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Electronic Labs_11

Electronic Labs_11 - A-4 Appendix A w the NOR function to...

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Unformatted text preview: A-4 Appendix A w the NOR function to be true, all of the variables must be false. The function is false when one or more of the variables is true. The logic circuit for the NOR function is an OR gate followed by an inverter as shown in Fig. A-5 (a). These two circuits are usually combined into a single NOR gate as shown in the symbol of (b). As with previous NOT functions, the small circle at the output of the NOR gate indicates inversion. The fundamental true and false relationships of the NOR gate are shown in the truth table of (c). The general forms of the NOR equation are: A+B+C+....=X MgAs The EXCLUSIVE OR Function. The EXCLUSIVE OR (X-OR) operation is a special case of the OR operation. An X-OR logic statement yields a true result only when an odd number of variables are true. Conversely, a false results when an even number of variables are true. For an X-OR statement having two variables, this means that a true result is obtained when one or the other of the variables is true, but not when both are true. This latter condition is what distinguishes the X-OR operation from the regular OR operation, that is, it excludes the condition whereby both variables are true. Thus, for the two-variable X-OR statement, there are two conditions by which a false result is obtained and that is when both variables are true or both are false. The X-OR operation having two variables can be implemented using the logic circuit shown in Fig. A-6 (a). Other configurations are possible depending on the logic components available, but the logic symbol of (b) is commonly used to indicate the XOR operation regardless of the type of circuit. It can be seen from the logic circuit why the X-OR function excludes the all 0's or all 1’s states. For example, if variables A and B are both true, the inverters insure that one input to each AND gate is 0, resulting in a 0 output from both AND gates and thus the output OR gate. If both input variables are false, the inverters insure that one input to each AND gate is 1, again resulting in a 0 output from both AND gates and the output OR gate. It is only when one variable is true while the other one is false that either AND gate has 1 ’s on both inputs and produces a 1 output from the X-OR circuit. The truth table of (c) lists all possible combinations of the X-OR gate input- output conditions just described. The expanded form of the two variable X-OR equation is generally stated as: X=A§+EB This expression is sometimes referred to as an inequality statement and its circuit referred to as an inequality comparator. The X-OR function is commonly signified in condensed form in terms of the input variable only, separated by a connective made up of the OR symbol enclosed in a circle (69). The condensed two variable X-OR equation thus becomes: X=A63B x-a-BJ-n -A-'.—B IGJ [M M Fig. A-6 The EXCLUSIVE NOR Function. The EXCLU- SIVE NOR (X-NOR) operation is the complement of the X-OR operation, or it can be viewed as a special case of the NOR operation. The X-NOR operation is indicated by a NOT symbol placed over an X-OR logic expression. An X-NOR logic statement yields a true result only when an even number of variables are identical. Conversely, a false results for any other combination of variables. For an X-NOR statement having two variables, this means that a true result is obtained when both variables are true or both are false, and that a false result is obtained when only one variable is true. This is the exact opposite or complement of the ...
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