  When I record a reading I frequently use the Boolean "difference" operator to generate an additional symbol representing the energy of change at work in the situation. This results in an extended reading structure for more in depth analysis.

I shall assume that the reader is familiar with a technique for generating a hexagram, including one or more changing lines. Whether it is one of the coin methods, the yarrow method, or one of the other available techniques does not matter; the notation described here can be applied regardless of how the reading is generated. Suppose that you threw the following lines: 6, 6, 7, 8, 9, 8. This would traditionally be notated as shown on the right. The first two lines are changing yin lines, the third line is stable yang, the fourth is stable yin, the fifth is changing yang, and the top line is stable yin.  This gives an initial hexagram of 39 - Limping. Once the changing lines have been taken in to account, this gives a second hexagram of 11 - Pervading or Peace. Typically, the main text from the first hexagram, some combination of the indicated line texts from the first hexagram, and the main text from the second hexagram are considered.

By applying a simple technique from Boolean Algebra, it is possible to construct readings which allow extra scope for interpreting the changing lines. This is sometimes helpful, especially when the texts of the lines seem to be contradictory. Using this notation, the reading presented above would be written as:

This equation says that when Limping is transformed by the energy of Natural Limitation, the resulting situation includes Peace. In general terms, this is P x Q = R, meaning a Principle symbol P, transformed by Quanta of Change Q, creates a Related symbol R. Notice that P and R are the symbols from the traditional notation, whilst the symbol Q has a Yang line where ever there is a changing line in P. It should not be assumed that there is a temporal relationship between P and R. Rather, both exist as part of the current situation.

The first hexagram is the hexagram that was actually thrown, the Principle symbol; as usual, this represents the dominant aspects of the situation as they relate to your question. The next hexagram is the outcome of the changing lines in the Principle hexagram, called the Related symbol; this represents the effect of the changing energies in the situation. The hexagram that sits between the Principle and Related symbols is called the Quanta of Change and this represents the energy of the change that is at work in the current situation. It is sometimes useful to think of the symbol Q as the representing the difference between the Principle and Related hexagrams.    Sometimes, instead of the algebraic equation, I use an equivalent graphical notation as shown on the left. Here the Principle symbol is the top hexagram, the Related symbol is the bottom hexagram, and the Quanta of Change is shown connecting the two.

A further notation, used for some of the more advanced analyses, is the use of lattice structures. There is an example of the construction of these structures here, and a technical description here.

Whilst it is not necessary to understand the mathematics of this construction in order to make use of it, from an algebraic perspective, Q is the exclusive or (usually abbreviated to XOR) of the Principle and Related hexagrams. The technical aspects of this construction are explained fully in my paper Boolean Algebra and the Yijing.