I - C h i n g

 

 I C h i n g Hexagram  Index

Index

01

34

05

26

11

09

14

43

25

51

03

27

24

42

21

17

06

40

29

04

07

59

64

47

33

62

39

52

15

53

56

31

12

16

08

23

02

20

35

45

44

32

48

18

46

57

50

28

13

55

63

22

36

37

30

49

10

54

60

41

19

61

38

58

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The Eight Trigrams Non-nuclear/Nuclear

Heaven Cloud Water Mountain
Earth Thunder Fire Lake
Embedded Image Sizes 57 x 57 Pixels

Quins 01{Alpha}
Heaven   Malego  Heaven Settle Feeling

  

         

 

 

01

28

01 

49 

44

      

     

   

Quins 02{Beta}

    Earth   

Effort  Earth Bounce Caring

 

   

 

    

 

02

23

02

24

27

    

     

   

    

 

Quins 03 {Gamma}

  Difficult

Comrade  Effort Tower Money

 

   

03

08

23

20

42

     

Quins 04 {Delta}

  Fool

Army  Think Advance Sacrifice

     

 

04

07

24

19

41

    

 

Quins 05 {Epsilon}

Water

Exhale  Care Bamboo Love

   

 

29

59

27

60

61

    

 

Quins 06 {Zeta}

Fire

Inhale  Malego Travel Femego

   

 

30

55

28

56

62

    

  

Quins 07 {Eta}

Harmeet

Aptfeel  

Family Exhaust Joy

  

    

  

   

 

06

10

37 

47

58

    

 

 

   

Quins 08 {Theta}

Hesitate 

Play  

Exhibit Well Gentle

 

 

  

   

 

05

09

38

48

57

     

 

 

   

Quins 09 {Iota}

Keen 

Justice  

Inhibit Progress Excite

 

 

  

   

 

16

21

39

35

51

     

 

 

   

Quins 10 {Kappa}

Aptact

Tactful  

Work Harmsep Calm

 

 

  

   

 

15

22

40

36

52

     

 

 

   

Quins 11 {Lambda}

Help

Rythmn

Resolve Force Cook

 

 

  

 

14

32

43

34

50

     

 

 

   

Quins 12 {Mu}

Friend

Influence

Feel Retreat Reform

 

  

 

13

31

44

33

49

 

   

Quins 13 {Nu}

War

Follow

Loyalty Naive Socialise

 

  

 

12

17

53

25

45

 

   

Quins 14 {Xi}

Peace

Heal

Lead Pause Roots

 

  

 

11

18

54

26

46

 

   

Quins 15 {Omicron}

Exhibit

Work

Subject Lead Object

 

  

 

38

40

63

54

64

 

   

Quins 16 {Pi}

Inhibit

Family

Object Loyalty Subject

 

  

39

37

64

53

63

 

   

<~><~><~><~><~><~><~>

Quods 01 {Alpha}

Peace

War

Heaven Earth

11

12

01

02

 

Quods 02 {Beta}

Pause

Socialise

Resolve Effort

26

45

43

23

 

Quods 03 {Gamma}

Hesitate

Progress

Help Comrade

05

35

14

08

 

Quods 04 {Delta}

Play

Keen

Force Tower

09

16

34

20

 

Quods 05 {Epsilon}

Harmsep

Harmeet

Friend Army

36

06

13

07

 

Quods 06 {Zeta}

Tactful

Exhaust

Reform Fool

22

47

49

04

 

Quods 07 {Eta}

Subinfin

Objinfin

Fire Water

63

64

43

23

 

Quods 08 {Theta}

Family

Work

Inhale Exhale

37

40

55

59

 

Quods 09 {Iota}

Advance

Retreat

Aptfeel Aptact

19

33

10

15

 

Quods 10 {Kappa}

Sacrifice

Influence

Joy Calm

41

31

58

52

 

Quods 11 {Lambda}

Bamboo

Travel

Exhibit Inhibit

60

56

38

39

 

Quods 12{Mu}

Love

Femego

Lead Loyalty

61

62

54

53

 

Quods 13 {Nu}

PushUp

Naive

Feel Think

46

25

44

24

 

Quods 14 {Xi}

Well

Justice

Cook Difficult

48

21

50

03

Quods 15 {Omicron}

Heal

Follow

Malego Care

18

17

28

27

 

Quods 16 {Pi}

Gentle

Excite

Rythmn Money

57

51

32

42

 

Binary Nos
02 = 000010
05 = 000101
08 = 001000
00 = 000000
03 = 000011
06 = 000110
09 = 001001
01 = 000001
04 = 000100
07 = 000111
10 = 001010

~><~><~><~><~><~><~> <~><~><~><~><~><~<~><~><~><~~>
Row 1 = Decimal Nos Row 2 = Binary Nos Row 3 = Hex. Nos Row 5 = Hex. Label
00
01
02
03
04
05
06
07

000000

000001 000010 000011 000100 000101 000110 000111
02
24
07
19
15
36
46
11

Earth
Bounce
Army
Advance
Appropriate Action
Separate in Harmony
Survival
Peace
~><~><~><~><~><~><~> <~><~><~><~><~><~<~><~><~><~~>
08
09
10
11
12
13
14
15
001000 001001 001010 001011 001100 001101 001110 001111
16
51
40
54
62
55
32
34

Keen
Excite
Work
Lead
Femego
Inhale
Rythmn
Force
~><~><~><~><~><~><~> <~><~><~><~><~><~<~><~><~><~~>
16
17
18
19
20
21
22
23
010000 010001 010010 010011 010100 010101 010110 010111
08
03
29
60
39
63
48
05

