7.4 Combinational Logic

Chapter 7.4 Combinational Logic

Physics Lecture Notes – Phys 395 Electronics Book
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Physics Lecture Notes – Phys 395 Electronics Book

  • CHAPTER 7. DIGITAL CIRCUITS1377.4Combinational LogicWe will design some useful circuits using the basic logic gates, and use these circuits lateron as building blocks for more complicated circuits.We describe the basic AND, NAND, OR or NOR gates as being satisfied when the inputsare such that a change in any one will change the output. A satisfied AND or NOR gatehas a true output, whereas a satisfied NAND or OR gate has a false output. We sometimesidentify the input logic variables A, B, C, etc. with an n-bit number ABC ....7.4.1Combinational Logic Design Using Truth TablesThe following steps are a useful formal approach to combinational problems:1. Devise a truth table of the independent input variables and the resulting output quan-tities.2. Write Boolean algebra statements that describe the truth table.3. Reduce the Boolean algebra.4. Mechanize the Boolean statements using the appropriate logic gates.Consider the truth table that defines the OR gate. Using the lines in this table that yielda true result gives.Q=A· B + A· B + A· B(7.18)=A· B + A· B + A· B + A· B(7.19)=A· (B + B)+ B· (A + A)(7.20)=A + B(7.21)Since Q is a two-state variable all other input state combinations must yield a false. If thetruth table had more than a single output result, each such result would require a separateequation. An alternative is to write an expression for the false condition.Q=A· B(7.22)Q=A· B(7.23)Q=A + B(7.24)=A + B(7.25)7.4.2The AND-OR GateSome logic families provide a gate known as an AND-OR-INVERT or AOI gate (figure 7.2).Q=A· B + C· D(7.26)Q=A· B + C· D(7.27)