Question 1

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

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.

Question 2

Write the reduced expressions for the following Karnaugh map.
-

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

Accepted Answer

The answer of Write the reduced expressions for the following...

Question 3

Give the Boolean expressions associated with each of the following gated circuits.
-

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

Accepted Answer

The answer of Give the Boolean expressions associated with each...

Question 4

Use Boolean algebra to simplify the following expressions, using x = 0.
-$x y \vee \left( x ^ { \prime } \vee y \right) ^ { \prime }$
A) 1
B) 0
C) $x$
D) $y ^ { \prime }$
E) None of these

Accepted Answer

The answer of Use Boolean algebra to simplify the following...

Question 5

Give the Boolean expressions associated with each of the following gated circuits.
-

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

Accepted Answer

The answer of Give the Boolean expressions associated with each...

Question 6

Write the Boolean expression associated with each of the following switching circuits.
-
A) $A ^ { \prime } B ^ { \prime } \vee A B$
B) $A ^ { \prime } B \vee A B ^ { \prime }$
C) $A ^ { \prime } B ^ { \prime } \vee A ^ { \prime } B$
D) $A ^ { \prime } B \vee A B$
E) None of these

Accepted Answer

The answer of Write the Boolean expression associated with each...

Question 7

Simplify each of the following Boolean expressions.
-$0 \vee z$
A) 1
B) 0
C) $z$
D) $z ^ { \prime }$
E) None of these

Accepted Answer

The Boolean expression $0 \vee z$ simplifies to $z$, because the OR operation with 0 leaves the other operand unchanged.

Question 8

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

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

Accepted Answer

The correct Boolean expression in DNF (Disjunctive Normal Form) for the given truth table is $A B ^ { \prime } C \vee A B ^ { \prime } C ^ { \prime } \vee A ^ { \prime } B ^ { \prime } C$, which corresponds to the rows where the function $f(A, B, C)$ is 1.

Question 9

Use Boolean algebra to simplify the following expressions, using x = 0.
-$\left( x \vee y ^ { \prime } \right) \vee \left( x \wedge y ^ { \prime } \right)$
A) 1
B) 0
C) $y$
D) $x ^ { \prime }$
E) None of these

Accepted Answer

The given expression can be simplified using Boolean algebra properties. The expression is $\left( x \vee y ^ { \prime } \right) \vee \left( x \wedge y ^ { \prime } \right)$. Using the absorption law, which states that $A + AB = A$, we can simplify the expression to $x \vee y ^ { \prime }$. Since the value of $x$ is given as 0, the expression further simplifies to $0 \vee y ^ { \prime }$, which is simply $y ^ { \prime }$. However, this option is not listed among the choices, so the correct answer is E) None of these.

Question 10

Use Boolean algebra to simplify the following expressions, using x = 0.
-$x ^ { \prime } \vee y ^ { \prime }$
A) 1
B) 0
C) $y$
D) $x ^ { \prime }$
E) None of these

Accepted Answer

Given $x = 0$, $x' = 1$ because the prime (') denotes NOT operation, which inverts the value. Therefore, $x' \vee y' = 1 \vee y'$. Since 1 OR anything ($1 \vee y'$) is always 1, the expression simplifies to 1.

Question 11

Give the Boolean expressions associated with each of the following gated circuits.
-

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

Accepted Answer

The answer of Give the Boolean expressions associated with each...

Question 12

Write the dnf expression corresponding to the shaded areas of the Venn diagram.

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

Accepted Answer

The answer of Write the dnf expression corresponding to the...

Question 13

Write the Boolean expression associated with each of the following switching circuits.
-

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

Accepted Answer

The answer of Write the Boolean expression associated with each...

Question 14

Write the reduced expressions for the following Karnaugh map.
-
A) $A ^ { \prime } B \vee B C ^ { \prime }$.
B) $A B \vee A ^ { \prime } C$
C) $A B \vee A ^ { \prime } C$.
D) $A B ^ { \prime } \vee B C$
E) None of these

Accepted Answer

The answer of Write the reduced expressions for the following...

Quiz 5: Boolean Circuits

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

Use Boolean algebra to simplify the following expressions, using x = 0. - $x y \vee \left( x ^ { \prime } \vee y \right) ^ { \prime }$

Simplify each of the following Boolean expressions. - $0 \vee z$

Use Boolean algebra to simplify the following expressions, using x = 0. - $\left( x \vee y ^ { \prime } \right) \vee \left( x \wedge y ^ { \prime } \right)$

Use Boolean algebra to simplify the following expressions, using x = 0. - $x ^ { \prime } \vee y ^ { \prime }$

Write the reduced expressions for the following Karnaugh map. - $Write the reduced expressions for the following Karnaugh map. - A) A ^ { \prime } B \vee B C ^ { \prime } . B) A B \vee A ^ { \prime } C C) A B \vee A ^ { \prime } C . D) A B ^ { \prime } \vee B C E) None of these$

Quiz 5: Boolean Circuits

Write the reduced expressions for the following Karnaugh map. -

Give the Boolean expressions associated with each of the following gated circuits. -

Use Boolean algebra to simplify the following expressions, using x = 0. - xy∨(x′∨y) ′x y \vee \left( x ^ { \prime } \vee y \right) ^ { \prime }xy∨(x′∨y) ′

Give the Boolean expressions associated with each of the following gated circuits. -

Write the Boolean expression associated with each of the following switching circuits. -

Simplify each of the following Boolean expressions. - 0∨z0 \vee z0∨z

Use Boolean algebra to simplify the following expressions, using x = 0. - (x∨y′) ∨(x∧y′) \left( x \vee y ^ { \prime } \right) \vee \left( x \wedge y ^ { \prime } \right) (x∨y′) ∨(x∧y′)

Use Boolean algebra to simplify the following expressions, using x = 0. - x′∨y′x ^ { \prime } \vee y ^ { \prime }x′∨y′

Give the Boolean expressions associated with each of the following gated circuits. -

Write the dnf expression corresponding to the shaded areas of the Venn diagram.

Write the Boolean expression associated with each of the following switching circuits. -

Write the reduced expressions for the following Karnaugh map. -

Use Boolean algebra to simplify the following expressions, using x = 0. - $x y \vee \left( x ^ { \prime } \vee y \right) ^ { \prime }$

Simplify each of the following Boolean expressions. - $0 \vee z$

Use Boolean algebra to simplify the following expressions, using x = 0. - $\left( x \vee y ^ { \prime } \right) \vee \left( x \wedge y ^ { \prime } \right)$

Use Boolean algebra to simplify the following expressions, using x = 0. - $x ^ { \prime } \vee y ^ { \prime }$

Write the reduced expressions for the following Karnaugh map. - $Write the reduced expressions for the following Karnaugh map. - A) A ^ { \prime } B \vee B C ^ { \prime } . B) A B \vee A ^ { \prime } C C) A B \vee A ^ { \prime } C . D) A B ^ { \prime } \vee B C E) None of these$