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 base10 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 base10 number n as a baseb 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 baseb 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 onoff 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. Flipflops—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


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Updated & Corrected 2004 03 15
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