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3.9 XOR AND EQV OPERATORS 99

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(a) (b)

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(c) (d)
FIGURE 3.25
Distinctive logic circuit symbols for XOR and EQV. (a) The XOR function circuit symbol, (b) The
EQV function circuit symbol, (c) and (d) illustrate the meaning of multiple input symbols.

Thus, if one writes X@Y, it is read as X XOR 7; XQY is read as X EQV Y. The EQV opera-
tor is also known as XNOR (for EXCLUSIVE NOR), a name that will not be used in this text.
Like the AND and OR functions, the XOR and EQV functions are best understood
in terms of the logic circuit symbols representing them. Figures 3.25a and 3.25b give
the commonly used XOR and EQV circuit symbols for which the following functional
descriptions apply:

The output of a logic XOR circuit symbol is active if one or the other of two inputs is
active but not both active or inactive — that is, if the inputs are not logically equivalent.

The output of a logic EQV circuit symbol is active if, and only if, both inputs are
active or both inputs are inactive — that is, if both inputs are logically equivalent.

A circuit symbol for either XOR or EQV consists of two and only two inputs. Multiple input
XOR or EQV circuit symbols are understood to have the meaning indicated in Figs. 3.25c
and 3.25d and are known as tree forms.
The defining relations for XOR and EQV are obtained from the functional descriptions
just given. In Boolean sum-of-products and Boolean product-of-sums form these defining
relations are

and

A Q B = A • B + A • B = (A + B) • (A + B). (3.5)

In words, the XOR function in Eq. (3.4) is active if only one of the two variables in its
defining relation is active but not both active or both inactive. Thus, A 0 B = 1 if only one