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Solved Examples · Example 23

Q.The four-variable Karnaugh map shown has an octet of eight adjacent 1s occupying the first two columns (C‾ D‾\overline{C}\,\overline{D} and C‾D\overline{C}D) across all four rows. Group this octet and write the simplified Boolean term.

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[!TLDR]

The octet spanning the C‾ D‾\overline{C}\,\overline{D} and C‾D\overline{C}D columns eliminates AA, BB and DD, leaving C‾\overline{C}.

An octet is a group of eight adjacent 1s (two full rows or two full columns). An octet removes the three variables that change within the group and keeps the single variable that is constant.

C‾ D‾\overline{C}\,\overline{D}C‾D\overline{C}DCDCDCD‾C\overline{D}
A‾ B‾\overline{A}\,\overline{B}1100
A‾B\overline{A}B1100
ABAB1100
AB‾A\overline{B}1100

The two encircled columns both correspond to C‾\overline{C} (C=0C=0); within them AA, BB and DD run through every combination and cancel. Grouping the eight product terms: …

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