CS231 Fall 05 Review Session

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CS231 (Fall 05)Review Session

• Xiao Ma (xiaoma2_at_cs.uiuc.edu)
• Sep 23, 2005

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Who am I?

• Hey! My name is Xiao Ma, a new Ph.D.
  student in the department of Computer Science at
  UIUC. My research interests are system
  architecture and operating system. Now Im a
  member of Opera group.

• Questions? ? Raise hand!
• Wrong saying? ? Point out!

CS231 Computer Architecture I (2005 Fall) Review
Session (9/23/2005) Xiao Ma (xiaoma2_at_cs.uiuc.edu)
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TA and Students
I hope Im not a monster like this in your eyes. ?
CS231 Computer Architecture I (2005 Fall) Review
Session (9/23/2005) Xiao Ma (xiaoma2_at_cs.uiuc.edu)
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TA and Students
We have the same goal.
CS231 Computer Architecture I (2005 Fall) Review
Session (9/23/2005) Xiao Ma (xiaoma2_at_cs.uiuc.edu)
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Outline

• Decoders

• Multiplexers

• Quizzes 6-7

• MP Example

CS231 Computer Architecture I (2005 Fall) Review
Session (9/23/2005) Xiao Ma (xiaoma2_at_cs.uiuc.edu)
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Decoder - General
A n-to-2n decoder takes an n-bit input and
produces 2n outputs. The n inputs represent a
binary number that determines which of the 2n
outputs is uniquely true.
CS231 Computer Architecture I (2005 Fall) Review
Session (9/23/2005) Xiao Ma (xiaoma2_at_cs.uiuc.edu)
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Decoder Whats inside?
Try to implement a 1-to-2 decoder. How about
2-4? 3-8?
CS231 Computer Architecture I (2005 Fall) Review
Session (9/23/2005) Xiao Ma (xiaoma2_at_cs.uiuc.edu)
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Decoder Expansion

• We can combine two same decoders by using EN
  inputs.

AB decoder 2 2A2B decoder ?
AB decoder 2 (A1)2B decoder
CS231 Computer Architecture I (2005 Fall) Review
Session (9/23/2005) Xiao Ma (xiaoma2_at_cs.uiuc.edu)
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Decoder Active-high vs Active-low

• Active-high decoders generate minterms.

• Active-low decoders generate maxterms.

• Please refer to slides 17-23 in the lecture.

CS231 Computer Architecture I (2005 Fall) Review
Session (9/23/2005) Xiao Ma (xiaoma2_at_cs.uiuc.edu)
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Outline

• Decoders

• Multiplexers

• Quizzes 6-7

• MP Example

CS231 Computer Architecture I (2005 Fall) Review
Session (9/23/2005) Xiao Ma (xiaoma2_at_cs.uiuc.edu)
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Multiplexer - General

• A 2n-to-1 multiplexer takes
• n select lines
• 2n data input lines
• makes
• 1 output

CS231 Computer Architecture I (2005 Fall) Review
Session (9/23/2005) Xiao Ma (xiaoma2_at_cs.uiuc.edu)
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Multiplexer Decoder?Multiplexer

• Can you use decoders and basic gates to make a
  multiplexer?

Selector 1 Selector 0 Input 3 Input 2 Input
1 Input 0
Output
CS231 Computer Architecture I (2005 Fall) Review
Session (9/23/2005) Xiao Ma (xiaoma2_at_cs.uiuc.edu)
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Multiplexer - Efficient implementation

• We can actually implement a function with 3
  variables with just one 22-to-1 mux, instead of
  an 23-to-1.

n variables ? 2n-1 -to-1 multiplexer
CS231 Computer Architecture I (2005 Fall) Review
Session (9/23/2005) Xiao Ma (xiaoma2_at_cs.uiuc.edu)
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Multiplexer - Whats inside?

• How to use AND gates and OR gates to implement an
  8-1 multiplexer.

• An NAND gates implementation of an 8-1
  multiplexer.

