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number of AND/OR gates, except for an occasional inverter. This is true only when both
normal and complemented inputs are available because the conversion forces certain
input variables to be complemented.
The Universal NOR Gate
The NOR function is the dual of the NAND function. For this reason, all procedures and
rules for NOR logic form a dual of the corresponding procedures and rules developed
from NAND logic. Like the NAND gate; the NOR gate is also universal because it is
alone sufficient to implement any Boolean function. To show that any Boolean function can be implemented with the sole use of NOR gates,
we need to only show that the logical operations AND, OR, and NOT can be
implemented with NOR gates. This is shown in Figure 6.31 below.
The NOT operation is obtained from a one-input NOR gate. Hence, a single input NOR
gate is yet another inverter circuit.
The OR operation requires two NOR gates. The first one produces the inverted OR and
the second one being a single input NOT gate, acts as an inverter to obtain the normal OR
The AND operation is achieved through a NOR gate with additional inverters in each
Similar to the NAND logic diagram, the implementation of Boolean functions with NOR
gates may be obtained by carrying out the following steps in sequence:
Step 1: For the given algebraic expression, draw the logic diagram with AND, OR, and
NOT gates. Assume that both the normal (A) and complement (Aj inputs are available.
Steo 2: Draw a second logic diagram with equivalent NOR logic substituted for each
AND, OR, and NOT gate.
Step 3: Remove any two cascaded inverters from the diagram since double inversion does
not perform any logical function. Also remove inverters connected to single external
inputs and complement the corresponding input variable. The new logic diagram so
obtained is the required NOR gate implementation of the given Boolean function.
Construct a logic diagram for the Boolean expression A • B + C • (A + B • D) using only
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This document was uploaded on 04/07/2014.
- Spring '14