Digital Electronics: Principles, Devices and Applications

Boolean Algebra and Simplification Techniques 223Figure 6.15Multiple Karnaugh map for a five-variable Boolean function.The multiple Karnaugh map for this five-variable expression is shown in Fig. 6.15. The constructionof the Karnaugh map and the formation of groups are self-explanatory.The minimized expression is given by the equationY = CDE + ABCD + ACDE + ABDE (6.55)As another illustration, consider a six-variable Boolean function given by the equationY =ABCDEF + ABCDEF + ABCDEF + ABCDEF + ABCDEF+ ABCDEF + ABCDEF (6.56)Figure 6.16 gives the Karnaugh map for this six-variable Boolean function, comprising four fourvariableKarnaugh maps. The figure also shows the formation of groups. The minimized expression isgiven by the equationY = ABCDE + ABCDF + ABCDEF + ABCDEF + ABCDEF (6.57)Example 6.11Minimize the Boolean functionfA B C = ∑ 0 1 3 5 + ∑ 2 7using the mapping method in both minimized sum-of-products and product-of-sums forms.