Half Subtractor MCQ Quiz - Objective Question with Answer for Half Subtractor - Download Free PDF
Last updated on Apr 19, 2025
Latest Half Subtractor MCQ Objective Questions
Half Subtractor Question 1:
A half subtractor is an arithmetic circuit which performs subtraction operation on _______ input bits.
Answer (Detailed Solution Below)
Half Subtractor Question 1 Detailed Solution
Concept:
A half subtractor is a combinational circuit that is used to perform the subtraction of two single-bit words.
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 |
Explanation:
From the above circuit we get,
\(F=A\oplus\ B\ and \ G=\bar AB\)
F implements the Difference and G implements the barrow. So the given circuit acts like a Half Subtractor
Half Subtractor Question 2:
In a half-subtractor circuit with X and Y as inputs, the Borrow (M) and Difference (N = X - Y) are given by
Answer (Detailed Solution Below)
Half Subtractor Question 2 Detailed Solution
The Truth Table for a half subtractor is drawn as:
| X | Y | Difference (N) | Borrow (M) |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 0 | 1 | 1 | 1 |
| 1 | 0 | 1 | 0 |
| 1 | 1 | 0 | 0 |
The Boolean expression for difference can be written as:
N = X̅ Y + XY̅
N = X ⊕ Y
And the Boolean expression for the borrow can be written as:
M = X̅ Y
Half Subtractor Question 3:
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)
Half Subtractor Question 3 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 |
\( Difference = A⊕B = A\bar B + \bar AB \)
\(Borrow = X=\bar AB\)
Half Subtractor Question 4:
Find the Boolean expression for Borrow (B) as the circuit shown below
Answer (Detailed Solution Below)
\(p\bar q + pr + \bar qr\)
Half Subtractor Question 4 Detailed Solution
obtain truth table for above circuit we get
|
q |
r |
p |
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|
D |
B |
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0 |
0 |
0 |
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0 |
0 |
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0 |
0 |
1 |
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1 |
1 |
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0 |
1 |
0 |
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1 |
1 |
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0 |
1 |
1 |
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0 |
1 |
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1 |
0 |
0 |
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1 |
0 |
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1 |
0 |
1 |
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0 |
0 |
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1 |
1 |
0 |
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0 |
0 |
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1 |
1 |
1 |
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1 |
1 |
Obtain k – map for B
\(\begin{array}{l} B = \bar qp + rp + \bar qr\\ = p\bar q + pr + \bar qr \end{array}\)
Half Subtractor Question 5:
What is the circuit?
Answer (Detailed Solution Below)
Half Subtractor Question 5 Detailed Solution
Concept:
A half subtractor is a combinational circuit that is used to perform the subtraction of two single-bit words.
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 |
Explanation:
From the above circuit we get,
\(F=A\oplus\ B\ and \ G=\bar AB\)
F implements the Difference and G implements the barrow. So the given circuit acts like a Half Subtractor
Top Half Subtractor MCQ Objective Questions
A half subtractor is an arithmetic circuit which performs subtraction operation on _______ input bits.
Answer (Detailed Solution Below)
Half Subtractor Question 6 Detailed Solution
Download Solution PDFConcept:
A half subtractor is a combinational circuit that is used to perform the subtraction of two single-bit words.
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 |
Explanation:
From the above circuit we get,
\(F=A\oplus\ B\ and \ G=\bar AB\)
F implements the Difference and G implements the barrow. So the given circuit acts like a Half Subtractor
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)
Half Subtractor Question 7 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 |
\( Difference = A⊕B = A\bar B + \bar AB \)
\(Borrow = X=\bar AB\)
In a half-subtractor circuit with X and Y as inputs, the Borrow (M) and Difference (N = X - Y) are given by
Answer (Detailed Solution Below)
Half Subtractor Question 8 Detailed Solution
Download Solution PDFThe Truth Table for a half subtractor is drawn as:
| X | Y | Difference (N) | Borrow (M) |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 0 | 1 | 1 | 1 |
| 1 | 0 | 1 | 0 |
| 1 | 1 | 0 | 0 |
The Boolean expression for difference can be written as:
N = X̅ Y + XY̅
N = X ⊕ Y
And the Boolean expression for the borrow can be written as:
M = X̅ Y
Which of the following is true about the Half Subtractor circuit?
