Write each of the Boolean functions as a Boolean expression in dnf.
-$\begin{array}{|c|c|c|}
\hline \boldsymbol{A} & \boldsymbol{B} & \boldsymbol{f}(\boldsymbol{A}, \boldsymbol{B}) \
\hline 1 & 1 & 1 \
\hline 1 & 0 & 0 \
\hline 0 & 1 & 1 \
\hline 0 & 0 & 0 \
\hline
\end{array}$

A) $A B \vee A B ^ { \prime }$
B) $A B \vee A ^ { \prime } B$
C) $A ^ { \prime } B \vee A ^ { \prime } B ^ { \prime }$
D) $A B ^ { \prime } \vee A ^ { \prime } B ^ { \prime }$
E) None of these

Question

Write each of the Boolean functions as a Boolean expression in dnf.
-$\begin{array}{|c|c|c|}
\hline \boldsymbol{A} & \boldsymbol{B} & \boldsymbol{f}(\boldsymbol{A}, \boldsymbol{B}) \
\hline 1 & 1 & 1 \
\hline 1 & 0 & 0 \
\hline 0 & 1 & 1 \
\hline 0 & 0 & 0 \
\hline
\end{array}$

A) $A B \vee A B ^ { \prime }$
B) $A B \vee A ^ { \prime } B$
C) $A ^ { \prime } B \vee A ^ { \prime } B ^ { \prime }$
D) $A B ^ { \prime } \vee A ^ { \prime } B ^ { \prime }$
E) None of these

Quizplus · Accepted Answer

The Disjunctive Normal Form (DNF) is a standardization (or normalization) of a logical formula in Boolean logic. For the given truth table, the function $f(A, B)$ is true when $A = 1, B = 1$ and when $A = 0, B = 1$. Thus, the correct Boolean expression in DNF that represents this function is $A B \vee A ^ { \prime } B$, which corresponds to choice B.

Write Each of the Boolean Functions as a Boolean Expression