Question 1

Boolean multiplication is symbolized by A + B.

Accepted Answer

Boolean multiplication is symbolized by A * B or simply AB, not A + B, which represents Boolean addition.

Question 2

In Boolean algebra, 1 · 0 = 0.

Accepted Answer

In Boolean algebra, the multiplication operation (·) is analogous to the AND operation, where 1 represents true and 0 represents false. Therefore, 1 AND 0 results in false, which is represented by 0.

Question 3

The complement of 1 is 0.

Accepted Answer

In binary, the complement of 1 is 0, and vice versa.

Question 4

The Boolean expression X = ABC describes a three- input AND gate.

Accepted Answer

The expression X = ABC implies that X is true only when A, B, and C are all true, which is the behavior of a three-input AND gate.

Question 5

When a two- input NAND gate has inputs of 1 and 0, the output is 0.

Accepted Answer

A two-input NAND gate gives an output of 1 when any of its inputs is 0, as the NAND operation is the inverse of the AND operation.

Question 6

The commutative law of Boolean algebra states that A + B = A · B.

Accepted Answer

The commutative law of Boolean algebra states that A + B = B + A and A · B = B · A, not A + B = A · B.

Question 7

-According to the distributive law, Figure 4- 1 shows one possible logic implementation of the expression X = A(B+C).

Accepted Answer

The distributive law in algebra states that A(B+C) = AB + AC, which means that the expression X = A(B+C) can be implemented in logic by distributing A across the sum of B and C, resulting in a logic circuit that performs the operation AB + AC.

Question 8

-For the circuit in Figure 4- 1, X = 0 whenever A = 0, regardless of the levels applied to inputs B and C.

Accepted Answer

In a typical digital logic circuit, if X is an output that depends on inputs A, B, and C, and the statement says "X = 0 whenever A = 0, regardless of the levels applied to inputs B and C," it implies that A is a controlling input in a configuration such as an AND gate or a similar setup where the output is determined to be 0 if A is 0, no matter the states of B and C. This behavior is characteristic of circuits where the presence of a '0' on a critical input can define the output independently of other inputs.

Question 9

DeMorgan's theorem states that

Accepted Answer

The answer of DeMorgan's theorem states that ...

Question 10

DeMorgan's theorem states that

Accepted Answer

The answer of DeMorgan's theorem states that ...

Question 11

The Karnaugh maps provide graphic approaches to simplifying Boolean expressions.

Accepted Answer

Karnaugh maps are graphical tools used to simplify Boolean algebra expressions, making it easier to minimize the logic needed for digital circuits.

Question 12

The Sum- of- Product (SOP) form is a standard form of Boolean expression.

Accepted Answer

The Sum-of-Product (SOP) form is indeed a standard form of Boolean expression that represents a Boolean function by summing (ORing) together products (ANDs) of literals.

Question 13

The Product- of- Sum (POS) form is a standard form of Boolean expression.

Accepted Answer

The Product-of-Sum (POS) form is indeed a standard form of Boolean expression, representing a logical function as a product (AND operation) of sums (OR operations) of literals.

Question 14

When mapping an SOP expression using a Karnaugh map a 0 is placed in each cell corresponding to the value of the product term.

Accepted Answer

In a Karnaugh map, a 1 is placed in each cell corresponding to the value of the product term in a Sum of Products (SOP) expression, not a 0.

Question 15

Which of the following is a correct form of Boolean addition?
A) 0 · 0 = 0
B) 0 · 1 = 0
C) 0 + 1 = 0
D) 0 + 1 = 1

Accepted Answer

In Boolean algebra, addition is equivalent to the logical operation OR. The statement 0 + 1 = 1 correctly reflects this, as either 0 or 1 being true (1) results in the whole expression being true (1).

Question 16

Which of the following is a correct form of Boolean multiplication?
A) 0 + 1 = 1
B) 0 · 1 = 0
C) 0 · 1 = 1
D) 0 + 1 = 0

Accepted Answer

In Boolean algebra, multiplication is analogous to the AND operation, where 0 AND 1 equals 0.

