Feng Shui/Xuan Kong Da Gua/Binary Representation of the 64 Hexagrams

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Binary Representation of the 64 Hexagrams[edit]

The following table transposes the circular arrangement of the hexagrams in a Luopan into a tabular form, where

  1. "GN" represents the Gua Number of a hexagram
  2. "Gua" is the hexagram itself
  3. "English" is the translation of the name of the hexagram
  4. "CN" is the order (Circular Number) of the hexagram, starting from 0 degrees to 360 degrees, on the concentric circle that lists the hexagrams on the Luopan.
  5. "Pinyin" is the transliteration of the Chinese name of the hexagram
  6. "SC" is the name of the hexagram in Simplified Chinese
  7. "Sector" is the sector, measured in degrees from North in a clockwise direction, where the hexagram is found on the concentric circle that lists the hexagrams on the Luopan
  8. "TC" is the name of the hexagram in Traditional Chinese
  9. "Binary Rep." is the binary representation of a Gua, where "1" represents a Yang line (an unbroken line) and "0" represents a Yin line (a broken line). A line is called a "Yao" in Chinese.
  10. "N" refers to the number assigned to the upper trigram of each hexagram, in the order Kun (1), Xun (2), Li (3), Dui (4), Gen (6), Kan (7), Zhen (8) and Qian (9). Kun is represented by 3 broken lines, and Qian is represented by 3 unbroken lines. In Chinese, the column "N" is known as the "五行" column.
  11. "M" refers to the outer circle of numbers assigned to each hexagram in a Luopan. In Chinese, the column "M" is known as the "卦运" column.
  12. "HS" refers to the "Heavenly Stem" notation of Ba Zi. In Chinese, this is known as the "天干" column.
  13. "EB" refers to the "Earthly Branch" notation of Ba Zi. In Chinese, this is known as the "地支" column.
  14. "GR" is the group under which a hexagram belongs. There are a total of eight groups/trigrams. Hexagrams are grouped by their respective lower trigram. These trigrams are also used in the I Ching, where Zhen represents Thunder, Qian represents Heaven, Kun represents Earth, etc.
GN Gua English CN Pinyin SC Sector (deg)° TC Binary
Rep.
N M HS EB GR
24 Turning Back 01 0 to 5.625 000001 1 8 H1 E1 Zhen
27 Nourishing 02 5.625 to 11.25 100001 6 3 H3 E1 Zhen
03 Beginning 03 zhūn 11.25 to 16.875 010001 7 4 H5 E1 Zhen
42 Increasing 04 16.875 to 22.5 110001 2 9 H7 E1 Zhen
51 Taking Action 05 zhèn 22.5 to 28.125 001001 8 1 H9 E1 Zhen
21 Eradicating 06 shì kè 噬嗑 28.125 to 33.75 噬嗑 101001 3 6 H2 E4 Zhen
17 Following 07 suí 33.75 to 39.375 011001 4 7 H4 E2 Zhen
25 Without Falsehood 08 wú wàng 无妄 39.375 to 45 無妄 111001 9 2 H6 E9 Zhen
36 Brilliance Injured 09 míng yí 明夷 45 to 50.625 明夷 000101 1 3 H8 E2 Li
22 Adorning 10 50.625 to 56.25 100101 6 8 H10 E2 Li
63 Already Fulfilled 11 jì jì 既济 56.25 to 61.875 既濟 010101 7 9 H1 E3 Li
37 Household 12 jiā rén 家人 61.875 to 67.5 家人 110101 2 4 H3 E3 Li
55 Abundance 13 fēng 67.5 to 73.125 001101 8 6 H5 E3 Li
30 Brightness 14 73.125 to 78.75 101101 3 1 H7 E3 Li
49 Abolishing The Old 15 78.75 to 84.375 011101 4 2 H7 E3 Li
13 Seeking Harmony 16 tóng rén 同人 84.375 to 90 同人 111101 9 7 H9 E3 Li
19 Approaching 17 lín 90 to 95.625 000011 1 4 H2 E4 Dui
41 Decreasing 18 sǔn 95.625 to 101.25 100011 6 9 H4 E4 Dui
