Theory Lecture 13
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Transcript of Theory Lecture 13
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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