Subtractor MCQ Quiz - Objective Question with Answer for Subtractor - Download Free PDF
Last updated on Jun 12, 2025
Latest Subtractor MCQ Objective Questions
Subtractor Question 1:
Which Boolean expression correctly represents the Difference (D) output of a Full Subtractor?
Answer (Detailed Solution Below)
Subtractor Question 1 Detailed Solution
Explanation:
The correct option for the Boolean expression that correctly represents the Difference (D) output of a Full Subtractor is Option 2: D = A ⊕ B ⊕ Bin.
A Full Subtractor is a combinational logic circuit used to perform the subtraction of three bits: the minuend (A), subtrahend (B), and the borrow-in (Bin). The Full Subtractor has two outputs: the Difference (D) and the Borrow-out (Bout).
Full Subtractor Truth Table:
| A | B | Bin | D (Difference) | Bout (Borrow-out) |
|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 1 | 1 |
| 0 | 1 | 0 | 1 | 1 |
| 0 | 1 | 1 | 0 | 1 |
| 1 | 0 | 0 | 1 | 0 |
| 1 | 0 | 1 | 0 | 0 |
| 1 | 1 | 0 | 0 | 0 |
| 1 | 1 | 1 | 1 | 1 |
The Difference (D) output can be derived from the truth table. The Boolean expression for the Difference (D) in a Full Subtractor is given by:
D = A ⊕ B ⊕ Bin
The XOR (⊕) operation is used because it outputs true (1) when an odd number of inputs are true (1). This property makes it ideal for calculating the difference in a subtraction operation.
Analysis of Other Options:
- Option 1: D = A ⊕ B ⊕ Cout - This option is incorrect because Cout (Carry-out) is not part of the inputs for calculating the Difference (D) in a Full Subtractor. The correct inputs are A, B, and Bin (Borrow-in).
- Option 3: D = A ⊕ B - This option is incorrect because it does not account for the Borrow-in (Bin) input, which is essential in the subtraction process in a Full Subtractor.
- Option 4: D = A AND B - This option is incorrect because the AND operation does not correctly represent the difference calculation. The correct operation involves the XOR function to handle the subtraction logic.
- Option 5: (Blank Option) - This option is not applicable as it does not provide any expression.
In summary, the correct Boolean expression for the Difference (D) output of a Full Subtractor is D = A ⊕ B ⊕ Bin, as it correctly considers all necessary inputs and their respective operations to perform the subtraction.
Subtractor Question 2:
Which Boolean expression correctly represents the Difference (D) output of a Full Subtractor?
Answer (Detailed Solution Below)
Subtractor Question 2 Detailed Solution
Explanation:
The correct option for the Boolean expression that correctly represents the Difference (D) output of a Full Subtractor is Option 2: D = A ⊕ B ⊕ Bin.
A Full Subtractor is a combinational logic circuit used to perform the subtraction of three bits: the minuend (A), subtrahend (B), and the borrow-in (Bin). The Full Subtractor has two outputs: the Difference (D) and the Borrow-out (Bout).
Full Subtractor Truth Table:
| A | B | Bin | D (Difference) | Bout (Borrow-out) |
|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 1 | 1 |
| 0 | 1 | 0 | 1 | 1 |
| 0 | 1 | 1 | 0 | 1 |
| 1 | 0 | 0 | 1 | 0 |
| 1 | 0 | 1 | 0 | 0 |
| 1 | 1 | 0 | 0 | 0 |
| 1 | 1 | 1 | 1 | 1 |
The Difference (D) output can be derived from the truth table. The Boolean expression for the Difference (D) in a Full Subtractor is given by:
D = A ⊕ B ⊕ Bin
The XOR (⊕) operation is used because it outputs true (1) when an odd number of inputs are true (1). This property makes it ideal for calculating the difference in a subtraction operation.
Subtractor Question 3:
For a binary half subtractor having two inputs A and B, the correct set of logical expressions for the outputs D (difference) and X (borrow) is
Answer (Detailed Solution Below)
Subtractor Question 3 Detailed Solution
The correct option is 3
Concept:
Truth Table for half subtractor:
| A | B | Difference | Borrow |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 0 | 1 | 1 | 1 |
| 1 | 0 | 1 | 0 |
| 1 | 1 | 0 | 0 |
\( Difference = A⊕B = A\bar B + \bar AB \)
\(Borrow = X=\bar AB\)
Subtractor Question 4:
Half Subtractors require _____ bits.