CS231 Computer Architecture I (2005 Fall) Review
Session (9/23/2005) Xiao Ma (xiaoma2_at_cs.uiuc.edu)
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Outline

• Decoders

• Multiplexers

• Quizzes 6-7

• MP Example

CS231 Computer Architecture I (2005 Fall) Review
Session (9/23/2005) Xiao Ma (xiaoma2_at_cs.uiuc.edu)
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Quiz Quiz 6 Question 4

• small decoders -gt bigger decoer

A XY decoder can be constructed using (how
many? k) AB decoders with enable. A single
decoder of size (mn) selects the appropriate
one of these AB decoders.
Answer
k Y / B
mn log2k k
CS231 Computer Architecture I (2005 Fall) Review
Session (9/23/2005) Xiao Ma (xiaoma2_at_cs.uiuc.edu)
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Quiz Quiz 7 Question 2

• Write the expression for multiplexer(s) by truth
  table

Truth Table
K-Map
Expression
CS231 Computer Architecture I (2005 Fall) Review
Session (9/23/2005) Xiao Ma (xiaoma2_at_cs.uiuc.edu)
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Quiz Quiz 7 Question 2

• Write the expression for multiplexer(s) directly.

h zy zx
f (z)y zh zy z(zy zx) zy
zy
g yh yx y(zy zx) yx
y(zy)(zx) yx yzx yx xy xz
CS231 Computer Architecture I (2005 Fall) Review
Session (9/23/2005) Xiao Ma (xiaoma2_at_cs.uiuc.edu)
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Quiz Quiz 7 Question 3

• Use multiplexer in the efficient way without
  using invertors.

What can you do to change the situation?
Use other variables as the selectors.
CS231 Computer Architecture I (2005 Fall) Review
Session (9/23/2005) Xiao Ma (xiaoma2_at_cs.uiuc.edu)
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Quiz Quiz 7 Question 4

• The same question as before!

CS231 Computer Architecture I (2005 Fall) Review
Session (9/23/2005) Xiao Ma (xiaoma2_at_cs.uiuc.edu)
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Outline

• Decoders

• Multiplexers

• Quizzes 6-7

• MP Example

CS231 Computer Architecture I (2005 Fall) Review
Session (9/23/2005) Xiao Ma (xiaoma2_at_cs.uiuc.edu)
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MP Example - Problem

• Input

The input to your circuit will be the low 4
bits of the ASCII value for the character being
displayed. These values are shown as N3-N0 in the
truth table below. Since you are only
implementing letters A-J, you may assume that the
remaining six 4-bit patterns will never be used,
and so are don't care situations.
CS231 Computer Architecture I (2005 Fall) Review
Session (9/23/2005) Xiao Ma (xiaoma2_at_cs.uiuc.edu)
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MP Example - Problem

• Output

Your circuit will produce seven outputs, one for
each of the seven line segments. We'll name the
outputs T, U, V, W, X, Y, Z, as illustrated right.
A B C D E F G H
I J
CS231 Computer Architecture I (2005 Fall) Review
Session (9/23/2005) Xiao Ma (xiaoma2_at_cs.uiuc.edu)
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MP Example Truth Table
CS231 Computer Architecture I (2005 Fall) Review
Session (9/23/2005) Xiao Ma (xiaoma2_at_cs.uiuc.edu)
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MP Example K-Maps
CS231 Computer Architecture I (2005 Fall) Review
Session (9/23/2005) Xiao Ma (xiaoma2_at_cs.uiuc.edu)
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MP Example K-Map Simplification
CS231 Computer Architecture I (2005 Fall) Review
Session (9/23/2005) Xiao Ma (xiaoma2_at_cs.uiuc.edu)
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MP Example K-Map Simplification
CS231 Computer Architecture I (2005 Fall) Review
Session (9/23/2005) Xiao Ma (xiaoma2_at_cs.uiuc.edu)
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MP Example Two Level Implementation
CS231 Computer Architecture I (2005 Fall) Review
Session (9/23/2005) Xiao Ma (xiaoma2_at_cs.uiuc.edu)
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MP Example NAND Implementation
CS231 Computer Architecture I (2005 Fall) Review
Session (9/23/2005) Xiao Ma (xiaoma2_at_cs.uiuc.edu)
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MP Example Decoder Implementation
CS231 Computer Architecture I (2005 Fall) Review
Session (9/23/2005) Xiao Ma (xiaoma2_at_cs.uiuc.edu)
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MP Example Multiplexer Implementation
CS231 Computer Architecture I (2005 Fall) Review
Session (9/23/2005) Xiao Ma (xiaoma2_at_cs.uiuc.edu)
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Outline

• Decoders

• Multiplexers

• Quizzes 6-7

• MP Example

CS231 Computer Architecture I (2005 Fall) Review
Session (9/23/2005) Xiao Ma (xiaoma2_at_cs.uiuc.edu)
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THANK YOU!
Is this session helpful for you? Feed back is
welcome and appreciated!
CS231 Computer Architecture I (2005 Fall) Review
Session (9/23/2005) Xiao Ma (xiaoma2_at_cs.uiuc.edu)