Tag: Free Book Digital

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 side of the 4-variable map. See below. Reductions of 4 Variable K Maps The following…

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 some contrived examples in this section, leaving most of the real world applications for the…

Who Developed the Karnaugh Map? Maurice Karnaugh, a telecommunications engineer, developed the Karnaugh map at Bell Labs in 1953 while designing digital logic based telephone switching circuits. The Use of Karnaugh Map Now that we have developed the Karnaugh map with the aid of Venn diagrams, let’s put it to use. Karnaugh maps reduce logic…

Starting with circle A in a rectangular A’ universe in figure (a) below, we morph a Venn diagram into almost a Karnaugh map. We expand circle A at (b) and (c), conform to the rectangular A’ universe at (d), and change A to a rectangle at (e). Anything left outside of A is A’ .…

The fourth example has A partially overlapping B. Though, we will first look at the whole of all hatched area below, then later only the overlapping region. Let’s assign some Boolean expressions to the regions above as shown below. Below left there is a red horizontal hatched area for A. There is a blue vertical…

Mathematicians use Venn diagrams to show the logical relationships of sets (collections of objects) to one another. Perhaps you have already seen Venn diagrams in your algebra or other mathematics studies. If you have, you may remember overlapping circles and the union and intersection of sets. We will review the overlapping circles of the Venn…

Why learn about Karnaugh maps? The Karnaugh map, like Boolean algebra, is a simplification tool applicable to digital logic. See the “Toxic waste incinerator” in the Boolean algebra chapter for an example of Boolean simplification of digital logic. The Karnaugh Map will simplify logic faster and more easily in most cases. Boolean simplification is actually…