Transcript Transistors and Logic Gates

Chapter 3
Digital Logic
Structures
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Transistor: Building Block of Computers
Microprocessors contain millions of transistors
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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 switch
Combined to implement logic functions
• AND, OR, NOT
Combined to build higher-level structures
• Adder, multiplexor, decoder, register, …
Combined to build processor
• LC-3
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Transistors
http://www.brew-wood.co.uk/computers/transistor.htm
First transistor: Bell Labs
in 1947; developed by
J. Bardeen, W. Shockley
& W. Brattain
A 2011 processor with 1.17 billion
transistors positioned in 240 sq.
millimeters
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Simple Switch Circuit
Switch open:
• No current through circuit
• Light is off
• Vout is +2.9V
Switch closed:
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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 Transistor
MOS = Metal Oxide Semiconductor
• two types: N-type and P-type
N-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
Drain
Animation
Source
Gate = 0
GND
Terminal #2 must be
connected to GND (0V).
GND
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P-type MOS Transistor
P-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)
+2.9V
Gate = 1
GND
Source
Gate = 0
Terminal #1 must be
connected to +2.9V.
Drain
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CMOS Circuit
Complementary MOS
Uses both N-type and P-type MOS transistors
• P-type
Attached to + voltage
Pulls output voltage UP when input is zero
• N-type
Attached to GND
Pulls 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)
High Voltage
Truth table
Ground
In
Out
0 V 2.9 V
2.9 V
0V
In
Out
0
1
1
0
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Logical Operations
http://www.computerhistory.org/revolution/digital-logic/12/269
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.
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NOR Gate (NOT OR)
High Voltage
Ground
Note: Serial structure on top, parallel on bottom.
A
B
C
0
0
1
0
1
0
1
0
0
1
1
0
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OR Gate
A
B
C
0
0
0
0
1
1
1
0
1
1
1
1
Add inverter to NOR.
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NAND Gate (NOT-AND)
Note: Parallel structure on top, serial on bottom.
A
B
C
0
0
1
0
1
1
1
0
1
1
1
0
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AND Gate
A
B
C
0
0
0
0
1
0
1
0
0
1
1
1
Add inverter to NAND.
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Basic Logic Gates
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More than 2 Inputs?
AND/OR can take any number of inputs.
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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.
A
B
A
B
C
C
A
B
C
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Logical Completeness
Can implement ANY truth table with AND, OR, NOT.
A
B
C
D
0
0
0
0
0
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
1.AND combinations
that yield a "1" in the
truth table.
Put a “bubble” (inverter)
for every 0, a straightin for every 1 in a row
2. OR the results
of the AND gates.
D
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 Law
Converting AND to OR (with some help from NOT)
Consider the following gate:
A B
A
B
A B
A B
0 0
1
1
1
0
0 1
1
0
0
1
1 0
0
1
0
1
1 1
0
0
0
1
To convert AND to OR
(or vice versa),
invert inputs and output.
Same as A OR B!
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Summary
MOS transistors are used as switches to implement
logic 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
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