Answer (Detailed Solution Below)
Subtractor Question 4 Detailed Solution
Concept:
A half subtractor is a combinational circuit that is used to perform the subtraction of two single-bit words, i.e. it requires 2 input bits.
It subtracts two single-bits A & B and produces difference d & borrow b.
The equation for half subtractor is :
d = A'B + AB' or A ⊕ B
b = A'B
Truth Table for half subtractor:
| A | B | Difference | Borrow |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 0 | 1 | 1 | 1 |
| 1 | 0 | 1 | 0 |
| 1 | 1 | 0 | 0 |
Circuit Diagram:
Subtractor Question 5:
The circuit shown in the given figure is a
Answer (Detailed Solution Below)
Subtractor Question 5 Detailed Solution
P = B ⊕ C
S = A ⊕ P
S = A ⊕ B ⊕ C
This gives the sum
Q = A̅ .P
Q = A̅ .(B ⊕ C)
R = B.C
E = Q + R
E = A̅ .(B ⊕ C) + B.C
Full subtractor truth table:
| A |
B |
C |
S |
E |
|
0 |
0 |
0 |
0 |
0 |
|
0 |
0 |
1 |
1 |
1 |
|
0 |
1 |
0 |
1 |
1 |
|
0 |
1 |
1 |
0 |
1 |
|
1 |
0 |
0 |
1 |
0 |
|
1 |
0 |
1 |
0 |
0 |
|
1 |
1 |
0 |
0 |
0 |
|
1 |
1 |
1 |
1 |
1 |
S = A̅ B̅ C + A̅ BC̅ + AB̅C̅ + ABC
S = A̅ (B ⊕ C) + A (B ⊙ C)
\(\because A \odot B = \overline{A ⊕ B}\)
S = A ⊕ B ⊕ C
Also
E = A̅ (B̅C + BC̅) + (A̅ + A)BC
E = A̅(B ⊕ C) + BC
∴ it is a full subtractor
Top Subtractor MCQ Objective Questions
For a binary half-subtractor having two inputs A and B, the correct set of logical expression for the outputs D (= A minus B) and X (= borrow) are
Answer (Detailed Solution Below)
Subtractor Question 6 Detailed Solution
Download Solution PDFTruth Table for half substractor:
| A | B | Difference | Borrow |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 0 | 1 | 1 | 1 |
| 1 | 0 | 1 | 0 |
| 1 | 1 | 0 | 0 |
\( Difference = A⊕B = A\bar B + \bar AB \)
\(Borrow = X=\bar AB\)
Which Boolean expression correctly represents the Difference (D) output of a Full Subtractor?
Answer (Detailed Solution Below)
Subtractor Question 7 Detailed Solution
Download Solution PDFExplanation:
The correct option for the Boolean expression that correctly represents the Difference (D) output of a Full Subtractor is Option 2: D = A ⊕ B ⊕ Bin.
A Full Subtractor is a combinational logic circuit used to perform the subtraction of three bits: the minuend (A), subtrahend (B), and the borrow-in (Bin). The Full Subtractor has two outputs: the Difference (D) and the Borrow-out (Bout).
Full Subtractor Truth Table:
| A | B | Bin | D (Difference) | Bout (Borrow-out) |
|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 1 | 1 |
| 0 | 1 | 0 | 1 | 1 |
| 0 | 1 | 1 | 0 | 1 |
| 1 | 0 | 0 | 1 | 0 |
| 1 | 0 | 1 | 0 | 0 |
| 1 | 1 | 0 | 0 | 0 |
| 1 | 1 | 1 | 1 | 1 |
The Difference (D) output can be derived from the truth table. The Boolean expression for the Difference (D) in a Full Subtractor is given by:
D = A ⊕ B ⊕ Bin
The XOR (⊕) operation is used because it outputs true (1) when an odd number of inputs are true (1). This property makes it ideal for calculating the difference in a subtraction operation.
Analysis of Other Options:
- Option 1: D = A ⊕ B ⊕ Cout - This option is incorrect because Cout (Carry-out) is not part of the inputs for calculating the Difference (D) in a Full Subtractor. The correct inputs are A, B, and Bin (Borrow-in).
- Option 3: D = A ⊕ B - This option is incorrect because it does not account for the Borrow-in (Bin) input, which is essential in the subtraction process in a Full Subtractor.
