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?

  1. D = A ⊕ B ⊕ Cout
  2. D = A ⊕ B ⊕ Bin
  3. D = A ⊕ B
  4. D = A AND B

Answer (Detailed Solution Below)

Option 2 : D = A ⊕ B ⊕ Bin

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?

  1. D = A ⊕ B
  2. D = A AND B
  3. D = A ⊕ B ⊕ Cout
  4. D = A ⊕ B ⊕ Bin

Answer (Detailed Solution Below)

Option 4 : D = A ⊕ B ⊕ Bin

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 

qImage652d30070ec38d2cb73cdda7

  1. full adder
  2. full subtractor
  3. shift register
  4. decade counter

Answer (Detailed Solution Below)

Option 2 : full subtractor

Full Subtractor Question 3 Detailed Solution

qImage652d30070ec38d2cb73cdda7

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 (B̅C + BC̅) + A(B̅C̅  + BC)

S = A̅ (B ⊕ C) + A (B ⊙   C)

\(\because A \odot B = \overline{A ⊕ B}\)

S = A B C

Also

E = A̅ B̅ C + A̅ B C̅  + A̅  BC + ABC

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?

  1. D = A ⊕ B ⊕ Cout
  2. D = A ⊕ B ⊕ Bin
  3. D = A ⊕ B
  4. D = A AND B

Answer (Detailed Solution Below)

Option 2 : D = A ⊕ B ⊕ Bin

Full Subtractor Question 4 Detailed Solution

Download Solution PDF

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.

Which Boolean expression correctly represents the Difference (D) output of a Full Subtractor?

  1. D = A ⊕ B
  2. D = A AND B
  3. D = A ⊕ B ⊕ Cout
  4. D = A ⊕ B ⊕ Bin

Answer (Detailed Solution Below)

Option 4 : D = A ⊕ B ⊕ Bin

Full Subtractor Question 5 Detailed Solution

Download Solution PDF

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 6:

Which Boolean expression correctly represents the Difference (D) output of a Full Subtractor?

  1. D = A ⊕ B ⊕ Cout
  2. D = A ⊕ B ⊕ Bin
  3. D = A ⊕ B
  4. D = A AND B

Answer (Detailed Solution Below)

Option 2 : D = A ⊕ B ⊕ Bin

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 

qImage652d30070ec38d2cb73cdda7

  1. full adder
  2. full subtractor
  3. shift register
  4. decade counter

Answer (Detailed Solution Below)

Option 2 : full subtractor

Full Subtractor Question 7 Detailed Solution

qImage652d30070ec38d2cb73cdda7

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 (B̅C + BC̅) + A(B̅C̅  + BC)

S = A̅ (B ⊕ C) + A (B ⊙   C)

\(\because A \odot B = \overline{A ⊕ B}\)

S = A B C

Also

E = A̅ B̅ C + A̅ B C̅  + A̅  BC + ABC

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?

  1. D = A ⊕ B
  2. D = A AND B
  3. D = A ⊕ B ⊕ Cout
  4. D = A ⊕ B ⊕ Bin

Answer (Detailed Solution Below)

Option 4 : D = A ⊕ B ⊕ Bin

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?

  1. number of NAND or NOR gates – 9 
  2. number of NAND or NOR gates – 5
  3. number of NOR or NAND gates – 10
  4. number of NOR or NAND gates - 10

Answer (Detailed Solution Below)

Option :

Full Subtractor Question 9 Detailed Solution

Key Points

Minimum number of NAND or NOR gates required for Full subtractor is=9

fullsub

Additional Information

  NAND NOR    
Half adder 5 5 ⊕ B sum  AB Carry
Half subtractor 5 5 ⊕ 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

 

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