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
|
~><~><~><~><~><~><~>
<~><~><~><~><~><~<~><~><~><~~>
|
|||||||
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 used0, 1, 2, 3, 4, 5, 6, 7, 8, and 9depends 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 digits0, 1suffice to represent a number in the binary system; 6 digits0, 1, 2, 3, 4, 5are needed to represent a number in the sexagesimal system; and 16 digits0, 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-flopselectronic 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 impulsecan 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
|
|
<~><~><~><~><~><~><~>
Updated & Corrected 2004 03 15
<~><~><~><~><~><~><~>