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 faster than the Karnaugh map for a task involving two or fewer Boolean variables. It is still quite usable at three variables, but a bit slower. At four input variables, Boolean algebra becomes tedious.
Karnaugh maps are both faster and easier. Karnaugh maps work well for up to six input variables, are usable for up to eight variables. For more than six to eight variables, simplification should be by CAD (computer automated design).
Recommended logic simplification vs number of inputs | |||
---|---|---|---|
Variables | Boolean algebra | Karnaugh map | computer automated |
1 -2 | X | ? | |
3 | X | X | ? |
4 | ? | X | ? |
5 - 6 | X | X | |
7 - 8 | ? | X | |
> 8 | X |
In theory any of the three methods will work. However, as a practical matter, the above guidelines work well. We would not normally resort to computer automation to simplify a three input logic block. We could sooner solve the problem with pencil and paper.
However, if we had seven of these problems to solve, say for a BCD (Binary Coded Decimal) to seven segment decoder, we might want to automate the process.
A BCD to seven segment decoder generates the logic signals to drive a seven segment LED (light emitting diode) display.
Examples of computer automated design languages for simplification of logic are PALASM, ABEL, CUPL, Verilog, and VHDL. These programs accept a hardware descriptor language input file which is based on Boolean equations and produce an output file describing a reduced (or simplified) Boolean solution.
We will not require such tools in this chapter. Let’s move on to Venn diagrams as an introduction to Karnaugh maps.
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