6.002x CIRCUITS AND 0 ELECTRONICS 0 101 The Digital ... fileThe Digital Abstraction Reading: Chapter...
Transcript of 6.002x CIRCUITS AND 0 ELECTRONICS 0 101 The Digital ... fileThe Digital Abstraction Reading: Chapter...
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6.002x CIRCUITS AND ELECTRONICS
The Digital Abstraction
Reading: Chapter 5 of A&L
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Review l Discretize matter by observing lumped matter discipline
l Analysis tool kit KVL/KCL, composition, node, superposition, Thévenin, Norton
Lumped Circuit Abstraction
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In this Sequence
Interestingly, we will see shortly that the tools learned in the previous three lectures are sufficient to analyze simple digital circuits
Discretize value
Digital abstraction
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Analog signal processing
But first, why digital?
and might represent the outputs of two sensors, for e.g. 1 V 2 V Shorthand notation
(from node method)
+ – + –
+
-
V1
V2
V0
R1
R2
In the past …
+ – + –
V1
R1
R2
V2
V0
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Analog signal processing Why digital?
The above is an “adder” circuit.
+ – + –
V1
V2
V0
R1
R2
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Noise Problem with Analog
Noise hampers our ability to distinguish between small differences in value — e.g. between 3.1V and 3.2V.
Receiver: huh?
t
t
+ – + –
V1
V2
V0
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Idea: Value Discretization (or lumped values)
Restrict values to be one of two
…like two digits 0 and 1
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Why is this discretization useful?
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Digital System
sender receiver
“0” “0” “1”
0 V
2.5 V
5 V HIGH
LOW
t
VS
“0” “0” “1”
0 V 2.5 V
5 V t
VR
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Digital System
sender receiver
With noise VS VR
“0” “0” “1”
0 V 2.5 V
5 V
VS
t
0.2 V t
“0” “0” “1”
2.5 V
VR
t 0 V
5 V
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Digital System
Better noise immunity à Lots of “noise margin” For “1”: noise margin 5 V to 2.5 V = 2.5 V For “0”: noise margin 0V to 2.5 V = 2.5 V
“0” “0” “1”
2.5 V
Vs
t 0 V
5 V
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The Big Picture
The world The EECS playground (lump matter)
Linear circuits
Digital land (lump value)
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Digital System Sender-Receiver Contract
sender receiver VS VR
noise VN
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Voltage Thresholds and Logic Values
sender receiver
0 V
5 V
But, but, but … What about 2.5V?
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Hmmm… Idea! Create “no man’s land” or forbidden region
sender receiver
0 V
5 V Remember, we can do so with impunity because it is our choice as to what discipline we agree on in our digital playground
Does this work?
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forbidden region
V H
V L
3 V
2 V
“No Man’s Land” or Forbidden Region
sender receiver
0 V
5 V
1 1
0 0
“1”: V à 3V H
“0”: V à 2V L
Where’s the noise margin? What if the sender sent 1: VH
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sender receiver
Hold the Sender to Tougher Standards!
5V
0V
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“1” noise margin: “0” noise margin:
Together, the VOH, VIH, VOL, VIL thresholds define a discipline or standard that digital devices follow so they can talk to each other
sender receiver
5V
0V
1 1
0 0
V 0H
V 0L
V IH
V IL
Noise Margins
Noise margins
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Digital systems follow static discipline: if inputs to the digital system meet valid input thresholds, then the system guarantees its outputs will meet valid output thresholds.
receiver
t
5V V
0H
V 0L
0V
V IH
V IL
0 1 0 1
sender 0 1 0 1
t
5V V
0H
V 0L
0V
V IH
V IL
Noise Immunity
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Processing Digital Signals
Recall, we have only two values —
1,0 Map naturally to logic: T, F
What is 1011? Check Chapter 5.6 of A&L
Can also represent numbers
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Processing Digital Signals Boolean Logic
If X is true and Y is true Then Z is true, else Z is false.
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Processing Digital Signals
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Z = X • Y
What is the Output Of This Gate? X
t
Y
t
Z
t
Z X Y
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Combinational Gate Abstraction
Digital logic designers do not have to care about what is inside a gate.
n Adheres to static discipline n Outputs are a function of
inputs alone.
Z X Y
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Logic Gates AND gate Z X
Y
Z X Y 0 0 0 0 1 0 1 0 0 1 1 1
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Another Gate Example If (A is true) OR (B is true) then C is true else C is false
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Implement: output = A + B • C
Digital Circuits
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Numbers larger than 1 can be represented using multiple binary digits and coding, much like using multiple decimal digits to represent numbers greater than 9. The binary number 101 has decimal value:
Representing Numbers
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A Two-Bit Adder Circuit
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Demo
Z X Y
Z = X • Y
Z
Y
X