Logic Circuits Experiment 4

7/28/2019 Logic Circuits Experiment 4

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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.

Logic Circuits Experiment 4

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