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| King Wen sequence of fourteen hexagrams in binary formats. |
King Wen sequence is the sky computed in 2 raised to the power of 6.
Mathematically,
King Wen Sequence (KWS) = 2⁶
= 64
2 stands for the binary digits 0 and 1 encoded as broken and unbroken lines representing yin and yang. 6 stands for 6 bits, and 64 is the total number of binary numbers derivable from six binary digits.
The 64 binary numbers obtained from 6 bits are encoded as 64 I Ching or Yi Jing hexagrams arranged in a sequence called King Wen sequence.
The 64 hexagrams or divination figures are categorised into a group of eight single hexagrams and a group of twenty eight pairs.
A pair of hexagram is is an object and its image created by inverting a hexagram. The remaining eight hexagrams are excluded from the twenty eight pairs because their mirror images are exactly the same as the objects.
The eight symmetrical or single hexagrams are ||||||, ¦¦¦¦¦¦, |¦¦¦¦|, ¦||||¦, ¦|¦¦|¦, |¦||¦|, ||¦¦|| and ¦¦||¦¦.
To convert King Wen sequence to binary numbers, broken line is substituted by 0 and unbroken line is replaced by 1. The 64 hexagrams and their corresponding binary numbers are listed below.
111111 → ||||||
000000 → ¦¦¦¦¦¦
100010 → |¦¦¦|¦ ← 010001
111010 → |||¦|¦ ← 010111
010000 → ¦|¦¦¦¦ ← 000010
111011 → |||¦|| ← 110111
111000 → |||¦¦¦ ← 000111
101111 → |¦|||| ← 111101
001000 → ¦¦|¦¦¦ ← 000100
100110 → |¦¦||¦ ← 011001
110000 → ||¦¦¦¦ ← 000011
100101 → |¦¦|¦| ← 101001
000001 → ¦¦¦¦¦| ← 100000
100111 → |¦¦||| ← 111001
100001 → |¦¦¦¦|
011110 → ¦||||¦
010010 → ¦|¦¦|¦
101101 → |¦||¦|
001110 → ¦¦|||¦ ← 011100
001111 → ¦¦|||| ← 111100
000101 → ¦¦¦|¦| ← 101000
101011 → |¦|¦|| ← 110101
001010 → ¦¦|¦|¦ ← 010100
110001 → ||¦¦¦| ← 100011
111110 → |||||¦ ← 011111
000110 → ¦¦¦||¦ ← 011000
010110 → ¦|¦||¦ ← 011010
101110 → |¦|||¦ ← 011101
100100 → |¦¦|¦¦ ← 001001
001011 → ¦¦|¦|| ← 110100
101100 → |¦||¦¦ ← 001101
011011 → ¦||¦|| ← 110110
010011 → ¦|¦¦|| ← 110010
110011 → ||¦¦||
001100→ ¦¦||¦¦
101010 → |¦|¦|¦ ← 010101
The binary numbers on the left are products of counting each hexagram from left to right. The binary numbers on the right are products of counting the hexagram from right to left.
The kingdom is about balance between up and down, back and front, left and right, black and white, off and on, etc.
Therefore, the remaining eight hexagrams are divided into four unique pairs in which single line in a hexagram is mirrored by a double line in its pair. The four pairs created from this formula are: |||||| and ¦¦¦¦¦¦, |¦¦¦¦| and ¦||||¦, ¦|¦¦|¦ and |¦||¦|, ||¦¦|| and ¦¦||¦¦.
King Wen sequence is an arrangement of the 64 hexagrams in the Book of Changes into 32 pairs.
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