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ENGG1007
Foundations of Computer Science
Graphs
Graphs
Hamiltonian Graphs 2
Hamiltonian Graphs 2
Professor Francis Chin, Dr SM Yiu
November 15/17, 2010
Chapter 9.5
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ENGG1007
FCS
Rotating Drum
Rotating Drum
First bit
Third bit
Second bit
3
ENGG1007
FCS
Rotating Drum Positioning revisited
Rotating Drum Positioning revisited
The 2
n
positions of the drum can be
determined by the contacts of
n
rings.
The innermost ring is for the first bit, …
and the outermost ring for the
last bit.
111 000
110
001
101
010
100 011
First bit
Second bit
Third bit
Errors might easily be introduced at
the position transition.
For example: 001 to 010, we might have
001
____
010
Perfect transition
001
010
000
Gap introduces error
001
010
011
Overlap introduces error
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ENGG1007
FCS
Rotating Drum Positioning revisited
Rotating Drum Positioning revisited
111 000
110
001
101
010
100 011
100 000
101
001
111
011
110
010
First bit
Second bit
Third bit
Errors might easily be introduced at
the transition from one position to
the next if the change of the bit
positions is more than one bit.
EG. Transition between 111 and 000.
Any bit representation is possible.
Thus the bit representations of two
adjacent positions should not differ
too much (with only 1 bit transition).
100
111
101
000
5
ENGG1007
FCS
Gray Code
Gray Code
Consider bit strings {000,001,010,011,100,101,110,111}
Can you permute them so that adjacent bit strings defer by
one bit only?
Transform to G(V,E), where
V = set of bit strings,
E = { (x,y) if x and y differ by 1 bit }
000
001
010
100
101
110
111
011
First bit
Second bit
Third bit
It is easy to see that G is a hypercube.
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This note was uploaded on 02/10/2011 for the course ENGG 1007 taught by Professor Unknown during the Spring '11 term at HKU.
 Spring '11
 Unknown
 Computer Science

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