decoder/code converter circuit

7/31/2019 Decoder/Code Converter Circuit

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ECE 4104(Logic Circuits and Switching Theory)

Experiment No. 4Decoder/Code Converter Circuit

Submitted by:

GROUP # 3

BURGOS, Arman

DIOCADES, Erna Mae

FAIGONES, Russel

Lab. Schedule: Th 7:00 10:00 AM

Date Submitted: August 2012

Instructor: Engr. Ramon Alguidano Jr.


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I. OBJECTIVES

1. To be able to convert 8-4-2-1 code into gray code.

2. To be able to formulate the simplified minterm equation using karnaugh

mapping or Boolean algebra.

3. To be able to generate the truth table.

4. To construct the actual circuit as designed from the truth table description.

5. To verify the given truth table and test the individuality of each output by

recording the actual data of the circuit constructed.

6. To learn how to simulate the logical operations of the circuit using any

electronic simulation software and compare with the actual results.


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II. BASIC THEORY

Decoders

In digital electronics, a decoder can take the form of a multiple-input, multiple-

output logic circuit that converts coded inputs into coded outputs, where the input and

output codes are different e.g. n-to-2n , binary-coded decimal decoders. Decoding is

necessary in applications such as data multiplexing, 7 segment display and memory

address decoding.

The example decoder circuit would be an AND gate because the output of an

AND gate is "High" (1) only when all its inputs are "High." Such output is called as

"active High output". If instead of AND gate, the NAND gate is connected the output will

be "Low" (0) only when all its inputs are "High". Such output is called as "active low

output".

A slightly more complex decoder would be the n-to-2n type binary decoders.

These types of decoders are combinational circuits that convert binary information from

'n' coded inputs to a maximum of 2n unique outputs. In case the 'n' bit coded

information has unused bit combinations, the decoder may have less than 2n outputs.

2-to-4 decoder, 3-to-8 decoder or 4-to-16 decoder are other examples.

The input to a decoder is parallel binary number and it is used to detect the

presence of a particular binary number at the input. The output indicates presence or

absence of specific number at the decoder input.


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A decoder is a combinational circuit that converts binary information from n input

lines to a maximum of 2n output lines. Logic circuit implementation with basic logic

gates involves obtaining simplified Boolean expressions for each output.

Implementation with MSI decoders is very simple and straightforward and may require a

few external gates. The implementation of functions F = (1, 2, 3) and G = (5, 6, 7,

8, 9) using a 4 x 16 decoder is shown below. Since a decoder generates minterms at its

outputs we need only to sum the minterms for which F and G are 1. Hence, we require

OR gates to produce F and G.

If the decoder is constructed using NAND gates, then it has active low outputs. In this

case, NAND and/or AND gates could be used to sum the minterms of F and G.


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Code Converters

A code converter is a circuit that makes two digital systems using different codes for the

same information compatible even though each uses a different code. To convert from

binary code A to binary code B, the input lines must supply the bit combination of

elements as specified by code A and the output lines must generate the corresponding

bit combination of code B.

The circuit for this code converter can be implemented using basic logic gates or with

available MSI devices such as Decoders, and Multiplexers. The unused input

combinations can be treated as dont cares.


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III. SCHEMATIC DIAGRAMS


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IV. EQUIPMENT/MATERIALS/COMPONENT NEEDED


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V. PROCEDURES AND RESULTS

1) Given the 8-4-2-1 code, convert it into gray code using any simplification

technique. Generate the truth table and output of the gray code.

Using Boolean Algebra:

1st

Bit

F(A,B,C,D) = 'AB'CD+'ABC'D+'ABCD+A'B'C'A+A'B'CD

F(A,B,C,D) = 'ABD+A'B'C+'ABC

2nd

Bit

F(A,B,C,D) = 'AB'C'A+'AB'CD

F(A,B,C,D) ='AB'C

3rd

Bit

F(A,B,C,D) = 'A'BC'D+'A'BCD+'AB'C'D+'AB'CD+'ABC'D+'ABCD

F(A,B,C,D) = 'AB+'AC

4th

Bit

F(A,B,C,D) = 'A'B'CD+'A'BC'D+'ABCD+A'B'C'D

F(A,B,C,D) = 'B'C(AD)+ 'AC' (BD)


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2) Test the individuality of each output using actual practice and simulation

software.

Using TINA: (1ST Bit)


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2ND Bit:


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3RD Bit:


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NI Simulation:


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Actual Results:


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VI. OBSERVATION

During the conduction of this experiment the group has noted the following

observations:

It was found out that a certain coded output can be specified by a code

converter logic circuit with different input.

The said code converter can be made with multiple inputs and outputs.

In this experiment an 8421 coded input is converted into gray code.

The said circuit was implemented with basic logic gates using integrated

circuits 7404, 7408, 7432 and 7486.

It was noted that the implemented circuit involves obtaining simplified

Boolean expressions for each output as part of the gray code.

Actual outputs were verified as the resulting data were similar to that of the

results from the simulation process.

Moreover, similar results were also observed by doing a written Boolean

algebra simplification.


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VII. CONCLUSION

After conducting this experiment regarding the decoder or code converter, the

group therefore concludes that a decoder can take the form of a multiple-input,

multiple-output logic circuit that converts coded inputs into different coded outputs. In

this case an 8421 code was converted to gray code.

The mentioned decoder logic circuit was implemented with basic logic gates

using Integrated circuits 7404, 7408, 7432 and 7486. This circuit involves obtaining

simplified Boolean expressions for each output as part of the gray code.

Results from both simulation and written processes such as the Karnaugh

mapping and Boolean algebra simplification proved the actual results to be valid

and correct for they are similar.

Moreover, the group has learned how to make a decoder logic circuit that

convert 8-4-2-1 code into gray code by formulating its simplified minterm equation

using Karnaugh mapping or Boolean algebra basing on the truth table description

and then constructing the actual circuit designed based on simplified equation

obtained. The group was able to verify the individuality of each output by recording

the actual data of the circuit constructed.


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VIII. DESIGN PROBLEM

Design a code converter circuit that converts 8-4-2-1 to 6-3-1-1 code. Show Boolean algebra,

Karnaugh mapping, truth table and the simulation.

A B C D 6 3 1 1 Code

0 0 0 0 0 0 0 0

0 0 0 1 0 0 0 1

0 0 1 0 0 0 1 1

0 0 1 1 0 1 0 0

0 1 0 0 0 1 0 1

0 1 0 1 0 1 1 1

0 1 1 0 1 0 0 0

0 1 1 1 1 0 0 1

1 0 0 0 1 0 1 1

1 0 0 1 1 1 0 0

Boolean Algebra

1st

Bit

F(A,B,C,D) = 'ABC'D+'ABCD+A'B'C'D+A'B'CD

F(A,B,C,D) = 'ABC+A'B'C

2nd

Bit

F(A,B,C,D) = 'A'BCD+'AB'C'D+'AB'CD+A'B'CD

F(A,B,C,D) = 'BD(AC)+'AB'C

3rd

Bit

F(A,B,C,D) = 'A'BC'D+'AB'CD+A'B'C'D

F(A,B,C,D) = 'B'D(AC)+'AB'CD

4th

Bit

F(A,B,C,D) = 'A'B'CD+'A'BC'D+'AB'C'D

+'AB'CD+'ABCD+A'B'C'D

F(A,B,C,D) = 'AB'C+'B'D(AC)'AD' (BC)


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decoder/code converter circuit

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