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Electronic Labs_10

Electronic Labs_10 - Postulate 9 A A = A(not 2A mmmwio A...

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Unformatted text preview: Postulate 9 A + A = A (not 2A) mmmwio A+A=1 Postulate 11 A + 1 = 1 Postulate 12 A + 0 = A For Postulate 9, it can be seen that regardless of whether element A is 0 or 1, the result will be identical because either element is the same. For Postulate 10, the result will alwals be a true statement (1) because if A is true, A is false and vice-versa. Postulate 11 states that the result will always be 1 regardless of whether A is 1 or 0 because the one element is true. Postulate 12 says that the result will be determined by the value of A; if A is true, the result is true, and if A is false the result is false. The OR operation is performed using the logic OR gate shown in Fig. A-3 (a). The truth table of (b) shows the fundamental relationships of true and false conditions applied to the gate. The OR operation pertains to any number of variables. The general statement of the OR function is: A+B+C+....=X INPUTS { X=A+B [I] 1 ‘l 'I D 0 II D D Fig. A-3 Combined Operations The basic NOT, AND and OR operations can be combined to give four additional operations that are unique to Boolean algebra. These are: NAND, NOR, EXCLUSIVE OR and EXCLUSIVE NOR, which are described in the subsequent paragraphs. The NAND Function. The NAND operation is the complement of the AND operation. The term NAND is a contraction of NOT AND. The NAND operation is indicated by a NOT symbol placed over a logic expression that results from AND and NOT operations. For example, the NAND logic expression for variables A and B is A- B: X. It can also be stated that X— — A- B. The result indicates that the variables are ﬁrst combined into a single term or combination of terms, which is then complemented. The four possible combinations of the NAND operation can be stated in terms of the elements 1 and 0 used as two independent variables. 1AND1=T=0 1AND0=6=1 Appendix A A—3 * OAND1=6=1 0AND0=6=1 It can be seen from these results that the NAND function is the inverse of the AND function. For the NAND function to be true, one or more of the variables must be false. The function is false only when all the variables are true. The logic circuit for the NAND function is an AND gate followed by an inverter as shown in Fig. A-4 (a). These two circuits are usually combined into a single N AND gate as shown by the symbol of (b). The small circle at the output of the NAND gate symbol indicates inversion. The truth table of (c) shows the fundamental true and false relation- ships of the NAND gate. The general forms of the NAND equation are: ABCum=X OI X=ABCmu A INPUTS 5 w “3 >. (Hi (C) Fig. A-4 The NOR Function. The NOR operation is the complement of the OR operation. The term NOR is a contraction of NOT OR. The NOR operation is indicated by a NOT symbol placed over a logic expression that results from OR and NOT opera— tions. For example, the NOR log_ic expression for variables A and B is A + B = X. It can also be stated that X = A + B. The result indicates that a single term or combination of terms is first obtained for the variables, which is then com- plemented. The true-false elements 1 and 0, used as two independent variables, provide the four fundamental logic relationships of the NOR function. 10R1=T=0 10R0=i=0 00R1=i=0 00R0=6=1 These relationships clearly show that the NOR operation is the inverse of the OR operation. For ...
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