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CSE 140 Lecture 12 Standard Combinational Modules

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CSE 140 Lecture 12 Standard Combinational Modules Professor CK Cheng CSE Dept. UC San Diego * * Part III - Standard Combinational Modules (Chapter 5) Signal Transport ... – PowerPoint PPT presentation

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Title: CSE 140 Lecture 12 Standard Combinational Modules


1
CSE 140 Lecture 12 Standard Combinational Modules
  • Professor CK Cheng
  • CSE Dept.
  • UC San Diego

2
Part III - Standard Combinational Modules
(Chapter 5)
  • Signal Transport
  • Decoder Decode address
  • Encoder Encode address
  • Multiplexer (Mux) Select data by address
  • Demultiplexier (DeMux) Direct data by address
  • Shifter Shift bit location
  • Data Operator
  • Adder Add two binary numbers
  • Multiplier Multiply two binary numbers

3
Interconnect Decoder, Encoder, Mux, DeMux
4
1. Decoder
  • Definition
  • Logic Diagram
  • Application (Universal Set)
  • Tree of Decoders

5
iClicker Decoder Definition
  1. A device that decodes
  2. An electronic device that converts signals from
    one form to another
  3. A machine that converts a coded text into
    ordinary language
  4. A device or program that translates encoded data
    into its original format
  5. All of the above

6
Decoder Definition A digital module that
converts a binary address to the assertion of the
addressed device
EN (enable)
y0 y1 y7
0 1 2 3 4 5 6 7
0
I0
. .
1
I1
I2
2
n to 2n decoder function
2n outputs 23 8
n inputs n 3
yi 1 if En 1 (I2, I1, I0 ) i yi 0
otherwise
7
1. Decoder Definition
  • N inputs, 2N outputs
  • One-hot outputs only one output HIGH at once

EN
EN 1
8
Decoder Logic Diagram
En
yi mi En
I0
y0
I1
I2
y0 1 if (I2, I1, I0 )(0,0,0) En 1
I0
y1
I1
I2
. .
I0
y7
I1
I2
y7 1 if (I2, I1, I0 )(1,1,1) En 1
9
Decoder Application universal set Decoder, OR
Implement functions f1(a,b,c) Sm(1,2,4)
Example
f2(a,b,c) Sm(2,3), and
f3(a,b,c) Sm(0,5,6)
with a 3-input decoder and OR gates.
y1
y2
y4
f1
y2
y3
f2
y0
y5
y6
f3
10
Decoders
  • OR minterms

En
11
Tree of Decoders
Implement a 4-24 decoder with 3-23 decoders.
y0 y1 y7
0 1 2 3 4 5 6 7
d
I0
c
I1
b
I2
y8 y9 y15
0 1 2 3 4 5 6 7
I0
I1
I2
a
12
Tree of Decoders
Implement a 6-26 decoder with 3-23 decoders.
En
En
y0
D0
I2, I1, I0
y7
y8
I5, I4, I3
D1
I2, I1, I0
y15


y56
D7
I2, I1, I0
y63
13
2. Encoder
  • Definition
  • Logic Diagram
  • Priority Encoder

14
iClicker Definition of Encoder
  1. Any program, circuit or algorithm which encodes
  2. In digital audio technology, an encoder is a
    program that converts an audio WAV file into an
    MP3 file
  3. A device that convert a message from plain text
    into code
  4. A circuit that is used to convert between
    digital video and analog video
  5. All of the above

15
Encoder Definition A digital module that
converts the assertion of a device to the binary
address of the device.
Encoder Description
En
At most one Ii 1. (yn-1,.., y0 ) i if Ii 1
En 1 (yn-1,.., y0 ) 0 otherwise. A 1 if
En 1 and one i s.t. Ii 1 A 0 otherwise.
I0
0 1 2 3 4 5 6 7
y0
0 1 2
y1
y2
I7
3 outputs
A
8 inputs
16
Encoder Logic Diagram
En
y0
I1
I3
I5
I7
En
y1
I2
I3
I6
I7
17
Encoder Logic Diagram
En
y2
I4 I5 I6 I7
En
A
I0
I1
.
.
I6
I7
18
Priority Encoder Definition
Description Input (I2n-1,, I0), Output (yn-1
,,,y0)
(yn-1 ,,,y0) i if Ii 1 En 1 Ik 0
for all k gt i (high bit priority) or for all
klt i (low bit priority).
Eo 1 if En 1 Ii 0 for all i, Gs 1 if En
1 i s.t. Ii 1.
E
(Gs is like A, and Eo tells us if enable is true
or not).
19
Priority Encoder Implement a 32-input priority
encoder w/ 8 input priority encoders (high bit
priority).
En
y32, y31, y30
I31-24
Gs
Eo
y22, y21, y20
I25-16
Gs
Eo
y12, y11, y10
I15-8
Gs
Eo
y02, y01, y00
I7-0
Gs
Eo
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