Page 117 - Bebop to The Boolean Boogie An Unconventional Guide to Electronics Fundamentals, Components, and Processes
P. 117
98 ChapterTen
Similar maps can be constructed for 3-input and 4-input functions. In the
case of a 4-input map, the values associated with the c and d inputs must also
be ordered as a Gray code: that is, they must be ordered in such a way that the
values for adjacent rows vary by only a single bit (Figure 10-2).
4-input 1
Function Y,
Figure 10-2. Karnaugh Maps for 3-input
and 4-input functions
Minimization Using Karnaugh Maps
Karnaugh Maps often prove useful in the simplification and minimization
of Boolean functions. Consider an example 3-input function represented as a
black box with an associated truth table (Figure 10-3).3
The equation extracted from the truth table in sum-of-products form
contains four minterms? one for each of the 1s assigned to the output.
Algebraic simplification techniques could be employed to minimize this
equation, but this would necessitate every minterm being compared to each
of the others, which can be somewhat time-consuming.
3 The values assigned to output y in the truth table were selected randomly and have no
significance beyond the purposes of this example.
4 The concepts of mintem and mxtm were introduced in Chapter 9.
