This is shown in figure 631 below the not operation

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Unformatted text preview: e 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 output. The AND operation is achieved through a NOR gate with additional inverters in each input. 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. Example 6.15. Construct a logic diagram for the Boolean expression A • B + C • (A + B • D) using only NOR gates....
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This document was uploaded on 04/07/2014.

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