notes-326-set4

notes-326-set4 - Gates Gate: A simple electronic circuit (a...

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1 8 Elec 326 Gates and Logic Networks Gates ± Gate: A simple electronic circuit (a system) that realizes a logical operation. ² The direction of information flow is from the input terminals to the output terminal. ² The number of input and output terminals is finite and they carry binary-valued signals (i.e, 0 and 1). ² The transformation of input signals to output signals can be modeled as a logical operation. ± Reading assignment ² Sections 2.1—2.5 from the text X Y Z = f(X,Y) Gate 9 Elec 326 Gates and Logic Networks ± Truth Tables ² Since there is a finite number of input signal combinations, we can represent the behavior of a gate by simply listing all of it possible input configurations and the corresponding output signal. Such a list is called a truth table . ² For example, the following gate could have the behavior given by the following truth tables. ² The use of the symbols L and H usually correlates with the high and low voltages. GATE X Y Z XY Z L L L L H H H L H H H H XY Z 0 0 0 0 1 1 1 0 1 1 1 1 1 1 1 1 0 0 0 1 0 0 0 0
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2 3 Elec 326 Gates and Logic Networks ± Some standard gates and their symbols and truth tables: XZ 0 0 1 1 X Z a. Buffer 0 1 1 0 X Z b. Inverter X Y Z X Y Z 0 0 0 0 1 0 1 0 0 1 1 1 c. AND Gate X Y Z X Y Z 0 0 0 0 1 1 1 0 1 1 1 1 d. OR Gate X Y Z 0 0 1 0 1 1 1 0 1 1 1 0 or e. NAND Gate X Y Z X Y Z or X Y Z 0 0 1 0 1 0 1 0 0 1 1 0 f. NOR Gate X Y Z X Y Z X Y Z 0 0 0 0 1 1 1 0 1 1 1 0 g. Exclusive OR Gate X Y Z X Y Z 0 0 1 0 1 0 1 0 0 1 1 1 h. Equivalence Gate X Y Z 4 Elec 326 Gates and Logic Networks ² Gates with more than 3 inputs: ³ AND gates: The output is 1 if and only if … ? ³ OR gates: The output is 1 if and only if … ? ³ NAND gates: The output is 0 if and only if … ? ³ NOR gates: The output is 0 if and only if … ? ³ EXCLUSIVE OR gates: The output is 1 if and only if … ? ³ EQUIVALENCE gates: The output is 1 if and only if … ?
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3 5 Elec 326 Gates and Logic Networks ± Logical Expressions ² We can also represent the behavior of gates with a logical expressions constructed from variables and logical operations symbols. ² The following table gives the most common ones. C is 1 iff Both A and B are 1 or both A and B are 0. C = A B EQUIVALENCE C is 1 iff It is not the case that either A or B is 1. C = A B NOR C is 1 iff It is not the case that A and B are both 1. C = A B NAND C is 1 iff A or B is 1, both not both. C = A B EXCLUSIVE OR C is 1 iff A is 1 or B is 1. C = A+B OR C is 1 iff A is 1 and B is 1. C = A•B AND C is 1 iff A is 0. C = A' NEGATION Meaning Example Connective 6 Elec 326 Gates and Logic Networks ² Comments on the logical symbols ³ The NAND and NOR symbols are not very useful. ³ There are several different symbols that have been used for the logical connectives. ± Exercise: Determine how many different two-input gates there can be?
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notes-326-set4 - Gates Gate: A simple electronic circuit (a...

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