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

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Binary Representation of the 64 Hexagrams

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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 fù 复 0 to 5.625 復 000001 1 8 H1 E1 Zhen
27 ䷚ Nourishing 02 yí 颐 5.625 to 11.25 頤 100001 6 3 H3 E1 Zhen
03 ䷂ Beginning 03 zhūn 屯 11.25 to 16.875 屯 010001 7 4 H5 E1 Zhen
42 ䷩ Increasing 04 yì 益 16.875 to 22.5 益 110001 2 9 H7 E1 Zhen
51 ䷲ Taking Action 05 zhèn 震 22.5 to 28.125 震 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 随 33.75 to 39.375 隨 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 bì 贲 50.625 to 56.25 賁 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 丰 67.5 to 73.125 豐 001101 8 6 H5 E3 Li
30 ䷝ Brightness 14 lí 离 73.125 to 78.75 離 101101 3 1 H7 E3 Li
49 ䷰ Abolishing The Old 15 gé 革 78.75 to 84.375 革 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 临 90 to 95.625 臨 000011 1 4 H2 E4 Dui
41 ䷨ Decreasing 18 sǔn 损 95.625 to 101.25 損 100011 6 9 H4 E4 Dui
60 ䷻ Restricting 19 jié 节 101.25 to 106.875 節 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 睽 118.125 to 123.75 睽 101011 3 2 H1 E5 Dui
58 ䷹ Joyful 23 duì 兑 123.75 to 129.375 兌 011011 4 1 H3 E5 Dui
10 ䷉ Fulfillment 24 lǚ 履 129.375 to 135 履 111011 9 6 H5 E5 Dui
11 ䷊ Advance 25 tài 泰 135 to 140.625 泰 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 xū 需 146.25 to 151.875 需 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 夬 168.75 to 174.375 夬 011111 4 6 H10 E6 Qian
01 ䷀ Initiating 32 qián 乾 174.375 to 180 乾 111111 9 1 H1 E7 Qian
44 ䷫ Encountering 33 gòu 姤 180 to 185.625 姤 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 鼎 191.25 to 196.875 鼎 101110 3 4 H5 E7 Xun
32 ䷟ Long Lasting 36 héng 恒 196.875 to 202.5 恆 001110 8 9 H7 E7 Xun
57 ䷸ Proceeding Humbly 37 xùn 巽 202.5 to 208.125 巽 110110 2 1 H9 E7 Xun
48 ䷯ Replenishing 38 jǐng 井 208.125 to 213.75 井 010110 7 6 H2 E8 Xun
18 ䷑ Remedying 39 gǔ 蛊 213.75 to 219.375 蠱 100110 6 7 H4 E8 Xun
46 ䷭ Growing Upward 40 shēng 升 219.375 to 225 升 000110 1 2 H6 E8 Xun
06 ䷅ Contention 41 sòng 讼 225 to 230.625 訟 111010 9 3 H8 E8 Kan
47 ䷮ Exhausting 42 kùn 困 230.625 to 236.25 困 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 解 241.875 to 247.5 解 001010 8 4 H3 E9 Kan
59 ䷺ Dispersing 45 huàn 涣 247.5 to 253.125 渙 110010 2 6 H5 E9 Kan
29 ䷜ Darkness 46 kǎn 坎 253.125 to 258.75 坎 010010 7 1 H7 E9 Kan
04 ䷃ Childhood 47 méng 蒙 258.75 to 264.375 蒙 100010 6 2 H7 E9 Kan
07 ䷆ Multitude 48 shī 师 264.375 to 270 師 000010 1 7 H9 E9 Kan
33 ䷠ Retreat 49 dùn 遯 270 to 275.625 遯 111100 9 4 H2 E10 Gen
31 ䷞ Mutual Influence 50 xián 咸 275.625 to 281.25 咸 011100 4 9 H4 E10 Gen
56 ䷷ Travelling 51 lǚ 旅 281.25 to 286.875 旅 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 渐 292.5 to 298.125 漸 110100 2 7 H10 E10 Gen
39 ䷦ Hardship 54 jiǎn 蹇 298.125 to 303.75 蹇 010100 7 2 H1 E11 Gen
52 ䷳ Keeping Still 55 gèn 艮 303.75 to 309.375 艮 100100 6 1 H3 E11 Gen
15 ䷎ Humbleness 56 qiān 谦 309.375 to 315 謙 000100 1 6 H5 E11 Gen
12 ䷋ Hindrance 57 pǐ 否 315 to 320.625 否 111000 9 9 H7 E11 Kun
45 ䷬ Bringing Together 58 cuì 萃 320.625 to 326.25 萃 011000 4 4 H9 E11 Kun
35 ䷢ Proceeding Forward 59 jìn 晋 326.25 to 331.875 晉 101000 3 3 H2 E12 Kun
16 ䷏ Delight 60 yù 豫 331.875 to 337.5 豫 001000 8 8 H4 E12 Kun
20 ䷓ Watching 61 guān 观 337.5 to 343.125 觀 110000 2 2 H6 E12 Kun
08 ䷇ Union 62 bǐ 比 343.125 to 348.75 比 010000 7 7 H8 E12 Kun
23 ䷖ Falling Away 63 bō 剥 348.75 to 354.375 剝 100000 6 6 H10 E12 Kun
02 ䷁ Responding 64 kūn 坤 354.375 to 360 坤 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
坤
☷
2
Xun
巽
☴
3
Li
离
☲
4
Dui
兑
☱
6
Gen
艮
☶
7
Kan
坎
☵
8
Zhen
震
☳
9
Qian
乾
☰

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

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