CS 140 Lecture 13 Combinational Standard Modules

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CS 140 Lecture 13Combinational Standard Modules

• Professor CK Cheng
• CSE Dept.
• UC San Diego

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Part III. Standard Modules
Interconnect Modules 1. Decoder, 2.
Encoder 3. Multiplexer, 4. Demultiplexer
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Multiplexer

• Definition
• Logic Diagram
• Application

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3. Mux (Multiplexer) Definition
Description If En 1 y Di where i (Sn-1,
.. , S0) Else y 0
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Multiplexer (Mux) Definition

• Selects between one of N inputs to connect to the
  output.
• log2N-bit select input control input
• Example 21 Mux

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Multiplexer Definition Example
En
If D0 0 and S1S0 00 gt y 0 If D0 1 and
S1S0 00 gt y 1
D0
0
D1
1
y
D2
2
D3
3
S1
S0
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Multiplexer Logic Diagram

• Tristates
• For an N-input mux, use N tristates
• Turn on exactly one to select the appropriate
  input

• Logic gates
• Sum-of-products form

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Multiplexer Application

• Mux as a lookup table

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Multiplexer Application
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Multiplexer Application universal set Mux
Example 1 Given f (a,b,c) Sm (0,1,7) Sd(2),
implement with an 8-input Mux.
En
Id a b c f 0 0 0
0 1 1 0 0 1
1 2 0 1 0 - 3 0 1
1 0 4 1 0 0
0 5 1 0 1 0 6 1 1
0 0 7 1 1 1 1
1
0 1 2 3 4 5 6 7
1
0
0
y
0
0
0
1
S0
S1
S2
a
b
c
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Multiplexer Application Example 2 Given f
(a,b,c) Sm (0,1,7) Sd(2), implement with
4-input Muxes.
D (c) D0 (c) 1 D1 (c) 0 D2 (c) 0 D3 (c) c
a 0 0 1 1
b 0 1 0 1
c 0 1 - 0 0
c 1 1 0 0 1
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Multiplexer Application Example 3 Given f
(a,b,c) Sm (0,1,7) Sd(2), implement with
2-input Muxes.
a 0 1
00 01 10 11 1 1 - 0 0 0
0 1
D (b,c) D0 (b,c) D1 (b,c)
D0 (b,c) b
D1 (b,c) bc

• -
• 1 0

0 0 0 1
c
c
b
b
D1 (b,c)
b 0 1
c 0 0 0
c 1 0 1
l1(0) 0 l1(c) c
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4. Demultiplexers
En
yi x if i (Sn-1, .. , S0) En 1 yi 0
otherwise
y2n-1 -y0
x
(Control Input)
Sn-1
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Shifter
yi xi-1 if En 1, s 1, and d L xi1
if En 1, s 1, and d R xi if En
1, s 0 0 if En 0
Can be implemented with a mux
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Barrel Shifter
shift
x
0 1
0 1
0 1
O or 1 shift
s0
O or 2 shift
s1
0 1
0 1
0 1
0 1
0 1
O or 4 shift
s2
0 1
0 1
0 1
0 1
y
0 1
0 1