- Option 4: D = A AND B - This option is incorrect because the AND operation does not correctly represent the difference calculation. The correct operation involves the XOR function to handle the subtraction logic.
- Option 5: (Blank Option) - This option is not applicable as it does not provide any expression.
In summary, the correct Boolean expression for the Difference (D) output of a Full Subtractor is D = A ⊕ B ⊕ Bin, as it correctly considers all necessary inputs and their respective operations to perform the subtraction.
For a binary half subtractor having two inputs A and B, the correct set of logical expressions for the outputs D (difference) and X (borrow) is
Answer (Detailed Solution Below)
Subtractor Question 8 Detailed Solution
Download Solution PDFThe correct option is 3
Concept:
Truth Table for half subtractor:
| A | B | Difference | Borrow |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 0 | 1 | 1 | 1 |
| 1 | 0 | 1 | 0 |
| 1 | 1 | 0 | 0 |
\( Difference = A⊕B = A\bar B + \bar AB \)
\(Borrow = X=\bar AB\)
Which Boolean expression correctly represents the Difference (D) output of a Full Subtractor?
Answer (Detailed Solution Below)
Subtractor Question 9 Detailed Solution
Download Solution PDFExplanation:
The correct option for the Boolean expression that correctly represents the Difference (D) output of a Full Subtractor is Option 2: D = A ⊕ B ⊕ Bin.
A Full Subtractor is a combinational logic circuit used to perform the subtraction of three bits: the minuend (A), subtrahend (B), and the borrow-in (Bin). The Full Subtractor has two outputs: the Difference (D) and the Borrow-out (Bout).
Full Subtractor Truth Table:
| A | B | Bin | D (Difference) | Bout (Borrow-out) |
|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 1 | 1 |
| 0 | 1 | 0 | 1 | 1 |
| 0 | 1 | 1 | 0 | 1 |
| 1 | 0 | 0 | 1 | 0 |
| 1 | 0 | 1 | 0 | 0 |
| 1 | 1 | 0 | 0 | 0 |
| 1 | 1 | 1 | 1 | 1 |
The Difference (D) output can be derived from the truth table. The Boolean expression for the Difference (D) in a Full Subtractor is given by:
D = A ⊕ B ⊕ Bin
The XOR (⊕) operation is used because it outputs true (1) when an odd number of inputs are true (1). This property makes it ideal for calculating the difference in a subtraction operation.
Subtractor Question 10:
For a binary half-subtractor having two inputs A and B, the correct set of logical expression for the outputs D (= A minus B) and X (= borrow) are
Answer (Detailed Solution Below)
Subtractor Question 10 Detailed Solution
Truth Table for half substractor:
| A | B | Difference | Borrow |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 0 | 1 | 1 | 1 |
| 1 | 0 | 1 | 0 |
| 1 | 1 | 0 | 0 |
\( Difference = A⊕B = A\bar B + \bar AB \)
\(Borrow = X=\bar AB\)
Subtractor Question 11:
Which Boolean expression correctly represents the Difference (D) output of a Full Subtractor?
Answer (Detailed Solution Below)
Subtractor Question 11 Detailed Solution
Explanation:
The correct option for the Boolean expression that correctly represents the Difference (D) output of a Full Subtractor is Option 2: D = A ⊕ B ⊕ Bin.
A Full Subtractor is a combinational logic circuit used to perform the subtraction of three bits: the minuend (A), subtrahend (B), and the borrow-in (Bin). The Full Subtractor has two outputs: the Difference (D) and the Borrow-out (Bout).
Full Subtractor Truth Table:
| A | B | Bin | D (Difference) | Bout (Borrow-out) |
|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 1 | 1 |
| 0 | 1 | 0 | 1 | 1 |
| 0 | 1 | 1 | 0 | 1 |
| 1 | 0 | 0 | 1 | 0 |
| 1 | 0 | 1 | 0 | 0 |
| 1 | 1 | 0 | 0 | 0 |
| 1 | 1 | 1 | 1 | 1 |
The Difference (D) output can be derived from the truth table. The Boolean expression for the Difference (D) in a Full Subtractor is given by:
D = A ⊕ B ⊕ Bin
The XOR (⊕) operation is used because it outputs true (1) when an odd number of inputs are true (1). This property makes it ideal for calculating the difference in a subtraction operation.
