|
|
 |
| These discussions were abstracted from the book, Bebop to the Boolean Boogie (An Unconventional Guide to Electronics), with the kind permission of LLH Technology Publishing, Eagle Rock, VA, USA. Bebop to the Boolean Boogie provides a superb introduction to a smorgasbord of contempory digital electronics, including atoms, transistors, logic gates, Eskimo counting systems, fuzzbuttons, smoked fish, musical socks, Reed-Müller logic, seafood gumbo, integrated circuits, circuit boards, hybrids, multichip modules, optical interconnects, protein memories & switches, holographic interconnects, superconductors, nanotechnology, and much, much more! |
| Karnaugh Maps Part 5: Populating Maps Using 0s Versus 1s |
| When a Karnaugh map is populated using the 1s assigned to the truth table's output, the resulting Boolean expression is extracted from the map in sum-of-products form. As an alternative, the Karnaugh map can be populated using the 0s assigned to the truth table's output. In this case, groupings of 0's are used to generate expressions in product-of-sums format (Figure 9). | ||
| Although the sum-of-products and product-of-sums expressions appear to be somewhat different, they do produce identical results. The expressions can be shown to be equivalent using algebraic means, or by constructing truth tables for each expression and comparing the outputs. (Note that the sum of products and product of sums canonical forms are introduced in Chapter 9 of Bebop to the Boolean Boogie.) |
Figure 9: Karnaugh maps populated using 0s versus 1s. |
|
| Karnaugh maps are most often used to represent 3-input and 4-input functions. It is possible to create similar maps for 5-input and 6-input functions, but these maps can become unwieldy and difficult to use. The Karnaugh technique is generally not considered to have any application for functions with more than six inputs. | ||
 |
 |
|
|
|
to return to our main pages for other goodies. |
|