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A259061
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Gillham Code, a modified Gray code for use in encoded altimeters.
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0
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40, 60, 20, 30, 10, 410, 430, 420, 460, 440, 640, 660, 620, 630, 610, 210, 230, 220, 260, 240, 340, 360, 320, 330, 310, 710, 730, 720, 760, 740, 540, 560, 520, 530, 510, 110, 130, 120, 160, 140, 4140, 4160, 4120, 4130, 4110, 4510, 4530, 4520, 4560, 4540, 4740, 4760, 4720, 4730, 4710, 4310, 4330
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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-12,1
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COMMENTS
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Gray codes are named after Frank Gray, who patented their use for shaft encoders in 1953. (F. Gray, "Pulse Code Communication", U.S. Patent 2,632,058, March 17, 1953.)
All entries are four digits long and therefore leading zeros are implied. Each place is the decimal equivalent of an octal number.
Aircraft encoded altimeters report in hundred-foot increments beginning with index -12, which implies minus 1200 feet Pressure Altitude. The scheme is good up to 126700 feet.
The order of the bits from MSB (most significant) to LSB (least significant) is D1 D2 D4 A1 A2 A4 B1 B2 B4 C1 C2 C4.
When the code was designed it was suspected that the method for encoding dealt with multiples of 500ft separately from multiples of 100ft. This may be why the bits from D1-B4 store the number of 500ft increments and C1-C4 store the number of 100ft increments +1 from the lowest altitude datum (-1200ft).
The 500ft values are coded in standard Gray code.
The C1-4 bits are coded using a nonlinear Gray code. That is to say if you convert these bits from Gray code to binary you find that the values follow a pattern: 1, 2, 3, 4, 7, 7, 4, 3, 2, 1, 1, 2, 3, 4, 7 which repeats ramping up and down.
This scheme of encoding is implemented in such a way that the failure of any single sensor/pickup will report an altitude value that is obviously preposterous.
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REFERENCES
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M. Gardner, "The Binary Gray Code." Ch. 2 in Knotted Doughnuts and Other Mathematical Entertainments. New York: W. H. Freeman, 1986, p. 15.
M. Gardner, Mathematical Games, Sci. Amer. Vol. 227 (No. 2, Feb. 1972), p. 107.
C. A. Pickover, The Math Book, Sterling, NY, 2009; see p. 392.
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LINKS
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EXAMPLE
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At 0' MSL (feet mean sea level), the encoder is "squawking" or reporting to other aviation shareholders, particularly Air Traffic Controllers and commercial airliners equipped with TCAS, "0620".
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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