Comrade
Difficult
Water
Bamboo
Inhibit
Subjective
Well
Hesitate
24
25
26
27
28
29
30
31
011000 011001 011010 011011 011100 011101 011110 011111
45
17
47
58
31
63
28
43

Socialise
Follow
Exhaust
Joy
Influence
Reform
Malego
Resolve
~><~><~><~><~><~><~> <~><~><~><~><~><~<~><~><~><~~>
32
33
34
35
36
37
38
39
100000 100001 100010 100011 100100 100101 100110 100111
23
27
04
41
52
22
18
26

Effort
Caring
Fool
Sacrifice
Calm
Tactful
Heal
Pause
~><~><~><~><~><~><~> <~><~><~><~><~><~<~><~><~><~~>
40
41
42
43
44
45
46
47
101000 101001 101010 101011 101100 101101 101110 101111
35
21
64
38
56
30
50
14

f

Progress
Justice
Objective
Exhibit
Travel
Fire
Cook
Help
~><~><~><~><~><~><~> <~><~><~><~><~><~<~><~><~><~~>
48
49
50
51
52
53
54
55
110000 110001 110010 110011 110100 110101 110110 110111
20
42
59
61
53
37
57
09

f

Tower
Money
Exhale
Love
Loyalty
Family
Gentle
Play
~><~><~><~><~><~><~> <~><~><~><~><~><~<~><~><~><~~>
56
57
58
59
60
61
62
63
111000 111001 111010 111011 111100 111101 111110 111111
12
25
06
10
33
13
44
01

War
Naive
Meet in Harmony
Appropriate Feeling
Retreat
Friend
Feel
Heaven
~><~><~><~><~><~><~> <~><~><~><~><~><~<~><~><~><~~>

 

Number Systems, in mathematics, various notational systems that have been or are being used to represent the abstract quantities called numbers. A number system is defined by the base it uses, the base being the number of different symbols, or numerals, required by the system to represent any of the infinite series of numbers. Thus, the decimal system in universal use today (except for computer application) requires ten different symbols, or digits, to represent numbers and is therefore a base-10 system.Throughout history many different number systems have been used; in fact, any whole number greater than 1 can be used as a base. Some cultures have used systems based on the numbers 3, 4 or 5. The Babylonians used the sexagesimal system, based on the number 60, and the Romans used (for some purposes) the duodecimal system, based on the number 12. The Mayans used the vigesimal system, based on the number 20. The binary system, based on the number 2, was used by some tribes and, together with the system based on 16, is used today in computer systems.

 

Place Values The position of a symbol denotes the value of that symbol in terms of exponential values of the base. That is, in the decimal system, the quantity represented by any of the ten symbols used—0, 1, 2, 3, 4, 5, 6, 7, 8, and 9—depends on its position in the number. Thus, the number 3,098,323 is an abbreviation for (3 106) + (0 105) + (9 104) + (8 103) + (3 102) + (2 101) + (3 100, or 3 1). The first 3 (reading from right to left) represents 3 units; the second 3, 300 units; and the third 3, 3 million units.

Two digits—0, 1—suffice to represent a number in the binary system; 6 digits—0, 1, 2, 3, 4, 5—are needed to represent a number in the sexagesimal system; and 16 digits—0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A (ten), B (eleven), C (twelve), … , F (fifteen)—are needed to represent a number in the hexadecimal system. The number 30155 in the sexagesimal system is the number (3 64) + (0 63) + (1 62) + (5 61) + (5 60) = 3959 in the decimal system; the number 2EF in the duodecimal system is the number (2 162) + (14 161) + (15 160) = 751 in the decimal system.To write a given base-10 number n as a base-b number, divide (in the decimal system) n by b, divide the quotient by b, the new quotient by b, and so on until the quotient 0 is obtained. The successive remainders are the digits in the base-b expression for n. For example, to express 3959 (base 10) in the base 6, one writes

from which we see that 395910 = 301556. (The base is frequently written in this way as a subscript of the number.) The larger the base, the more symbols are required, but fewer digits are needed to express a given number.

 

Binary System The binary system plays an important role in computer technology. The first 20 numbers in the binary notation are 1, 10, 11, 100, 101, 110, 111, 1000, 1001, 1010, 1011, 1100, 1101, 1110, 1111, 10000, 10001, 10010, 10011, 10100. Any number can be expressed in the binary system by the sum of different powers of two. For example, starting from the right, 10101101 represents (1 20) + (0 21) + (1 22) + (1 23) + (0 24) + (1 25) + (0 26) + (1 27) = 173.

Arithmetic operations in the binary system are extremely simple. The basic rules are: 1 + 1 = 10, and 1 1 = 1. Zero plays its usual role: 1 0 = 0, and 1 + 0 = 1. Addition, subtraction, and multiplication are done in a fashion similar to that of the decimal system:

Because only two digits (or bits) are involved, the binary system is used in computers, since any binary number can be represented by, for example, the positions of a series of on-off switches. The on position corresponds to a 1, and the off position to a 0. Instead of switches, magnetized dots on a magnetic tape or disk also can be used to represent binary numbers: a magnetized dot stands for the digit 1, and the absence of a magnetized dot is the digit 0. Flip-flops—electronic devices that can only carry two distinct voltages at their outputs and that can be switched from one state to the other state by an impulse—can also be used to represent binary numbers. Logic circuits in computers carry out the different arithmetic operations of binary numbers; the conversion of decimal numbers to binary numbers for processing, and of binary numbers to decimal numbers for the readout, is done electronically.

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Updated & Corrected 2004 03 12

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