ICT-TR-2014-01
sequences for the columns and rows. The patterns are shown in the order they are pro-
jected as indicated by the time arrow i.e the first pattern to be projected corresponds
to the most significant bit and appears as the last one in the diagram, followed by the
remaining. As time progresses the frequency of the pattern increases until it reaches
the highest frequency which represents the least significant bit in binary pattern.
The result is a sequence of binary encoded patterns where each pattern represents one
bit of the binary sequence. This produces images containing vertical stripes in the case
of the columns, and horizontal stripes in the case of the rows.
Figure 3: Encoding the information into a sequence of patterns in temporal domain.
0.4.2 Gray-code Encoding
The Gray-code encoding works in a similar way as the binary encoding previously
described, however it ensures that there is only one bit different between consecutive
patterns. Figure 4 shows a comparison between Gray and Binary encoding for the
columns of an 8x8 area. As it is evident, in the case of Gray codes there is a maximum
of one bit difference between any two consecutive encoding of values. Figure 6b shows
a sequence of encoded patterns using Gray-codes, corresponding to the same area of
8x8 as in Figure 6a.
Decimal Value Gray-code Binary code
0 000 000
1 001 001
2 011 010
3 010 011
4 110 100
5 111 101
6 101 110
7 100 111
Figure 4: Comparison between Gray codes and binary codes. In the case of Gray
codes there is only one bit difference between any two consecutive encodings.
Gray codes can be calculated by first computing the Binary representation of a number
and then converting it as follows: copy the most significant bit as is, and then for the
remaining bits (taking one bit at a time), replace with the result of an XOR operation
of the current bit with the previous bit of higher significance in the binary form. An
4
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