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9-bit, single-track Gray code, displaying one degree angular resolution. Since this 30 degree example was added, there has been a lot of interest in examples with higher angular resolution. In 2008, Gary Williams, [83] [user-generated source?] based on previous work, [80] discovered a 9-bit single track Gray code that gives a 1 degree resolution.
Examples of six-bit binary codes are: International Telegraph Alphabet No. 4 [4] Six-bit BCD (Binary Coded Decimal), used by early mainframe computers. Six-bit ASCII subset of the primitive seven-bit ASCII; Braille – Braille characters are represented using six dot positions, arranged in a rectangle. Each position may contain a raised dot or ...
The reason for adding 6 is that there are 16 possible 4-bit BCD values (since 2 4 = 16), but only 10 values are valid (0000 through 1001). For example: 1001 + 1000 = 10001 9 + 8 = 17 10001 is the binary, not decimal, representation of the desired result, but the most significant 1 (the "carry") cannot fit in a 4-bit binary number.
The 5-bit Baudot code used in early synchronous multiplexing telegraphs can be seen as an offset-1 (excess-1) reflected binary (Gray) code. One historically prominent example of offset-64 ( excess-64 ) notation was in the floating point (exponential) notation in the IBM System/360 and System/370 generations of computers.
This 4-bit RGBI schema is used in several platforms with variations, so the table given below is a simple reference for the palette richness, and not an actual implemented palette. For this reason, no numbers are assigned to each color, and color order is arbitrary. Note that "dark white" is a lighter gray than "bright black" in this example.
Powers of the 4-bit Gray code permutation (compare A195467) The permutation matrices are arranged in a cycle graph of the cyclic group Z 4 like , but the identity is in the top left position, so that the symmetric matrices are mirrored at the diagonal. Cayley table of the cyclic group (The orange vectors are the same as in the cycle graph.)
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