New Considerations for Spectral Classification of Boolean Switching Functions

Table 1

The effect of negation of an input variable (𝑥₁) on the truth table of a Boolean switching function. Note that the output vector of the function is generally referred to as 𝑍, with 𝑧_𝑖 being individual elements of 𝑍.

𝑥3𝑥2𝑥1	𝑓(𝑋)		𝑥3𝑥2𝑥1	𝑓(𝑋)
000	𝑧0		000	𝑧1
001	𝑧1		001	𝑧0
010	𝑧2		010	𝑧3
011	𝑧3	→	011	𝑧2
100	𝑧4		100	𝑧5
101	𝑧5		101	𝑧4
110	𝑧6		110	𝑧7
111	𝑧7		111	𝑧6