that DONT CARE conditions are considered when simplifying Boolean
functions?
Because when using the DONT CARE it doesnt mean its useless it means we dont care if
any on that output are 1s or 0s which means if any value are showed it will not affect the
equated value.
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III. DISCUSSION
In this experiment it is discussed that proving a certain truth table using a circuit
Diagrams of logic gates and satisfy the equivalent values of the truth table. The problem is that
how many gates are can be use to prove the truth tables without lacking off ICs materials.
Boolean algebra finds its most practical use in the simplification of logic circuits. If we
translate a logic circuit's function into symbolic (boolean) form, and apply certain algebraic
rules to the resulting equation to reduce the number of terms and/or arithmetic operations, the
simplified equation may be translated back into circuit form for a logic circuit performing the
same function with fewer components. If equivalent function may be achieved with fewer
components, the result will be increased reliability and decreased cost of manufacture.
By applying Boolean algebra rules with DeMorgans Theorem, we can cancel out redundant
terms and variables from an SOP or POS expression. This is called Boolean algebra
simplification.
To accomplish Boolean algebra simplification, group and manipulate expressions, and
reduce the number of redundant terms much like you would do with a classic algebra
manipulation of a numeric expression. AND terms can be treated like multiplied terms, and OR
expressions can be treated like addition + signs in arithmetic expressions. Terms can be factored
out of expressions, and parenthesis can be added and removed to and from grouped terms as
needed. The similarity ends when the results are interpreted. AND is not multiplication, and OR
is not addition in digital logic expressions.
A Karnaugh Map is a method of mapping truth tables onto a matrix that identifies places
where two or more different combinations of the input variables yield the same result. In
addition to identifying redundant terms, the K map also cancels them, leaving only the
minimized Boolean algebra expressions that will yield the same truth table outputs as the
unreduced terms.
The best way to understand K- maps is to go through an actual simplification process
using a K- map. We will start with a three variable truth table. Three variables have 2 to the 3rd,
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or 8 possible combinations of 1s and 0s.This means that the K map must have 8 cells, one for
every possible combination of input variables. The input variables can be mapped in any order
on the K map, but it must follow the same organization as the truth table being mapped.
IV. CONCLUSION
In this experiment we are able to determine the importance of a SOP (sums of
products) and POS (products of sums) which are used to determine the canonical values of truth
table, with the help of karnaugh mapping to determine the resulted output and the Boolean
expression of the truth table. In this case the value or advantage of this Boolean function is to
create a better and shorter diagram or to prove that the value output is exact with the truth table.