cec 220 digital circuit design timing diagrams, muxs, and buffers wed, february 18 cec 220 digital...
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CEC 220 Digital Circuit DesignTiming Diagrams, MUXs, and Buffers
Wed, February 18 CEC 220 Digital Circuit Design Slide 1 of 20
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Lecture Outline
Wed, February 18 CEC 220 Digital Circuit Design
• Timing Diagrams• Multiplexers• Tri-State Buffers
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Timing Diagrams
Wed, February 18 CEC 220 Digital Circuit Design
• Problem: Real signals do NOT change instantaneously Real hardware (i.e., gates) do not respond immediately
• Resolution: Look at the signals vs time Timing diagrams!!
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Timing DiagramsEffect of Gate Delays
Wed, February 18 CEC 220 Digital Circuit Design
• Consider the simple circuit: Assume that all gates have
a 10 ns delay
The outputs may not be defined at the start!!
10 ns
10 ns
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0 50 100 150
Timing DiagramsHazards in Combinational Logic
Wed, February 18 CEC 220 Digital Circuit Design
• Glitches: The inverter has a 10 ns delay The AND gate has a 5 ns delay
A
B
C
Ideally, . In the “real world” glitches occur!!
10 ns
5 ns
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Timing DiagramsHazards in Combinational Logic
Wed, February 18 CEC 220 Digital Circuit Design
A Static 1-Hazard A Static 0-Hazard
Dynamic Hazards
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MultiplexersA 2:1 Multiplexer
Wed, February 18 CEC 220 Digital Circuit Design
• A Multiplexer (or data selector) uses a control input(s) to select one of multiple inputs.
Z = I0 if is true, or I1 if is true
Z = I0 + I1
Z
I0
I1
=0=1
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Multiplexers4:1 and 8:1 Multiplexers
Wed, February 18 CEC 220 Digital Circuit Design
2n inp
ut d
ata
lines
n select lines0 1 2 3Z I AB I AB I AB I AB
4:1 MUX
0
1
2
30S
1S
I0
I1
I2
I3
A B
Z
Dat
a In
puts
Control Inputs
0S1S
2S
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MultiplexersAn Example
Wed, February 18 CEC 220 Digital Circuit Design
• Problem: Use an 8:1 MUX to implement the following truth table.
A B C Z
0 0 0 0
0 0 1 0
0 1 0 1
0 1 1 1
1 0 0 1
1 0 1 0
1 1 0 1
1 1 1 0
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Buffers
Wed, February 18 CEC 220 Digital Circuit Design
• Problem: Real world gates have limited output current drive
capability (fan-out)
The OR gate may NOT be able toDrive all of the AND gates
Solution: Use a buffer
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Tri-State Buffers
Wed, February 18 CEC 220 Digital Circuit Design
• A Tri-State or Three-State buffer Output can be low, high, or high impedance (High-Z)
B=0B=1
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Tri-State Buffers
Wed, February 18 CEC 220 Digital Circuit Design
• Four kinds of Tri-State State buffers Output can be low (0), high (1), or high impedance (Z)
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Tri-State Buffers
Wed, February 18 CEC 220 Digital Circuit Design
• Can use tri-state buffers to build a MUX:
When B is low select A, orWhen B is high select C
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Tri-State Buffers
Wed, February 18 CEC 220 Digital Circuit Design
• Problem: IC’s have a limited number of pins Can use a given pin for either input or output
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Examples
Wed, February 18 CEC 220 Digital Circuit Design
• Realize a 4:1 MUX, using an 8:1 MUX.
0S1S
2S
0S1S
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Examples
Wed, February 18 CEC 220 Digital Circuit Design
• Make an 8:1 MUX, using four 2:1 & one 4:1 MUX
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Examples
Wed, February 18 CEC 220 Digital Circuit Design
• Use an 8:1 MUX to implement the function
f ABC ABC ABC ABC A B C f
0 0 0 1
0 0 1 0
0 1 0 1
0 1 1 1
1 0 0 0
1 0 1 0
1 1 0 0
1 1 1 1
A B C f
0 0 0
0 0 1
0 1 0
0 1 1
1 0 0
1 0 1
1 1 0
1 1 1
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Examples
Wed, February 18 CEC 220 Digital Circuit Design
• Use an 4:1 MUX to implement the function
A B C f
0 0 0 1
0 0 1 0
0 1 0 1
0 1 1 1
1 0 0 0
1 0 1 0
1 1 0 0
1 1 1 1
f ABC ABC ABC ABC
C10C
A B
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0f AB AB BC C C CAB A
f
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Examples
Wed, February 18 CEC 220 Digital Circuit Design
• Use an 2:1 MUX to implement the function
A B C f
0 0 0 1
0 0 1 0
0 1 0 1
0 1 1 1
1 0 0 0
1 0 1 0
1 1 0 0
1 1 1 1
f ABC ABC ABC ABC
A BC BC BC A BC
A BC B A BC
A C B A BC A BC 0 1
00 1 0
01 0 0
11 1 1
10 1 0
f BC AC
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A
C
B
B
C
f
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Next Lecture
Wed, February 18 CEC 220 Digital Circuit Design
• Decoders and Encoders• Read-Only Memories (ROMs)
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