

A259061


Gillham Code, a modified Gray code for use in encoded altimeters.


0



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
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OFFSET

12,1


COMMENTS

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 hundredfoot 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 D1B4 store the number of 500ft increments and C1C4 store the number of 100ft increments +1 from the lowest altitude datum (1200ft).
The 500ft values are coded in standard Gray code.
The C14 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.


REFERENCES

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.


LINKS

Table of n, a(n) for n=12..44.
AirSport Avionics, Table of Mode A and Mode C Encoder Data.
Google/Patents, US Patent Feb.8,1977, nbr: 4,006,638 for an aircraft altimeterencoder.
InfoRapid Knowledge Portal, Gillham Code.
D. R. Treffeisen, Image of an Aircraft Altimeter Encoder Optical Wheel.
Wikipedia, Gillham code


EXAMPLE

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".


CROSSREFS

Cf. A003188.
Sequence in context: A260602 A116309 A126816 * A035120 A094619 A052475
Adjacent sequences: A259058 A259059 A259060 * A259062 A259063 A259064


KEYWORD

nonn,base


AUTHOR

David Dewhirst, Charles Pine, and Robert G. Wilson v, Jun 17 2015


STATUS

approved



