Digital Basics - Department of Physics and Astronomycremaldi/PHYS321/Chaper11-DigitalBasics.pdf ·...
Transcript of Digital Basics - Department of Physics and Astronomycremaldi/PHYS321/Chaper11-DigitalBasics.pdf ·...
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Digital Basics
• Analogue Communications over long distances often were hampered by noise, fluctuations, etc.
• Analogue communications can have high band width. AM and FM radio! (information transfer/sec)
• Digital communications are more robust but can suffer from band width limitations. Drums, Smoke Signals, Morse Code, Internet, etc.
• Analogue-to-digital & Digital-to-Analogue translators important for research and communications.
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In the transistor switch we can create a situation where a small input current can turn a transistor “On” or “Off”, the two states needed for digital electronics. Early computers used the vacuum tubes, but in the 1950’s Silicon rectifiers and diodes were being developed for this purpose. The “On” “Off” state is refered to as a “bit” short for “binary digit”.
Vref
Vin Vout
Digital Comparator
Vin > Vref Vout = 1 HIGH Vin < Vref Vout = 0 LOW
Transistor Switch and Comparator
On
Off
Switch IB high saturating transistor
IB low
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BITS and BYTES
• Digital information is sent over data packets. bit bit bit bit bit bit bit bit
8 bits = 1byte
• Internet packet = 32 bits • Computer word packet = 32 bits long word Computer word packet = 64 bits double precision • Computer memory = 1 Gbyte = 109 x 8 bits • Hard disk = >50 GB 2 TB (1012) • CD = 700 MB ( 80 minutes of audio) • DVD = 4.7 GB (2 hrs HR video ) • Blue Ray = 100-125 GB
bit 0 or 1
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AND A
B
AB =C
A+B =C
A
NAND A
B
A B AND 0 0 0 0 1 0 1 0 0 1 1 1
NAND
1 1 0
1
TRUTH TABLE
A B OR
0 0 0 0 1 1 1 0 1 1 1 1
NOR 1 0 0 0
XOR 0 1 1 0
TRUTH TABLE
Digital Gates
A A INERTER
XOR A
B
B NOR
A
B OR
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A . B = C A .and. B = C
A+B= C A .or. B = C
A . B = C A .and. B = C
A+B = C A .or. B = C
Boolean Theorems
(1) A+A = A
(2) A . A = A
(3) A + 1 = 1
(4) A . 1 = A
(5) A + 0 = A
(6) A . 0 = A
(7) A + A = A
(8) A . A = 0
(9) A = A
(10) A + A . B = A
(11) A .(A + B) = A
(12) A .(A + B) = A.B
(13) A + A . B = A + B
(14) A + A . B = A + B
(15) A + A . B = A + B
(16) A . B = A + B
(17) A + B = A . B DeMorgan’s Theorems
Boolean Algebra
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(1) A+A = A
A A A+A 0 0 0 1 1 1
(2) A . A = A
A A AA
0 0 0 1 1 1
(8) A . A = 0
A A AA
0 1 0 1 0 0
(11) A (A+B) = A
A A+B 0 0 1 1
B 0 0
0 1 1 1
1 1
A(A+B) 0 1 0 1
Boolean Proofs by Truth Table
(16) A B = A + B
A AB 0 0 1 0
B 0 0
0 1 1 1
0 1
AB 1 1 1 0
A+B 1 1 1 0
A 1 0
B 1 1
1 0 0 0
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• F = A(A+B) =AA+AB = 0 + AB -8 = AB -5
• #6(a) • F = ABCD + ABCD = A(B+B)CD = A(1)CD -7 = ACD
• #6(b) • F = AB + AC + ABC(AB+C) = AB + AC + ABCAB+ABCC) = AB + AC + (AA)(BB)C+ABCC) 2,8 = AB + AC + (A)(0)C +ABC = A(B+BC) + AC = A(B+C) + AC 13 = AB +AC +AC = = AB
