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When a pair of logic signals, A and B, are to be generated and thereafter combined symmetrically, it may be more efficient to generate a pair of functions of the two signals instead of the two signals.
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Substituting Symmetric Functions of Signals for the Signals
When a pair of logic signals, A and B, are to be generated and thereafter
combined symmetrically, it may be more efficient to generate a pair of functions
of the two signals instead of the two signals.
A simple application for this approach is the generation of the inputs to a bit
position of an adder. In such an application, we are interested in whether A and
B are both off, both on, or only one is on regardless of which one. Because of
symmetry, using (A Times B) and A+B), instead of A and B, is a more efficient
way to generate the various conditions: both off = A B, both on = A Times B, and
one on = (A B) (A Times B). In general, any pair of the three conditions, in true or
complement form, could serve that purpose. For example A B and AVB could
generate the three conditions: both off = A B, both on = (A B) Times (AVB), and
one on = (AVB).
Fig. 1 shows an example of generating a pair of functions of two signals in
place of the two signals.
A more indirect application of this principle occurs when the pair of logic
signals generated cannot be combined symmetrically to perform a function, but
can be replaced by two signals that can. For example, in the multi-input addition
of three or more words that occurs in high-speed multiply, two carries, C1 and
C2, of weights 1 and 2, respectively, may be generated. These carries are
subsequently added, but into different bit positions. If C1 and C2 are mutually