First is relay ladder logic, then logic gates, a truth table, a Karnaugh map, and a Boolean equation. We show five individual items above, which are just different ways of representing the same thing: an arbitrary 2-input digital logic function. Given a choice, most students do logic simplification with Karnaugh maps rather than Boolean algebra once they learn this tool. We define lowest cost as being the lowest number of gates with the lowest number of inputs per gate. We like to simplify logic to a lowest cost form to save costs by elimination of components. By reduce we mean simplify, reducing the number of gates and inputs. Karnaugh maps reduce logic functions more quickly and easily compared to Boolean algebra. Now that we have developed the Karnaugh map with the aid of Venn diagrams, let’s put it to use. Maurice Karnaugh, a telecommunications engineer, developed the Karnaugh map at Bell Labs in 1953 while designing digital logic based telephone switching circuits.
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