Boolean Algebra and Simplification Techniques
223
Figure 6.15 Multiple Karnaugh map for a five-variable Boolean function.
The multiple Karnaugh map for this five-variable expression is shown in Fig. 6.15. The construction
of the Karnaugh map and the formation of groups are self-explanatory.
The minimized expression is given by the equation
Y = CCDDE + AABBCCD + AACCDDE + AABBDDE
(6.55)
As another illustration, consider a six-variable Boolean function given by the equation
Y =AABBCCDDEEF + AABBCCDDEEF + AABBCCDDEEF + AABBCCDDEEF + AABBCCDDEEF
+ AABBCCDDEEF + AABBCCDDEEF
(6.56)
Figure 6.16 gives the Karnaugh map for this six-variable Boolean function, comprising four fourvariable Karnaugh maps. The figure also shows the formation of groups. The minimized expression is
given by the equation
Y = AABBCCDDE + AABBCCDDF + AABBCCDDEEF + AABBCCDDEEF + AABBCCDDEEF
(6.57)
Example 6.11
Minimize the Boolean function
ffAA BB CC =
0 1 3 5 +
2 7
using the mapping method in both minimized sum-of-products and product-of-sums forms.