Logic Circuit Design from Boolean Expressions Quiz (Undergraduate Level)

1) A Boolean function maps:

Variables to constants

Constants to variables

Variables to {0, 1}

Operators to variables

A Boolean function takes one or more Boolean variables as inputs and maps them to an output value in the set {0, 1}. This binary output defines the function's behavior, such as in truth tables. It does not map variables to constants arbitrarily, constants to variables, or operators to variables.

Explanation

A Boolean function takes one or more Boolean variables as inputs and maps them to an output value in the set {0, 1}. This binary output defines the function's behavior, such as in truth tables. It does not map variables to constants arbitrarily, constants to variables, or operators to variables.

2) A 2-input gate has this truth table: (0,0) -> 0, (0,1) -> 1, (1,0) -> 1, (1,1) -> 1. Which gate is it?

AND gate

XOR gate

NAND gate

OR gate

The truth table shows output 1 when at least one input is 1, which is characteristic of an OR gate. An AND gate outputs 1 only for (1,1), XOR outputs 1 only when inputs differ, and NAND outputs 0 only for (1,1), so none match except OR.

Explanation

The truth table shows output 1 when at least one input is 1, which is characteristic of an OR gate. An AND gate outputs 1 only for (1,1), XOR outputs 1 only when inputs differ, and NAND outputs 0 only for (1,1), so none match except OR.

3) A Boolean variable's truth table has:

2^n rows

2 rows

N rows

N^2 rows

For n Boolean variables, the truth table must list all possible combinations of inputs. Each variable has 2 states (0 or 1), so the total number of rows is 2^n. This ensures all input scenarios are covered, unlike fixed row counts like 2, n, or n^2.

Explanation

For n Boolean variables, the truth table must list all possible combinations of inputs. Each variable has 2 states (0 or 1), so the total number of rows is 2^n. This ensures all input scenarios are covered, unlike fixed row counts like 2, n, or n^2.

4) A 2-input gate has this truth table: (0,0) -> 0, (0,1) -> 1, (1,0) -> 1, (1,1) -> 0. Which gate is it?

AND gate

XOR gate

OR gate

XNOR gate

This truth table outputs 1 when the inputs are different, which is the definition of an XOR gate. XNOR outputs 1 when inputs are the same, AND outputs 1 only for (1,1), and OR outputs 1 for any input except (0,0), so only XOR fits.

Explanation

This truth table outputs 1 when the inputs are different, which is the definition of an XOR gate. XNOR outputs 1 when inputs are the same, AND outputs 1 only for (1,1), and OR outputs 1 for any input except (0,0), so only XOR fits.

5) The expression A · B + C represents a circuit with:

An AND gate's output and C as inputs to an OR gate.

An OR gate's output and C as inputs to an AND gate.

An AND gate's output and C as inputs to another AND gate.

An OR gate's output and C as inputs to another OR gate.

The expression A · B + C means first compute A AND B, then OR the result with C. So, A and B are inputs to an AND gate, and the output of that AND gate is fed along with C into an OR gate. This order of operations is critical in logic circuit design.

Explanation

The expression A · B + C means first compute A AND B, then OR the result with C. So, A and B are inputs to an AND gate, and the output of that AND gate is fed along with C into an OR gate. This order of operations is critical in logic circuit design.

6) The expression (A + B) · C represents a circuit with:

An AND gate's output and C as inputs to an OR gate.

An OR gate's output and C as inputs to an AND gate.

A NAND gate's output and C as inputs to an OR gate.

A NOR gate's output and C as inputs to an AND gate.

The expression (A + B) · C means first compute A OR B, then AND the result with C. Thus, A and B are inputs to an OR gate, and the output of that OR gate is fed along with C into an AND gate. This implements the logical AND of the OR result with C.

Explanation

The expression (A + B) · C means first compute A OR B, then AND the result with C. Thus, A and B are inputs to an OR gate, and the output of that OR gate is fed along with C into an AND gate. This implements the logical AND of the OR result with C.

7) How would you implement the expression A' + B?

Input A to a NOT gate, then its output and B to an OR gate.

Inputs A and B to an OR gate, then the output to a NOT gate.

Input A to a NOT gate, then its output and B to an AND gate.

Inputs A and B to an AND gate, then the output to a NOT gate.

The expression A' + B requires first inverting A to get A', then ORing that with B. So, A is connected to a NOT gate, and the output of the NOT gate (A') and B are connected to an OR gate. Other configurations would yield different expressions, like (A + B)' or A' · B.

Explanation

The expression A' + B requires first inverting A to get A', then ORing that with B. So, A is connected to a NOT gate, and the output of the NOT gate (A') and B are connected to an OR gate. Other configurations would yield different expressions, like (A + B)' or A' · B.

8) The circuit for (A · B)' is a single:

AND gate

NOR gate

NAND gate

OR gate

The expression (A · B)' is the negation of A AND B, which is exactly the function of a NAND gate. A NAND gate outputs 0 only when both inputs are 1, and 1 otherwise, matching (A · B)'. Other gates like AND, NOR, or OR do not directly implement this.

