Binary and Octal Numbers
Ba Gua and Yi Jing Numbers

Yi Jing Page


Chinese Yi Jing [I Ching] employs binary and octal numbering systems.

Here is brief description of the binary and octal numbers.


In binary numbering system, 2 possible numbers can be expressed with "one binary digit" :

0
1

Of course, it is entirely arbitrary to adopt "0" and "1" as the symbols for these two possible numbers. In Yi Jing, we use "broken line" and "solid line" to represent the two numbers 0 and 1 respectively - like this:

0
1
In English, the name of the symbol "0" is "zero", and the name of the symbol "1" is "one."
In Ba Gua, the name of the symbol "0" in "ying", and the name of the symbol is "yang."

Furthermore, instead of calling these two symols "zero" and "one", we may choose to call them "one" and "two", which we often do when we speak of these as part of "digital numbers."


Using two binary digits, there are 4 possible numbers:

00
01
10
11

The Yi Jing symbol representations are:

00  
 
01  
 
10  
 
11  
 
The two binary numbers are place horizontally and should be read from left to right.
The Bagua numbers are placed on a vertical line, and should be read from bottom up


Going up to three binary digits, there are 8 possible numbers:

000
001
010
011
100
101
110
111

These 8 numbers can be expressed in decimal system. We may choose to use these 8 numbers to represent 0 to 7; or to repsent 1 to 8. See below:

000 0 1
001 1 2
010 2 3
011 3 4
100 4 5
101 5 6
110 6 7
111 7 8

Binary Digital Yi Jing symbol Ba Gua Name
000 0 1  
 
 
kun1
001 1 2  
 
 
gen4
010 2 3  
 
 
kan3
011 3 4  
 
 
sun4
100 4 5  
 
 
zhen
101 5 6  
 
 
li2
110 6 7  
 
 
dui1
111 7 8  
 
 
qian2

This is what modern mathematicians call the "octal numbers" and Yi Jing calls "Ba Gua."

Both words, "octal" and "Ba", stand for 8.


Finally, 8 times 8 equals 64.
This requires either 6-digit binary numbers, or 2-digit octal numbers.

As it turns out, 6 binary digit numbers are awkward to use. So we use two-digit octal numbers in Yi Jing (Ba Gua).

Instead of writing a long list of 64 numbers, it is better to put the numbers in a square with 8 x 8 = 64 cells.

The row number represents one octal number, and the column number represents one octal number.

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