60 Restricting 19 jié 101.25 to 106.875 010011 7 8 H6 E4 Dui
61 Innermost Sincerity 20 zhōng fú 中孚 106.875 to 112.5 中孚 110011 2 3 H8 E4 Dui
54 Marrying Maiden 21 guī mèi 归妹 112.5 to 118.125 歸妹 001011 8 7 H10 E4 Dui
38 Diversity 22 kuí 118.125 to 123.75 101011 3 2 H1 E5 Dui
58 Joyful 23 duì 123.75 to 129.375 011011 4 1 H3 E5 Dui
10 Fulfillment 24 129.375 to 135 111011 9 6 H5 E5 Dui
11 Advance 25 tài 135 to 140.625 000111 1 9 H7 E5 Qian
26 Great Accumulation 26 dà chù 大畜 140.625 to 146.25 大畜 100111 6 4 H9 E5 Qian
05 Needing 27 146.25 to 151.875 010111 7 3 H2 E6 Qian
09 Little Accumulation 28 xiǎo chù 小畜 151.875 to 157.5 小畜 110111 2 8 H4 E6 Qian
34 Great Strength 29 dà zhuàng 大壮 157.5 to 163.125 大壯 001111 8 2 H6 E6 Qian
14 Great Harvest 30 dà yǒu 大有 163.125 to 168.75 大有 101111 3 7 H8 E6 Qian
43 Eliminating 31 guài 168.75 to 174.375 011111 4 6 H10 E6 Qian
01 Initiating 32 qián 174.375 to 180 111111 9 1 H1 E7 Qian
44 Encountering 33 gòu 180 to 185.625 111110 9 8 H1 E7 Xun
28 Great Exceeding 34 dà guò 大过 185.625 to 191.25 大過 011110 4 3 H3 E7 Xun
50 Establishing The New 35 dǐng 191.25 to 196.875 101110 3 4 H5 E7 Xun
32 Long Lasting 36 héng 196.875 to 202.5 001110 8 9 H7 E7 Xun
57 Proceeding Humbly 37 xùn 202.5 to 208.125 110110 2 1 H9 E7 Xun
48 Replenishing 38 jǐng 208.125 to 213.75 010110 7 6 H2 E8 Xun
18 Remedying 39 213.75 to 219.375 100110 6 7 H4 E8 Xun
46 Growing Upward 40 shēng 219.375 to 225 000110 1 2 H6 E8 Xun
06 Contention 41 sòng 225 to 230.625 111010 9 3 H8 E8 Kan
47 Exhausting 42 kùn 230.625 to 236.25 011010 4 8 H10 E8 Kan
64 ䷿ Not Yet Fulfilled 43 wèi jì 未济 236.25 to 241.875 未濟 101010 3 9 H1 E9 Kan
40 Relief 44 xiè 241.875 to 247.5 001010 8 4 H3 E9 Kan
59 Dispersing 45 huàn 247.5 to 253.125 110010 2 6 H5 E9 Kan
29 Darkness 46 kǎn 253.125 to 258.75 010010 7 1 H7 E9 Kan
04 Childhood 47 méng 258.75 to 264.375 100010 6 2 H7 E9 Kan
07 Multitude 48 shī 264.375 to 270 000010 1 7 H9 E9 Kan
33 Retreat 49 dùn 270 to 275.625 111100 9 4 H2 E10 Gen
31 Mutual Influence 50 xián 275.625 to 281.25 011100 4 9 H4 E10 Gen
56 Travelling 51 281.25 to 286.875 101100 3 8 H6 E10 Gen
62 Little Exceeding 52 xiǎo guò 小过 286.875 to 292.5 小過 001100 8 3 H8 E10 Gen
53 Developing Gradually 53 jiàn 292.5 to 298.125 110100 2 7 H10 E10 Gen
39 Hardship 54 jiǎn 298.125 to 303.75 010100 7 2 H1 E11 Gen
52 Keeping Still 55 gèn 303.75 to 309.375 100100 6 1 H3 E11 Gen
15 Humbleness 56 qiān 309.375 to 315 000100 1 6 H5 E11 Gen
12 Hindrance 57 315 to 320.625 111000 9 9 H7 E11 Kun
45 Bringing Together 58 cuì 320.625 to 326.25 011000 4 4 H9 E11 Kun
35 Proceeding Forward 59 jìn 326.25 to 331.875 101000 3 3 H2 E12 Kun
16 Delight 60 331.875 to 337.5 001000 8 8 H4 E12 Kun
20 Watching 61 guān 337.5 to 343.125 110000 2 2 H6 E12 Kun
08 Union 62 343.125 to 348.75 010000 7 7 H8 E12 Kun
23 Falling Away 63 348.75 to 354.375 100000 6 6 H10 E12 Kun
02 Responding 64 kūn 354.375 to 360 000000 1 1 H1 E1 Kun

In the above table, the upper trigram (in Traditional Chinese) of each hexagram is numbered as follows:

  1. Kun 坤 ☷
  2. Xun 巽 ☴
  3. Li 離 ☲
  4. Dui 兌 ☱
  5. (Not used)
  6. Gen 艮 ☶
  7. Kan 坎 ☵
  8. Zhen 震 ☳
  9. Qian 乾 ☰
Numbering of upper trigram
(in Simplified Chinese)
1
Kun




2
Xun



3
Li




4
Dui




6
Gen



7
Kan




8
Zhen




9
Qian



The meaning of each of the 64 hexagrams can be found in the I Ching.