Lab 5. 3-to-8 Decoder
Presenter: Chun-Hsien Ko
Contributors:
Chung-Ting Jiang and Lin-Kai Chiu
Dept. of Electrical and Computer Eng., NCTU
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Logic Design
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Lab 5. 3-to-8 Decoder
Chun-Hsien Ko
Outlines
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What is Decoder?
3-bit to 8-output Decoder
One-hot Logic Design
Lab 5: 3-to-8 Decoder
November 2, 2015: George Boole’s 200th Birthday
Dept. of Electrical and Computer Eng., NCTU
2
Lab 5. 3-to-8 Decoder
Logic Design

Chun-Hsien Ko
What is Decoder?
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Transformation between 2 different format
1-to-1 mapping
Example：Taking attendance for demo
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The process of mapping the ID number to the corresponding
name
ID number
Name
000
Tim
001
Sony
…
…
111
Tony
010
Dept. of Electrical and Computer Eng., NCTU
3
Logic Design

Lab 5. 3-to-8 Decoder
Chun-Hsien Ko
3-bit to 8-output Decoder
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Input: 3-bit binary variable
Output: 8 binary variable (only one “1” in 8-bit)
3 inputs → 23(8) outputs
Dept. of Electrical and Computer Eng., NCTU
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Logic Design

Lab 5. 3-to-8 Decoder
Chun-Hsien Ko
One-hot Logic Design
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Sum-of-product: Sum (OR) the productive (AND) term
For example: the output 𝐷0
D0  x ' y ' z '
X
Y
X’Y’Z’
Z
Dept. of Electrical and Computer Eng., NCTU
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Lab 5. 3-to-8 Decoder
Logic Design

Chun-Hsien Ko
Lab 5: 3-to-8 Decoder
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Input: 3-bit binary input with DIP switch
Output: 8 output with LED
How do you design your 3-to-8 decoder from truth table?
D0
D1
D2
D3
D4
D5
D6
D7
Please put the LEDs in line and use them to denote the outputs of circuit
Dept. of Electrical and Computer Eng., NCTU
6
Logic Design

Lab 5. 3-to-8 Decoder
Chun-Hsien Ko
Lab 5: 3-to-8 Decoder
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Tip: Follow the step and construct these outcomes
(X’Y’)Z’
(X’Y’)Z
X
Y
Z
X
Y
Z
X’
Y’
Z’
X’Y’
X’Y
XY’
XY
(X’Y)Z’
(X’Y)Z
(XY’)Z’
(XY’)Z
(XY)Z’
(XY)Z
Dept. of Electrical and Computer Eng., NCTU
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Lab 5. 3-to-8 Decoder
Logic Design
X
Y
Chun-Hsien Ko
Z
D0
D1
D2
D3
D4
D5
D6
D7
Dept. of Electrical and Computer Eng., NCTU
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Logic Design

Lab 5. 3-to-8 Decoder
Chun-Hsien Ko
November 2, 2015
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George Boole’s 200th Birthday
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http://www.google.com/doodles/george-booles-200th-birthday
https://en.wikipedia.org/wiki/George_Boole
http://history.pansci.asia/post/132377770300/%E7%A7%91%
E5%AD%B8%E5%8F%B2%E4%B8%8A%E7%9A%84%E4
%BB%8A%E5%A4%A9112%E5%B8%83%E7%88%BE%E
8%AA%95%E8%BE%B0george-boole-18151864
Dept. of Electrical and Computer Eng., NCTU
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Logic Design

Lab 5. 3-to-8 Decoder
Chun-Hsien Ko
November 2, 2015
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George Boole’s 200th Birthday
The Mathematical Analysis of Logic, by George Boole
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http://www.gutenberg.org/files/36884/36884-pdf.pdf
An Investigation of the Laws of Thought, by George Boole
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http://www.gutenberg.org/files/15114/15114-pdf.pdf
No matter how correct a mathematical theorem may
appear to be, one ought never to be satisfied that there
was not something imperfect about it until it gives the
impression of also being beautiful.
- George Boole
Dept. of Electrical and Computer Eng., NCTU
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