Full Subtractor MCQ Quiz - Objective Question with Answer for Full Subtractor - Download Free PDF
Last updated on Jun 12, 2025
Latest Full Subtractor MCQ Objective Questions
Full Subtractor Question 1:
Which Boolean expression correctly represents the Difference (D) output of a Full Subtractor?
Answer (Detailed Solution Below)
Full 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.
Full Subtractor Question 2:
Which Boolean expression correctly represents the Difference (D) output of a Full Subtractor?
Answer (Detailed Solution Below)
Full 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.
Full Subtractor Question 3:
The circuit shown in the given figure is a
Answer (Detailed Solution Below)
Full Subtractor Question 3 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 Full Subtractor MCQ Objective Questions
Which Boolean expression correctly represents the Difference (D) output of a Full Subtractor?
Answer (Detailed Solution Below)
Full Subtractor Question 4 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.
Which Boolean expression correctly represents the Difference (D) output of a Full Subtractor?
Answer (Detailed Solution Below)
Full Subtractor Question 5 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.
Full Subtractor Question 6:
Which Boolean expression correctly represents the Difference (D) output of a Full Subtractor?
Answer (Detailed Solution Below)
Full Subtractor Question 6 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.
Full Subtractor Question 7:
The circuit shown in the given figure is a
Answer (Detailed Solution Below)
Full Subtractor Question 7 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
Full Subtractor Question 8:
Which Boolean expression correctly represents the Difference (D) output of a Full Subtractor?
Answer (Detailed Solution Below)
Full Subtractor Question 8 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.
Full Subtractor Question 9:
Consider 2 input NAND and NOR gates. How many such gates (NAND / NOR only) gates required to implement Full subtractor?
Answer (Detailed Solution Below)
Full Subtractor Question 9 Detailed Solution
Minimum number of NAND or NOR gates required for Full subtractor is=9
Additional Information
| NAND | NOR | |||
| Half adder | 5 | 5 | A ⊕ B sum | AB Carry |
| Half subtractor | 5 | 5 | A ⊕ B sum | \(\bar A B\) borrow |
| Full adder | 9 | 9 | A ⊕ B ⊕ C sum | AB+BC+CA carry |
| Full subtractor | 9 | 9 | A ⊕B⊕C Diff | \(\bar A B+BC+C \bar A\) borrow |