Yijing Hexagram Binary Encoder and Decoder

Description

Encode six bottom-to-top binary lines as the sum of line[j]*2^j.

These tools represent a six-line figure as six binary values ordered from bottom to top, with yin represented by zero and yang by one. Three adjacent lines form a trigram. Binary encoding, line reversal, and changing selected lines are separate operations under this explicit representation.

Encode six bottom-to-top binary lines as the sum of line[j]*2^j.

When to use this tool

Use Yijing Hexagram Binary Encoder and Decoder when you need a reproducible binary line transformation with an inspectable output figure.

How to use the tool and how it works

Enter lines. Keep parallel arrays aligned. Use the units and conventions below.
Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
Read result. Expand result to inspect the returned fields.

Encode six bottom-to-top binary lines as the sum of line[j]*2^j. Return the numerical code, the supplied bits joined in bottom-to-top display order, and decodedLines as a round-trip witness inside result.^[1]

Input field	Meaning and units	Accepted input
lines	Lines	Required. Array of Finite number..

Output field	Interpretation	Returned shape
result	Result	Required. Object.

json

{
  "input": {
    "lines": [
      1,
      0,
      0,
      0,
      0,
      0
    ]
  },
  "output": {
    "result": {
      "code": 1,
      "bottomToTopBits": "100000",
      "decodedLines": [
        1,
        0,
        0,
        0,
        0,
        0
      ]
    }
  }
}

Limitations and assumptions

The leftmost character of bottomToTopBits represents the least significant bit, unlike ordinary most-significant-first binary notation. The code is not a King Wen sequence number.
Outputs are nested inside result. The field tables state structural bounds; the mechanics also specify cross-field constraints. Malformed inputs and unsupported domains cause errors. A successful false flag, empty branch value, or zero placeholder has the meaning stated above and is distinct from an input error.

Alternative or Complementary methods

Keep one explicit line-order and binary convention throughout. Use a separate attributed text or scholarly source when the task requires a figure name or interpretation.

References

Calculation and input contract: yijing/hexagram-binary-codec — tool.io

Similar or alternative tools

Yijing Upper and Lower Trigram Composer
Compose code=lowerCode+8*upperCode from integer trigram codes zero through seven.
Yijing Hexagram Trigram Splitter
Split six bottom-to-top binary lines into lower and upper three-bit trigram codes.