Answer (Detailed Solution Below)
Half Subtractor Question 9 Detailed Solution
Download Solution PDFHalf Subtractor Circuit
A Half Subtractor is a combinational logic circuit used for binary subtraction. It subtracts two binary digits and generates two outputs: the difference and the borrow-out. It is called a "Half Subtractor" because it does not take into account any borrow input from previous stages, unlike the Full Subtractor.
- Difference: The difference between two binary digits is calculated using the XOR (Exclusive OR) operation. The truth table for XOR illustrates that the output is 1 when the inputs are different (0 ⊕ 1 or 1 ⊕ 0), and the output is 0 when the inputs are the same (0 ⊕ 0 or 1 ⊕ 1).
- Borrow-out: Borrow-out is generated using the NOT AND (A̅ × B) operation, which determines whether borrowing is needed during subtraction. Borrow occurs when B is 1 and A is 0, indicating that the minuend is smaller than the subtrahend.
Truth Table:
| Input A | Input B | Difference (A ⊕ B) | Borrow-out (A̅ × B) |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 0 | 1 | 1 | 1 |
| 1 | 0 | 1 | 0 |
| 1 | 1 | 0 | 0 |
Half Subtractor Question 10:
A half subtractor is an arithmetic circuit which performs subtraction operation on _______ input bits.
Answer (Detailed Solution Below)
Half Subtractor Question 10 Detailed Solution
Concept:
A half subtractor is a combinational circuit that is used to perform the subtraction of two single-bit words.
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 |
Explanation:
From the above circuit we get,
\(F=A\oplus\ B\ and \ G=\bar AB\)
F implements the Difference and G implements the barrow. So the given circuit acts like a Half Subtractor
Half Subtractor Question 11:
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)
Half Subtractor Question 11 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 |
\( Difference = A⊕B = A\bar B + \bar AB \)
\(Borrow = X=\bar AB\)
Half Subtractor Question 12:
What is the circuit?
Answer (Detailed Solution Below)
Half 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.
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 |
Explanation:
From the above circuit we get,
\(F=A\oplus\ B\ and \ G=\bar AB\)
F implements the Difference and G implements the barrow. So the given circuit acts like a Half Subtractor
Half Subtractor Question 13:
In a half-subtractor circuit with X and Y as inputs, the Borrow (M) and Difference (N = X - Y) are given by
Answer (Detailed Solution Below)
Half Subtractor Question 13 Detailed Solution
The Truth Table for a half subtractor is drawn as:
| X | Y | Difference (N) | Borrow (M) |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 0 | 1 | 1 | 1 |
| 1 | 0 | 1 | 0 |
| 1 | 1 | 0 | 0 |
The Boolean expression for difference can be written as:
N = X̅ Y + XY̅
N = X ⊕ Y
And the Boolean expression for the borrow can be written as:
M = X̅ Y
Half Subtractor Question 14:
The minimum number of NAND gates required to implement the function f1 and f2 generated by the circuit is
Answer (Detailed Solution Below) 5
Half Subtractor Question 14 Detailed Solution
\(\begin{array}{l} {{\rm{F}}_1} = {\rm{\bar yx}} + {\rm{y\bar x}} = {\rm{x}} \oplus {\rm{y}}\\ {{\rm{F}}_2} = {\rm{\bar y}}\left( 0 \right) + {\rm{y\bar x}} = {\rm{\bar xy}} \end{array}\)
So the given circuit implements a half Subtractor
Hence minimum number of NAND gates required = 5
Half Subtractor Question 15:
Find the Boolean expression for Borrow (B) as the circuit shown below
Answer (Detailed Solution Below)
\(p\bar q + pr + \bar qr\)
Half 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 |
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1 |
1 |
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0 |
1 |
0 |
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1 |
1 |
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0 |
1 |
1 |
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|
0 |
1 |
|
1 |
0 |
0 |
|
|
1 |
0 |
|
1 |
0 |
1 |
|
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0 |
0 |
|
1 |
1 |
0 |
|
|
0 |
0 |
|
1 |
1 |
1 |
|
|
1 |
1 |
Obtain k – map for B
\(\begin{array}{l} B = \bar qp + rp + \bar qr\\ = p\bar q + pr + \bar qr \end{array}\)