Working with truth tables

Chapter Working with truth tables

Teach Yourself Electricity and Electronics Third Edition Book
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Summary of Contents

Teach Yourself Electricity and Electronics Third Edition Book

  • Suppose you want to find an arrangement of logic gates for some complex logic op-eration. This can be done in two ways. You can use either truth tables or Boolean al-gebra. For any complex logic operation, there might be several solutions, somerequiring more gates than others. A digital design engineer has the job not only of find-ing an arrangement of gates for a given complex operation, but of finding the schemethat will yield the desired result with the least number of gates.Working with truth tablesTruth tables are, in theory, infinitely versatile. It is possible to construct or break downlogic operations of any complexity by using these tables, provided you have lots of pa-per and a fondness for column-and-row matrix drawing. Computers can also be pro-grammed to work with truth tables, although the displays and printouts get horrible todeal with if the logic functions are messy.Building upYou can build complex logic operations up easily by means of a truth table. An exampleof such a building process is shown in Table 30-5.562 Basic digital principles30-4Four-input AND gate(A) and four-input NORgate (B).Table 30-5. Truth table for -(X + Y) + XZ.XYZX Y− (XY)XZ− (XY)XZ00001010010101010100001110001001000101101111010001111011