chapter 3 digital logic structures
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Chapter 3 Digital Logic Structures. Transistor: Building Block of Computers. Microprocessors contain millions of transistors Intel Pentium II: 7 million Compaq Alpha 21264: 15 million Intel Pentium III: 28 million Intel Pentium4: 55 Million Intel Core 2 Duo: 291 Million - PowerPoint PPT PresentationTRANSCRIPT
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Chapter 3Digital LogicStructures
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Transistor: Building Block of ComputersMicroprocessors contain millions of transistors
• Intel Pentium II: 7 million• Compaq Alpha 21264: 15 million• Intel Pentium III: 28 million• Intel Pentium4: 55 Million• Intel Core 2 Duo: 291 Million
Logically, each transistor acts as a switchCombined to implement logic functions
• AND, OR, NOTCombined to build higher-level structures
• Adder, multiplexor, decoder, register, …Combined to build processor
• LC-3
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Transistors
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First transistor: Bell Labs in 1947; developed byJ. Bardeen, W. Shockley & W. Brattain
A 2011 processor with 1.17 billion transistors positioned in 240 sq. millimeters
http://www.brew-wood.co.uk/computers/transistor.htm
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Simple Switch Circuit
Switch open:• No current through circuit• Light is off• Vout is +2.9V
Switch closed:• Short circuit across switch• Current flows• Light is on• Vout is 0V
Switch-based circuits can easily represent two states:on/off, open/closed, voltage/no voltage.
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N-type MOS TransistorMOS = Metal Oxide Semiconductor
• two types: N-type and P-typeN-type
• when Gate has positive voltage,short circuit between #1 and #2(switch closed)
• when Gate has zero voltage,open circuit between #1 and #2(switch open) Gate = 1
Gate = 0Terminal #2 must be
connected to GND (0V).
AnimationDrain
SourceGND
GND
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P-type MOS TransistorP-type is complementary to N-type
• when Gate has positive voltage,open circuit between #1 and #2(switch open)
• when Gate has zero voltage,short circuit between #1 and #2(switch closed)
Gate = 1
Gate = 0Terminal #1 must beconnected to +2.9V.
Source
Drain
GND
+2.9V
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CMOS CircuitComplementary MOSUses both N-type and P-type MOS transistors
• P-typeAttached to + voltagePulls output voltage UP when input is zero
• N-typeAttached to GNDPulls output voltage DOWN when input is one
For all inputs, make sure that output is either connected to GND or to +,but not both!
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Inverter (NOT Gate)
In Out0 V 2.9 V
2.9 V 0 V
In Out0 11 0
Truth table
High Voltage
Ground
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Logical Operations
In 1850, George Boole developed Boolean Algebra showing that all logical functions can be performed with just 3 operations (AND, OR & NOT). In 1937, Claude Shannon showed that Boolean Algebra could be applied to circuit design. 3-9
http://www.computerhistory.org/revolution/digital-logic/12/269
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NOR Gate (NOT OR)
A B C0 0 10 1 0
1 0 0
1 1 0
Note: Serial structure on top, parallel on bottom.
High Voltage
Ground
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OR Gate
Add inverter to NOR.
A B C0 0 00 1 1
1 0 1
1 1 1
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NAND Gate (NOT-AND)
A B C0 0 10 1 1
1 0 1
1 1 0
Note: Parallel structure on top, serial on bottom.
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AND Gate
Add inverter to NAND.
A B C0 0 00 1 0
1 0 0
1 1 1
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Basic Logic Gates
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More than 2 Inputs?AND/OR can take any number of inputs.
• AND = 1 if all inputs are 1.• OR = 1 if any input is 1.• Similar for NAND/NOR.• An AND gate with k inputs is called and ANDk gate (e.g., an AND2, AND3,
etc).Can implement AND3 with multiple AND2 gates,or with single transistor circuit.
• AND/OR are associative and commutative -- combine in any order.
ACB
C
AB
C
AB
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Logical CompletenessCan implement ANY truth table with AND, OR, NOT.
A B C D0 0 0 00 0 1 0
0 1 0 1
0 1 1 0
1 0 0 0
1 0 1 1
1 1 0 0
1 1 1 0
A B C
D
1.AND combinations
that yield a "1" in the truth table.
Put a “bubble” (inverter) for every 0, a straight-in for every 1 in a row
2. OR the resultsof the AND gates.
If there are N 1’s, there will be N and gates; the or gate will have N inputs
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DeMorgan's LawConverting AND to OR (with some help from NOT)Consider the following gate:
A B0 0 1 1 1 00 1 1 0 0 1
1 0 0 1 0 1
1 1 0 0 0 1
BA BA BA
Same as A OR B!
To convert AND to OR (or vice versa),
invert inputs and output.
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SummaryMOS transistors are used as switches to implementlogic functions.
• N-type: connect to GND, turn on (with 1) to pull down to 0• P-type: connect to +2.9V, turn on (with 0) to pull up to 1
Basic gates: NOT, NOR, NAND• Logic functions are usually expressed with AND, OR, and NOT
Properties of logic gates• Completeness
can implement any truth table with AND, OR, NOT• DeMorgan's Law
convert AND to OR by inverting inputs and output