数字电路与逻辑设计05.ppt

? 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved Floyd, Digital Fundamentals, 10th ed ? 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved Floyd, Digital Fundamentals, 10th ed Digital Fundamentals Tenth Edition Floyd Chapter 5 ? 2008 Pearson Education In Sum-of-Products (SOP) form, basic combinational circuits can be directly implemented with AND-OR combinations if the necessary complement terms are available. Summary Combinational Logic Circuits Summary An example of an SOP implementation is shown. The SOP expression is an AND-OR combination of the input variables and the appropriate complements. Combinational Logic Circuits SOP DE ABC A B C E D X = ABC + DE When the output of a SOP form is inverted, the circuit is called an AND-OR-Invert circuit. The AOI configuration lends itself to product-of-sums (POS) implementation. Summary An example of an AOI implementation is shown. The output expression can be changed to a POS expression by applying DeMorgan’s theorem twice. Combinational Logic Circuits POS DE ABC A B C E D X = ABC + DE X = ABC + DE X = (A + B + C)(D + E) X = (ABC)(DE) AOI DeMorgan The truth table for an exclusive-OR gate is Summary Exclusive-OR Logic A B Notice that the output is HIGH whenever A and B disagree. The Boolean expression is The circuit can be drawn as X Symbols: Distinctive shape Rectangular outline X = AB + AB The truth table for an exclusive-NOR gate is Summary Exclusive-NOR Logic A B Notice that the output is HIGH whenever A and B agree. The Boolean expression is The circuit can be drawn as X Symbols: Distinctive shape Rectangular outline X = AB + AB Summary For each circuit, determine if the LED should be on or off. (a) (b) (c) Circuit (a): XOR, inputs agree, output is LOW, LED is ON. Circuit (b): XNOR, inputs disagree, output is LOW, LED is ON. Circuit (c): XOR, inputs disagree, output is HIGH,