I - Ching & Binary Nos

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

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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

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

<change base 10 to base 6>
3,959<base 10 >
6
3,959
.
.
659
5
.
109
5
.
18
1
.
3
0
.
0
3
30155<base 6>

from which we see that 3959(base 10) = 30155(base 6)(The base is frequently written 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.To change 63(base 10) into (base 2)

<change base 10 to base2>
63<base 10 >
2
63
.
.
31
1
.
15
1
.
7
1
.
3
1
.
1
1
.
1
1
111,111<base 2 >

To change 64(base 10) into (base 2)

<change base 10 to base2>
64<base 10 >
2
64
.
.
32
0
.
16
0
.
8
0
.
4
0
.
2
0
.
1
0
.
.
1
1,000,000<base 2 >

 

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 Addition, subtraction, and multiplication are done in a fashion similar to that of the decimal system:

100101
1011010
.
,
.
1
0
1
+110101
-110101
.
x
1
0
0
1
1011010
100101
.
.
.
1
0
1
Addition
subtraction
.
.
0
0
0
.
.
.
.
0
0
0
.
.
.
.
1
0
1
.
.
.
.
.
1
0
1
1
0
1
.
.
multiplication

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.

 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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Updated & Corrected 2004 03 15

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