Question 17

In Boolean algebra, the expression "_________"means the complement of A.
A) not A
B) negative A
C) inverse A
D) A negative

Accepted Answer

The complement of A in Boolean algebra is commonly denoted as "not A," indicating the opposite or negation of A's value.

Question 18

The symbol shown below is a(n)______ and the output will be______ for the input shown.

A) inverter, 1
B) inverter, 
C) buffer, not A
D) buffer, 1

Accepted Answer

The answer of The symbol shown below is a(n)______ and...

Question 19

-The symbol shown in Figure 4- 2 is a(n)________gate.
A) AND- OR
B) AND
C) OR
D) NAND

Accepted Answer

The symbol described is for an AND gate, which performs a logical AND operation, outputting true only if all inputs are true.

Question 20

-The Boolean expression for the symbol in Figure 4- 2 is _______.
A) X = (A +B) (B +C)
B) X = ABCD
C) X = A + B + C + D
D) X = AB + BC

Accepted Answer

The answer of 
-The Boolean expression for the symbol in...

Quiz 4: Boolean Algebra and Logic Simplification

Boolean multiplication is symbolized by A + B.

In Boolean algebra, 1 · 0 = 0.

The complement of 1 is 0.

The Boolean expression X = ABC describes a three- input AND gate.

When a two- input NAND gate has inputs of 1 and 0, the output is 0.

The commutative law of Boolean algebra states that A + B = A · B.

-According to the distributive law, Figure 4- 1 shows one possible logic implementation of the expression X = A(B+C).

-For the circuit in Figure 4- 1, X = 0 whenever A = 0, regardless of the levels applied to inputs B and C.

DeMorgan's theorem states that

DeMorgan's theorem states that

The Karnaugh maps provide graphic approaches to simplifying Boolean expressions.

The Sum- of- Product (SOP) form is a standard form of Boolean expression.

The Product- of- Sum (POS) form is a standard form of Boolean expression.

When mapping an SOP expression using a Karnaugh map a 0 is placed in each cell corresponding to the value of the product term.

Which of the following is a correct form of Boolean addition?

Which of the following is a correct form of Boolean multiplication?

In Boolean algebra, the expression "_________"means the complement of A.

The symbol shown below is a(n) and the output will be for the input shown.

-The symbol shown in Figure 4- 2 is a(n) ________gate.

-The Boolean expression for the symbol in Figure 4- 2 is _______.

Quiz 4: Boolean Algebra and Logic Simplification

Boolean multiplication is symbolized by A + B.

In Boolean algebra, 1 · 0 = 0.

The complement of 1 is 0.

The Boolean expression X = ABC describes a three- input AND gate.

When a two- input NAND gate has inputs of 1 and 0, the output is 0.

The commutative law of Boolean algebra states that A + B = A · B.

-According to the distributive law, Figure 4- 1 shows one possible logic implementation of the expression X = A(B+C).

-For the circuit in Figure 4- 1, X = 0 whenever A = 0, regardless of the levels applied to inputs B and C.

DeMorgan's theorem states that

DeMorgan's theorem states that

The Karnaugh maps provide graphic approaches to simplifying Boolean expressions.

The Sum- of- Product (SOP) form is a standard form of Boolean expression.

The Product- of- Sum (POS) form is a standard form of Boolean expression.

When mapping an SOP expression using a Karnaugh map a 0 is placed in each cell corresponding to the value of the product term.

Which of the following is a correct form of Boolean addition?

Which of the following is a correct form of Boolean multiplication?

In Boolean algebra, the expression "_________"means the complement of A.

The symbol shown below is a(n) ______ and the output will be______ for the input shown.

-The symbol shown in Figure 4- 2 is a(n) ________gate.

-The Boolean expression for the symbol in Figure 4- 2 is _______.

The symbol shown below is a(n) and the output will be for the input shown.