6002 l4 oei12 gaps abstraccion digital
TRANSCRIPT
-
7/28/2019 6002 L4 Oei12 Gaps Abstraccion Digital
1/30
00
0
0
011
111
00
00
0
000
0
00
0
0
1
11
11
1111
11
1
1
0
1
1
0
00
0
0
0
0
6.002xCIRCUITS ANDELECTRONICS
The Digital Abstraction
Reading: Chapter 5 of A&L
-
7/28/2019 6002 L4 Oei12 Gaps Abstraccion Digital
2/30
Reviewl Discretize matter by observing lumped matte
l Analysis tool kitKVL/KCL, composition, node, superposition, Thvenin, N
Lumped Circuit Abstract
-
7/28/2019 6002 L4 Oei12 Gaps Abstraccion Digital
3/30
In this Sequence
Interestingly, we will see shortly that thetools learned in the previous three
lectures are sufficient to analyze simpledigital circuits
Discretize value Digital abstraction
-
7/28/2019 6002 L4 Oei12 Gaps Abstraccion Digital
4/30
Analog signal processing
But first, why digital?
and might represent the
outputs of two sensors, for e.g.1V 2V Shorthand
(from node
+
+
+
-
V1
V2
V0
R1
R2
In the past
+
+
V1
R1
R2
V2
-
7/28/2019 6002 L4 Oei12 Gaps Abstraccion Digital
5/30
Analog signal processing
Why digital?
The above is an adder ci
+
+
V1
V2
V0
R1
R2
-
7/28/2019 6002 L4 Oei12 Gaps Abstraccion Digital
6/30
Noise Problem with Analog
Noise hampers our ability to distinguishbetween small differences in value
e.g. between 3.1V and 3.2V.
t
t
+
+
V1
V2
V0
-
7/28/2019 6002 L4 Oei12 Gaps Abstraccion Digital
7/30
Idea: Value Discretization(or lumped values)
Restrict values to be one of two
like two digits 0 and 1
-
7/28/2019 6002 L4 Oei12 Gaps Abstraccion Digital
8/30
Why is this discretization useful?
-
7/28/2019 6002 L4 Oei12 Gaps Abstraccion Digital
9/30
Digital System
sender receiver
0 01
0V
2.5V
5
V HIGH
LOW
t
VS
0 01
0V
2.5V
5V
t
VR
-
7/28/2019 6002 L4 Oei12 Gaps Abstraccion Digital
10/30
Digital System
sender receiver
With noiseVS V
R
0 01
0V
2.5V
5V
VS
t
0.2V
t
0 01
2.5V
VR
0V
5V
V
-
7/28/2019 6002 L4 Oei12 Gaps Abstraccion Digital
11/30
Digital System
Better noise immunity Lots of noise margin
For 1: noise margin 5V to 2.5V = 2.5V
For 0: noise margin 0V to 2.5V = 2.5V
2.5V
Vs
0
-
7/28/2019 6002 L4 Oei12 Gaps Abstraccion Digital
12/30
The Big Picture
The world
The EECS playground (lump matter)
Linearcircuits
Digital land(lump value)
-
7/28/2019 6002 L4 Oei12 Gaps Abstraccion Digital
13/30
Digital System Sender-Receiver C
sender receiverVS VR
noiseVN
l h h ld d l
-
7/28/2019 6002 L4 Oei12 Gaps Abstraccion Digital
14/30
Voltage Thresholds and Logic Valu
sender receiver
0V
5V
But, but, but What about 2.5V?
-
7/28/2019 6002 L4 Oei12 Gaps Abstraccion Digital
15/30
Hmmm Idea! Create no mans landor forbidden region
sender receiver
0V
5V
Does this
-
7/28/2019 6002 L4 Oei12 Gaps Abstraccion Digital
16/30
forbiddenregion
VH
VL
3V
2
V
No Mans Land or Forbidden Region
sender receiver
0V
5V
1 1
0
0
1:V3VH
0:V2VL
Whnoi
Whsen
1:
H ld th S d t T h St d d
-
7/28/2019 6002 L4 Oei12 Gaps Abstraccion Digital
17/30
sender receiver
Hold the Sender to Tougher Standard
5V
0V
N i M i
-
7/28/2019 6002 L4 Oei12 Gaps Abstraccion Digital
18/30
1 noise margin:
0 noise margin:
TVtha st
dfocaot
sender receiver
5V
0V
11
00
V0H
V0L
VIH
VIL
Noise Margins
Noise margins
N i I it
-
7/28/2019 6002 L4 Oei12 Gaps Abstraccion Digital
19/30
Digital sfollow st
disciplinto the dsystem minput thrthen the
guaranteoutputs valid outthreshol
receiver
t
5VV0H
V0L
0V
VIH
VIL
0 1 0 1
sender 0 1 0 1
t
5VV
0H
V0L
0V
V
IHV
IL
Noise Immunity
-
7/28/2019 6002 L4 Oei12 Gaps Abstraccion Digital
20/30
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
P i Di it l Si l
-
7/28/2019 6002 L4 Oei12 Gaps Abstraccion Digital
21/30
Processing Digital SignalsBoolean Logic
If X is true and Y is true
Then Z is true, else Z is false.
P i Di it l Si l
-
7/28/2019 6002 L4 Oei12 Gaps Abstraccion Digital
22/30
Processing Digital Signals
-
7/28/2019 6002 L4 Oei12 Gaps Abstraccion Digital
23/30
Z = X
What is the Output Of This GaX
t
Y
t
Z
t
XY
-
7/28/2019 6002 L4 Oei12 Gaps Abstraccion Digital
24/30
Combinational Gate Abstraction
Digital logic designers do nothave to care about what is
inside a gate.
n Adheres to static discipline
n Outputs are a function ofinputs alone.
XY
Logic Gates X Y
-
7/28/2019 6002 L4 Oei12 Gaps Abstraccion Digital
25/30
Logic Gates
AND gateZXY
X Y0 00 1 01 1
A th G t E l
-
7/28/2019 6002 L4 Oei12 Gaps Abstraccion Digital
26/30
Another Gate ExampleIf (A is true) OR (B is true)
then C is true
else C is false
Digital Circuits
-
7/28/2019 6002 L4 Oei12 Gaps Abstraccion Digital
27/30
Implement: output = A + B C
Digital Circuits
Representing Numbers
-
7/28/2019 6002 L4 Oei12 Gaps Abstraccion Digital
28/30
Numbers larger than 1 can be represented usimultiple binary digits and coding, much like us
multiple decimal digits to represent numbersgreater than 9.
The binary number 101 has decimal value:
Representing Numbers
A Two Bit Adder Circuit
-
7/28/2019 6002 L4 Oei12 Gaps Abstraccion Digital
29/30
A Two-Bit Adder Circuit
-
7/28/2019 6002 L4 Oei12 Gaps Abstraccion Digital
30/30
X
Y
Z =
Z
Y
X