• With simple gate and combinational logic circuits, there is a definite output state for any given input state. Take the truth table of an OR gate, for instance: For each of the four possible combinations of input states (0-0, 0-1,…

  • As an example of using several circuits together, we are going to make a device that will have 16 inputs, representing a four digit number, to a four digit 7-segment display but using just one binary-to-7-segment encoder. First, the overall…

  • A multiplexer, abbreviated mux, is a device that has multiple inputs and one output. The schematic symbol for multiplexers is The truth table for a 2-to-1 multiplexer is Using a 1-to-2 decoder as part of the circuit, we can express…

  • A demultiplexer, sometimes abbreviated dmux, is a circuit that has one input and more than one output. It is used when a circuit wishes to send a signal to one of many devices. This description sounds similar to the description…

  • What is an Encoder? An encoder is a circuit that changes a set of signals into a code. Let’s begin making a 2-to-1 line encoder truth table by reversing the 1-to-2 decoder truth table. This truth table is a little…

  • A decoder is a circuit that changes a code into a set of signals. It is called a decoder because it does the reverse of encoding, but we will begin our study of encoders and decoders with decoders because they…

  • The half-adder is extremely useful until you want to add more that one binary digit quantities. The slow way to develop a two binary digit adders would be to make a truth table and reduce it. Then when you decide…

  • As a first example of useful combinational logic, let’s build a device that can add two binary digits together. We can quickly calculate what the answers should be: 0 + 0 = 0 0 + 1 = 1 1 +…

  • The term “combinational” comes to us from mathematics. In mathematics a combination is an unordered set, which is a formal way to say that nobody cares which order the items came in. Most games work this way, if you rolled…

  • Larger Karnaugh maps reduce larger logic designs. How large is large enough? That depends on the number of inputs, fan-ins, to the logic circuit under consideration. One of the large programmable logic companies has an answer. Altera’s own data, extracted…

  • Up to this point we have considered logic reduction problems where the input conditions were completely specified. That is, a 3-variable truth table or Karnaugh map had 2n = 23 or 8-entries, a full table or map. It is not…

  • For reference, this section introduces the terminology used in some texts to describe the minterms and maxterms assigned to a Karnaugh map. Otherwise, there is no new material here. Σ (sigma) indicates sum and lower case “m” indicates minterms. Σm…

  • So far we have been finding Sum-Of-Product (SOP) solutions to logic reduction problems. For each of these SOP solutions, there is also a Product-Of-Sums solution (POS), which could be more useful, depending on the application. Before working a Product-Of-Sums solution,…

  • Knowing how to generate Gray code should allow us to build larger maps. Actually, all we need to do is look at the left to right sequence across the top of the 3-variable map, and copy it down the left…

  • The logic simplification examples that we have done so far could have been performed with Boolean algebra about as quickly. Real world logic simplification problems call for larger Karnaugh maps so that we may do serious work. We will work…

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