Boolean Proofs by DeMorgan's Theorems
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2o 21 22 23 24 25 26 27
0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0
0 1 2 3 4 5 6 7 8
Decimel
Binary - base2
N2 = a0 20 + a1 21 + a2 22 + a3 23 + = (a3 a2 a1 a0)2
LSB MSB
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Other Systems
Binary 2-digi 0,1 N2 = a0 20 + a1 21 + a2 22 + a323 + Octal 8-digi 0,1,2,3,4,5,6,7 N8 = a0 80 + a1 81 + a2 82 + a383 + Decimal 10-digi 0,1,2,3,4,5,6,7,8,9 N10 = a0 100 + a1 101 + a2 102 + a3103 + Hexadecimal 16-digi 0,1,2,3,4,5,…..A,B,C,D,E,F N16 = a0 160 + a1 161 + a2 162 + a3163 + BCD binary coded decimal 9910 = 1001 1001BCD
a0 a1 a2 a3 … a4
1 0 0 1 1 0 0 1
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LOGIC FAMILIES
TTL Logic- Transistor-Transistor Logic gates Transistors are fully turned on. Excellent noise margin High power (1-20)mW/gate Single Vcc supply voltage. High>3-5V Low~0.2V
ECL Logic- Emitter Coupled Logic
High speed by not saturating transistors. Td < 1ns (gate speed) Low Power (0.5-1.0) mW/gate Multiple supply voltages Higher fan-in capability
CMOS- Complementary Metal Oxide Logic
Very Low Power Excellent Noise Margin Inexpensive Slower than TTL Td>10ns Fragile
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Case of Binary Addition A+B=C
1 1 0 1 0 0 0 0
1 0 0 0 0 0 0 0
A register +
0 1 1 0 0 0 0 0
0 0 1 1 0 0 0 0
B register
Carry A = 1110
B = 0110
C = 1210
10112 + 00012 = 11002 Base 2 notation
1110 + 0110 = 1210 Base 10 notation
registers
1
1
0
1 carry
add In-1
In-2
clock
GATE/FLIP-FLOP
=
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A B AND 0 0 0 0 1 0 1 0 0 1 1 1
NAND
1 1 0
1
TRUTH TABLE
OR 0 1 1 1
NOR 1 0 0 0
XOR 0 1 1 0
A
B
SUM
CARRY carry
add In-1
In-2
clock
0 0 A B SUM CARRY
0 0 0 1 1 0 1 0 1 0 1 1 0 1
ADDITION
XOR OR
A
B
SUM
CARRY
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Analogue-to-Digital
8v
7v
6v
5v
4v
3v
2v
1v
clk
Analogue signal
0 0 0 0 0 0 0 1
0 0 0 0 0 0 1 1
0 0 0 0 0 1 1 1
0 0 0 1 1 1 1 1
0 1 1 1 1 1 1 1
0 0 1 1 1 1 1 1
0 0 0 0 1 1 1 1
0 0 0 0 0 1 1 1
0 0 0 0 0 0 1 1
0 0 0 0 0 0 0 1
Time -->
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Open Collector and Tri-state Logic
• In standard ttl or cmos logic there is a problem with concatenating gates for an output. Consider Y=ABCD formed below from 2 NAND Gates. • When A=B=C=D=0 F=G=1 and Y=1 When A=0 B=C=D=1 F=1 G=0 and Y=?? indeterminant
7400 C
D
7400 A
B F
G Y
7403 C
D
7403 A
B F
G Y
+5V
tri C
D
tri A
B F
G Y
enable
Open collector Tri-state Standard
Tri-state chips can be enabled/disabled, effectvely setting them to infinite ground, virtually removing them from the circuit.
Outputs are pulled up to +5V when hi and virtual ground when low.
Output can be indeterminant!
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Epitaxial Gates
n n p
base
collector emitter
+V
+V G
Electron flow IC =b IB
BIPOLAR
n-channel
Indium bump p
p-diffusion
source drain
gate
depletion region
-V
G +V
JFET
n-channel
n++ n++
Si Substrate
MOSFET
SiO2
-V +V G source drain
gate