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Unformatted text preview: Solution:
The AND/OR implementation for the given Boolean expression is shown in Figure
6.32(a). Now each OR gate is substituted by a NOR gate followed by an inverter and
each AND gate is substituted by two input inverters followed by a NOR gate. Thus each
OR gate is substituted by two NOR gates and each AND gate is substituted by three NOR
gates. The logic diagram so obtained is shown in Figure 6.32(b). Note that Figure 6.32(b)
has eight inverters (single input NOR gates) and five twoinput NOR gates. One pair of
cascaded inverters (from the OR box to the AND box) may be removed. Also the five
external inputs A, B, B, D and C, which go directly to inverters, are complemented and
the corresponding inverters are removed.
The final NOR gate implementation so obtained is shown in Figure 6.32(c). The number
inside each NOR gate of Figure 6.32(c) corresponds to the NOR gate of Figure 6.32(b)
having the same number.
The number of NOR gates in this example equals the number of AND/OR gates plus an
additional inverter in theoutput (NOR gate number 6). In general, the number of NOR gates required to implement a Boolean function equals the number of AND/OR gates,
except for an occasional inverter. This is true only if both normal and complement inputs
are available because the conversion forces certain input variables to be complemented.
Combinational circuits are more frequently constructed with NAND or NOR gates than
with AND, OR and NOT gates. NAND and NOR gates are more popular than the AND
and OR gates because NAND and NOR gates are easily constructed with transistor
circuits and Boolean functions can be easily implemented with them. Moreover, NAND
and NOR gates are superior to AND and OR gates from the hardware point of view, as
they supply outputs that maintain the signal value without loss of amplitude. OR and
AND gates sometimes need amplitude restoration after the signal travels through a few
levels of gates.
ExclusiveOR and Equivalence Functions
ExclusiveOR and equivalence, denoted by (c) and (c) respectively, are binary operations
that perform the following Boolean functions:
A+B=A•B+A•B
A•B=A•B...
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This document was uploaded on 04/07/2014.
 Spring '14

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