Analysis of Other Options:
- Option 1: D = A ⊕ B ⊕ Cout - This option is incorrect because Cout (Carry-out) is not part of the inputs for calculating the Difference (D) in a Full Subtractor. The correct inputs are A, B, and Bin (Borrow-in).
- Option 3: D = A ⊕ B - This option is incorrect because it does not account for the Borrow-in (Bin) input, which is essential in the subtraction process in a Full Subtractor.
- Option 4: D = A AND B - This option is incorrect because the AND operation does not correctly represent the difference calculation. The correct operation involves the XOR function to handle the subtraction logic.
- Option 5: (Blank Option) - This option is not applicable as it does not provide any expression.
In summary, the correct Boolean expression for the Difference (D) output of a Full Subtractor is D = A ⊕ B ⊕ Bin, as it correctly considers all necessary inputs and their respective operations to perform the subtraction.
Subtractor Question 12:
Half Subtractors require _____ bits.
Answer (Detailed Solution Below)
Subtractor Question 12 Detailed Solution
Concept:
A half subtractor is a combinational circuit that is used to perform the subtraction of two single-bit words, i.e. it requires 2 input bits.
It subtracts two single-bits A & B and produces difference d & borrow b.
The equation for half subtractor is :
d = A'B + AB' or A ⊕ B
b = A'B
Truth Table for half subtractor:
| A | B | Difference | Borrow |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 0 | 1 | 1 | 1 |
| 1 | 0 | 1 | 0 |
| 1 | 1 | 0 | 0 |
Circuit Diagram:
Subtractor Question 13:
The circuit shown in the given figure is a
Answer (Detailed Solution Below)
Subtractor Question 13 Detailed Solution
P = B ⊕ C
S = A ⊕ P
S = A ⊕ B ⊕ C
This gives the sum
Q = A̅ .P
Q = A̅ .(B ⊕ C)
R = B.C
E = Q + R
E = A̅ .(B ⊕ C) + B.C
Full subtractor truth table:
| A |
B |
C |
S |
E |
|
0 |
0 |
0 |
0 |
0 |
|
0 |
0 |
1 |
1 |
1 |
|
0 |
1 |
0 |
1 |
1 |
|
0 |
1 |
1 |
0 |
1 |
|
1 |
0 |
0 |
1 |
0 |
|
1 |
0 |
1 |
0 |
0 |
|
1 |
1 |
0 |
0 |
0 |
|
1 |
1 |
1 |
1 |
1 |
S = A̅ B̅ C + A̅ BC̅ + AB̅C̅ + ABC
S = A̅ (B ⊕ C) + A (B ⊙ C)
\(\because A \odot B = \overline{A ⊕ B}\)
S = A ⊕ B ⊕ C
Also
E = A̅ (B̅C + BC̅) + (A̅ + A)BC
E = A̅(B ⊕ C) + BC
∴ it is a full subtractor
Subtractor Question 14:
For a binary half subtractor having two inputs A and B, the correct set of logical expressions for the outputs D (difference) and X (borrow) is
Answer (Detailed Solution Below)
Subtractor Question 14 Detailed Solution
The correct option is 3
Concept:
Truth Table for half subtractor:
| A | B | Difference | Borrow |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 0 | 1 | 1 | 1 |
| 1 | 0 | 1 | 0 |
| 1 | 1 | 0 | 0 |
\( Difference = A⊕B = A\bar B + \bar AB \)
\(Borrow = X=\bar AB\)
Subtractor Question 15:
Find the Boolean expression for Borrow (B) as the circuit shown below
Answer (Detailed Solution Below)
\(p\bar q + pr + \bar qr\)
Subtractor Question 15 Detailed Solution
obtain truth table for above circuit we get
|
q |
r |
p |
|
|
D |
B |
|
0 |
0 |
0 |
|
|
0 |
0 |
|
0 |
0 |
1 |
|
|
1 |
1 |
|
0 |
1 |
0 |
|
|
1 |
1 |
|
0 |
1 |
1 |
|
|
0 |
1 |
|
1 |
0 |
0 |
|
|
1 |
0 |
|
1 |
0 |
1 |
|
|
0 |
0 |
|
1 |
1 |
0 |
|
|
0 |
0 |
|
1 |
1 |
1 |
|
|
1 |
1 |
Obtain k – map for B
\(\begin{array}{l} B = \bar qp + rp + \bar qr\\ = p\bar q + pr + \bar qr \end{array}\)