Question

question 6
complete the truth table for the following expression:
(a b) + (a + b)

submit question
multiple choice - select expression given a diagram
question 7
find the output of the following circuit diagram:

Explanation:

Step1: Calculate \(\overline{A}\) and \(\overline{B}\)

• When \(A = 0\), \(\overline{A}=1\); when \(A = 1\), \(\overline{A}=0\)
• When \(B = 0\), \(\overline{B}=1\); when \(B = 1\), \(\overline{B}=0\)

Step2: Calculate \( (\overline{A}\overline{B})\)

• \( (\overline{A}\overline{B})\) is the logical AND of \(\overline{A}\) and \(\overline{B}\). So \( (\overline{A}\overline{B})=1\) only when \(\overline{A} = 1\) and \(\overline{B}=1\) (i.e., \(A = 0\), \(B = 0\))

Step3: Calculate \( (A + B)\)

• \( (A + B)\) is the logical OR of \(A\) and \(B\). \( (A + B)=0\) only when \(A = 0\) and \(B = 0\)

Step4: Calculate \( (\overline{A}\overline{B})+(A + B)\)

• \( (\overline{A}\overline{B})+(A + B)\) is the logical OR of \( (\overline{A}\overline{B})\) and \( (A + B)\)

\(A\)	\(B\)	\(\overline{A}\)	\(\overline{B}\)	\((\overline{A}\overline{B})\)	\((A + B)\)	\((\overline{A}\overline{B})+(A + B)\)
\(0\)	\(1\)	\(1\)	\(0\)	\(0\)	\(1\)	\(1\)
\(1\)	\(0\)	\(0\)	\(1\)	\(0\)	\(1\)	\(1\)
\(1\)	\(1\)	\(0\)	\(0\)	\(0\)	\(1\)	\(1\)

Answer:

\(A\)	\(B\)	\(\overline{A}\)	\(\overline{B}\)	\((\overline{A}\overline{B})\)	\((A + B)\)	\((\overline{A}\overline{B})+(A + B)\)
\(0\)	\(1\)	\(1\)	\(0\)	\(0\)	\(1\)	\(1\)
\(1\)	\(0\)	\(0\)	\(1\)	\(0\)	\(1\)	\(1\)
\(1\)	\(1\)	\(0\)	\(0\)	\(0\)	\(1\)	\(1\)