Question
Compute the truth table for the following functions:(a) $\mathrm{f}(A, B, C)=B \bar{C}+\bar{B} C$(b) $\mathrm{f}(A, B, C)=\bar{B}+C$
Step 1
The functions depend on three variables: \( A \), \( B \), and \( C \). However, note that \( A \) does not appear in either function, so we will focus on \( B \) and \( C \). Show more…
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The Boolean expression for the truth table is $$ \begin{array}{llll} \hline \boldsymbol{A} & \boldsymbol{B} & \boldsymbol{C} & \boldsymbol{f} \\ \hline 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 1 & 1 & 1 \\ 1 & 0 & 0 & 0 \\ 1 & 0 & 1 & 0 \\ 1 & 1 & 0 & 1 \\ 1 & 1 & 1 & 0 \\ \hline \end{array} $$ (A) $B(A+C)(\bar{A}+\bar{C})$ (B) $\bar{B}(A+\bar{C})(\bar{A}+\bar{C})$ (C) $B(A+\bar{C})(\bar{A}+C)$ (D) $\bar{B}(A+C)(\bar{A}+\bar{C})$
Digital Logic
Boolean Algebra and Minimization of Functions
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