Simplify: F = X Y Z' + X Z' + X' Y + X'' Y Z' using K-Map in both SOP | Digital Logic 2080

Digital Logic20805 marksNumerical: K-map simplificationKarnaugh map simplification

Simplify: F = X Y Z' + X Z' + X' Y + X'' Y Z' using K-Map in both SOP and POS. [5]

Function of three variables $X, Y, Z$ : $F = XYZ' + XZ' + X'Y + X''YZ'$ Note $X'' = X$ (double complement), so: $F = XYZ' + XZ' + X'Y + XYZ'$ Expand each term over minterms $m(X,Y,Z)$ : - $XYZ'$ : $X=1,Y=1,Z=0 \Rightarrow m6$ - $XZ'$ : $X=1,Z=0 \Rightarrow$ ( $Y=0$ ) $m4$ , ( $Y=1$ ) $m6$ - $X'Y$ :

Function of three variables $X, Y, Z$: $$F = XYZ' + XZ' + X'Y + X''YZ'$$ Note $X'' = X$ (double complement), so: $$F = XYZ' + XZ' + X'Y + XYZ'$$ Expand each term over minterms $m(X,Y,Z)$: - $XYZ'$: $X=1,Y=1,Z=0 \Rightarrow m6$ - $XZ'$: $X=1,Z=0 \Rightarrow$ ($Y=0$) $m4$, ($Y=1$) $m6$ - $X'Y$:

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