# The final nor gate implementation so obtained is

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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 two-input 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 the-output (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. Exclusive-OR and Equivalence Functions Exclusive-OR 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.

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