logic and integrated circuits
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Logic and Integrated Circuits. Lin Zhong ELEC101, Spring 2011. Key concepts. Binary numeral system Boolean logic Logic gates Functional completeness CMOS gates Integrated circuits. Binary computing. Modern computing are based on binary states - PowerPoint PPT PresentationTRANSCRIPT
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Logic and Integrated Circuits
Lin ZhongELEC101, Spring 2011
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Key concepts
• Binary numeral system• Boolean logic
– Logic gates– Functional completeness
• CMOS gates• Integrated circuits
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Binary computing
• Modern computing are based on binary states – Two values: HIGH vs. LOW, 1 vs. 0, true vs. false
• Why– Easy to implement– Robust against interference, noise,
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Computing with binary states
• Binary numeral system– Represent numeric values using two values: 0 and 1– The more “natural” numeral system is decimal
• 0, 1, 2, 3, 4, 5, 6, 7, 8, 9– One to one mapping between the two systems
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Decimal Binary
0 0
1 1
2 10
3 11
4 100
Decimal Binary
5 101
6 110
7 111
8 1000
9 1001
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Recall the single-input computer
• Inverter
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In Out
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How about a two-to-one computer
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Binary “states” for input and output: HIGH or LOW (1 or 0)
How many different computers are there?
A
OutB
A B Out
0 0
0 1
1 0
1 1
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How about a two-to-one computer
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Binary “states” for input and output: HIGH or LOW (1 or 0)
Useless ones: Out always 1; Out always 0; Out=A; Out=B
InverterOut= Invert (A); Out= Invert (B)
Useful ones:????
A
OutB
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Three basic logic operations• Inversion (NOT): Out = ¬ In
• AND: Out = A Λ B
• OR: Out = A V B
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In Out
0 1
1 0
A B Out
0 0 0
0 1 0
1 0 0
1 1 1
A B Out
0 0 0
0 1 1
1 0 1
1 1 1
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More gates
• NAND
• NOR
• XOR– A XOR B = [A Λ (¬B)] V [(¬A) Λ B]
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A B Out
0 0 0
0 1 1
1 0 1
1 1 0
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How about a two-to-one computer
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Binary “states” for input and output: HIGH or LOW (1 or 0)
Useless ones:Out = 0; Out =1; Out =A; Out=B;Inverters:Out= ¬A; Out= ¬B;
Useful ones:Out = A Λ B(AND), Out= A V B(OR), Out= A XOR BOut = ¬(A Λ B) (NAND), Out= ¬ (A V B) (NOR), Out = ¬ ( A XOR B)
A Λ (¬B); (¬A) Λ B; A V (¬B); (¬A) V B;
A
OutB
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Functional completeness
• NOT, AND and OR can be used to build ANY Boolean function– Functionally complete
• Can you prove the following?– NOR is functionally complete– NAND is functionally complete
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CMOS gates implementation
• NOT
• AND
• OR
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CMOS gates: NAND
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Gnd
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CMOS gates: NOR
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Vdd
Gnd
A
B
Out
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Lab: NAND gate
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Adder
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A B
Sum
Carry-out
A, B, and Sum are states that take value from 0 to 9
Carry-out is a state that take value from 0 to 1
A B Sum Carry-out
2 5 7 0
9 9 8 1
… … … …
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The simplest adder
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A B
Sum
Carry-out
A, B, and Sum are states that take value from 0 to 1
Carry-out is a state that take value from 0 to 1
A B Sum Carry-out
0 1 1 0
1 1 0 1
1 0 1 0
0 0 0 0
Truth table
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The simplest adder (Contd.)
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A B
Sum
Carry-out
A, B, and Sum are states that take value from 0 to 1
Carry-out is a state that take value from 0 to 1
A B Sum Carry-out
0 1 1 0
1 1 0 1
1 0 1 0
0 0 0 0
Truth table
Sum= A XOR BCarry-out = A AND B
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How many transistors do you need?
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Sum
Carry-out
Sum= A XOR B
Carry-out = A AND B
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AND
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XOR Sum= A XOR B = [A Λ (¬B)] V [(¬A) Λ B]
= [A AND (NOT B)] OR [(NOT A) AND B]
=[A NAND (NOT B)] NAND [(NOT A) NAND B]
= [(A AND B) NOR (A NOR B)]
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XOR (Contd.)
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Out
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XOR (Contd.)
23
Out
Vdd
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Computing with binary states (Contd.)• Boolean logic
– Variables are binary (0 or 1)– Three operations on binary variables
• Inversion (¬), AND (Λ), and OR (V)– Five axioms
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George Boole
1815-1864
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Integrated Circuit
25Shared Nobel Prize in Physics 2000
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Photolithography
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1969
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Ivan Sutherland won Turing Award in 1988 for his Ph.D. work in 1963
http://www.cl.cam.ac.uk/techreports/UCAM-CL-TR-574.pdf
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“Programmable” integrated circuit
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A B
Sum
Carry-out
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“Programmable” integrated circuit
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A B
Output
Control
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“Programmable” integrated circuit
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A B
Output
Control
Storage
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“Programmable” integrated circuit
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A B
Output
Control
Storage
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“Programmable” integrated circuit
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A B
Output
Control
Storage
0110100010101Instruction in machine code
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“Programmable” integrated circuit
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A B
Output
Control
Storage
Default start instruction
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Computing vs. human performance
Sources: intel.com and factmonster.com
1968 1972 1976 1980 1984 1988 1992 1996 2000 20041
10
100
1000
10000
100000
1000000Olympic Gold Metal winner: 100m dash (men)Olympic God Metal winner: 100m dash (women)# of transistors for Intel processorProcessor performance measured in MIPS
Year
Tim
es o
f im
prov
emen
t
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Computing vs. humanity
1965 1970 1975 1980 1985 1990 1995 2000 20050.000001
0.00001
0.0001
0.001
0.01
0.1
1
10
USA Federal minimum wage in 2003 dollar
Average transistor price for Intel processors in contemporary dollar
USA
$
Source: Intel.com and dol.gov
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38http://ftp.arl.army.mil/ftp/historic-computers/png/eniac4.png
Computing: 60 years agoWiring ENIAC with a new program