Explanation

The expression (A · B)' is the negation of A AND B, which is exactly the function of a NAND gate. A NAND gate outputs 0 only when both inputs are 1, and 1 otherwise, matching (A · B)'. Other gates like AND, NOR, or OR do not directly implement this.

9) A circuit implementing A' · B' would use:

Two NOT gates and one AND gate.

One NOT gate and two AND gates.

Two NOT gates and one OR gate.

One AND gate and one NOT gate.

To implement A' · B', first invert A and B using two NOT gates to get A' and B'. Then, feed A' and B' into an AND gate. This produces the output A' · B'. Using OR gates or fewer NOT gates would not yield the correct expression.

Explanation

To implement A' · B', first invert A and B using two NOT gates to get A' and B'. Then, feed A' and B' into an AND gate. This produces the output A' · B'. Using OR gates or fewer NOT gates would not yield the correct expression.

10) The expression A + B + C' is implemented with:

One 3-input NOR gate.

Three NOT gates and one 3-input OR gate.

One NOT gate and one 3-input AND gate.

One NOT gate and one 3-input OR gate.

The expression A + B + C' requires inverting C to get C', then ORing A, B, and C'. So, one NOT gate is used for C, and a 3-input OR gate combines A, B, and C'. Using AND gates or multiple NOT gates would not achieve the OR operation.

Explanation

The expression A + B + C' requires inverting C to get C', then ORing A, B, and C'. So, one NOT gate is used for C, and a 3-input OR gate combines A, B, and C'. Using AND gates or multiple NOT gates would not achieve the OR operation.

11) Which expression describes a circuit where two inputs are XORed, and the result is inverted?

(A + B)'

(A · B)'

A ⊕ B

(A ⊕ B)'

XOR is often denoted by ⊗ or ⊕. Inverting the XOR result gives XNOR, which is expressed as (A ⊕ B)'. This output is 1 when inputs are the same. (A + B)' is NOR, (A · B)' is NAND, and A ⊕ B is XOR without inversion.

Explanation

XOR is often denoted by ⊗ or ⊕. Inverting the XOR result gives XNOR, which is expressed as (A ⊕ B)'. This output is 1 when inputs are the same. (A + B)' is NOR, (A · B)' is NAND, and A ⊕ B is XOR without inversion.

12) The expression A · (B + C) requires which combination of gates?

One OR gate and one AND gate.

Two AND gates.

Two OR gates.

One AND gate and one NOT gate.

The expression A · (B + C) means first compute B OR C using an OR gate, then AND that result with A using an AND gate. Thus, one OR gate and one AND gate are needed. Other combinations would not correctly implement the expression.

Explanation

The expression A · (B + C) means first compute B OR C using an OR gate, then AND that result with A using an AND gate. Thus, one OR gate and one AND gate are needed. Other combinations would not correctly implement the expression.

13) To build a circuit for A ⊕ B (XOR), which Boolean expression correctly represents the implementation using basic gates?

One AND and one OR gate

(A + B) · (A' + B')

(A · B') + (A' · B)

One NOT gate only

The XOR operation can be implemented as (A AND NOT B) OR (NOT A AND B), which is expressed as (A · B') + (A' · B). This requires two NOT gates, two AND gates, and one OR gate. Option b represents XNOR, while options a and d are insufficient to implement XOR.

Explanation

The XOR operation can be implemented as (A AND NOT B) OR (NOT A AND B), which is expressed as (A · B') + (A' · B). This requires two NOT gates, two AND gates, and one OR gate. Option b represents XNOR, while options a and d are insufficient to implement XOR.

14) A circuit shows inputs A and B going into an AND gate, and the output going into a NOT gate. What is the expression?

A' · B'

(A + B)'

(A · B)'

A' + B'

The AND gate computes A · B, and the NOT gate inverts it, resulting in (A · B)'. This is the NAND operation. Other options like A' · B' would require NOT gates before AND, and (A + B)' would require an OR gate followed by NOT.

Explanation

The AND gate computes A · B, and the NOT gate inverts it, resulting in (A · B)'. This is the NAND operation. Other options like A' · B' would require NOT gates before AND, and (A + B)' would require an OR gate followed by NOT.

15) A circuit shows input A going to a NOT gate, and its output being ORed with B. What is the expression?

(A + B)

A' + B

A + B'

(A' + B)'

The NOT gate inverts A to A', and then A' is ORed with B, giving A' + B. This is the direct implementation. Option a is A OR B, c is A OR NOT B, and d is the negation of A' OR B, which is not correct.

Explanation

The NOT gate inverts A to A', and then A' is ORed with B, giving A' + B. This is the direct implementation. Option a is A OR B, c is A OR NOT B, and d is the negation of A' OR B, which is not correct.

Boolean Expressions and Logic Circuit Design Quiz