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MCT-212: DIGITAL LOGIC

DESIGN

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CODE CONVERTERS0000 = 0011 [o_0]?

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CODE CONVERTERS

In the digital domain, data or information is representedby a combination of0s and 1s.

A code is basically the pattern of these 0s and 1s used

to represent the data.

Code converters are a class of

combinational digital circuits

that are used to convert one type

of code in to another.

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CODE CONVERTERS

Some of the most prominently used codes in digitalsystems are Natural Binary Sequence, Binary Coded

Decimal, Excess-3 Code, Gray Code, ASCII Code etc.

Like any combinational digital circuit, a code converter

can be implemented by using a circuitry ofAND, OR andNOT gates.

We will be studying the following conversions:

Binary-to-Excess3 Conversion

Binary-Gray code conversion

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BINARY-to-EXCESS-3 CONVERSION

In excess-3 code, a small value of bias (3) is added tothe binary numbers.

The representation shifts each number by a value of

three.

when the sum of two XS-3 digits is greater than 9, the

carry bit of a four bit adder will be set high.

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BINARY-to-EXCESS-3 CONVERSION The truth table shows the conversion parameters.

A,B,C,D represent a binary/BCD number, while the

output w,x,y,z represent the excess-3 code.

A B C D w x y z

0 0 0 0 0 0 1 1

0 0 0 1 0 1 0 00 0 1 0 0 1 0 1

0 0 1 1 0 1 1 0

0 1 0 0 0 1 1 1

0 1 0 1 1 0 0 00 1 1 0 1 0 0 1

0 1 1 1 1 0 1 0

1 0 0 0 1 0 1 1

1 0 0 1 1 1 0 0

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BINARY-to-EXCESS-3 CONVERSION

A B C D w

0 0 0 0 00 0 0 1 0

0 0 1 0 0

0 0 1 1 0

0 1 0 00

0 1 0 1 1

0 1 1 0 1

0 1 1 1 1

1 0 0 0 1

1 0 0 1 1

ABCD

00

01

11

10

00 01 11 10

0 0 0

0 1 1

X X X X

1 1 X X

0

1

= + +

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BINARY-to-EXCESS-3 CONVERSION

A B C D x

0 0 0 0 00 0 0 1 1

0 0 1 0 1

0 0 1 1 1

0 1 0 0 1

0 1 0 1 0

0 1 1 0 0

0 1 1 1 0

1 0 0 0 0

1 0 0 1 1

ABCD

00

01

11

10

00 01 11 10

0 1 1

1 0 0

X X X X

0 1 X X

1

0

= ++

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BINARY-to-EXCESS-3 CONVERSION

A B C D y

0 0 0 0 10 0 0 1 0

0 0 1 0 0

0 0 1 1 1

0 1 0 0 1

0 1 0 1 0

0 1 1 0 0

0 1 1 1 1

1 0 0 0 1

1 0 0 1 0

1 0 1

1 0 1

X X X X

1 0 X X

ABCD

00

01

11

10

00 01 11 10

0

0

=+

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BINARY-to-EXCESS-3 CONVERSION

A B C D z

0 0 0 0 10 0 0 1 0

0 0 1 0 1

0 0 1 1 0

0 1 0 0 1

0 1 0 1 0

0 1 1 0 1

0 1 1 1 0

1 0 0 0 1

1 0 0 1 0

1 0 0

1 0 0

X X X X

1 0 X X

ABCD

00

01

11

10

00 01 11 10

1

1

=

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BINARY-to-EXCESS-3 CONVERSION

= =+

= + +

+ + =

+( + )( + )=

= + +

+ ( + )=

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BINARY-to-EXCESS-3 CONVERSION

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BINARY- GRAY CODE

CONVERTERS

Convert binary code into

gray code, or gray code

into binary code.

What are some uses of

gray code??

Binary Gray Code0 0 0 0 0 0 0 0

0 0 0 1 0 0 0 1

0 0 1 0 0 0 1 10 0 1 1 0 0 1 0

0 1 0 0 0 1 1 0

0 1 0 1 0 1 1 1

0 1 1 0 0 1 0 1

0 1 1 1 0 1 0 0

1 0 0 0 1 1 0 0

1 0 0 1 1 1 0 1

1 0 1 0 1 1 1 1

1 0 1 1 1 1 1 0

1 1 0 0 1 0 1 0

1 1 0 1 1 0 1 1

1 1 1 0 1 0 0 1

1 1 1 1 1 0 0 0

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BINARY- GRAY CODE

CONVERTERS

Binary Gray Code0 0 0 0 0 0 0 0

0 0 0 1 0 0 0 1

0 0 1 0 0 0 1 10 0 1 1 0 0 1 0

0 1 0 0 0 1 1 0

0 1 0 1 0 1 1 1

0 1 1 0 0 1 0 1

0 1 1 1 0 1 0 0

1 0 0 0 1 1 0 0

1 0 0 1 1 1 0 1

1 0 1 0 1 1 1 1

1 0 1 1 1 1 1 0

1 1 0 0 1 0 1 0

1 1 0 1 1 0 1 1

1 1 1 0 1 0 0 1

1 1 1 1 1 0 0 0

Binary to- Gray:

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BINARY- GRAY CODE

CONVERTERS

Binary Gray Code0 0 0 0 0 0 0 0

0 0 0 1 0 0 0 1

0 0 1 0 0 0 1 10 0 1 1 0 0 1 0

0 1 0 0 0 1 1 0

0 1 0 1 0 1 1 1

0 1 1 0 0 1 0 1

0 1 1 1 0 1 0 0

1 0 0 0 1 1 0 0

1 0 0 1 1 1 0 1

1 0 1 0 1 1 1 1

1 0 1 1 1 1 1 0

1 1 0 0 1 0 1 0

1 1 0 1 1 0 1 1

1 1 1 0 1 0 0 1

1 1 1 1 1 0 0 0

Gray to- Binary:

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ANY QUESTIONS?

Anyone willing to present?

Time allowed : 5 mins

Topic : Any Bonus Points : +3

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REFERENCES

Chapter no 4: Combinational Logic Digi tal Lo gic Designby Morris Mano

Chapter no 6: Functions of Combination Logic

Digi tal Fundamentalsby Floyd