Subtractors MCQ Quiz - Objective Question with Answer for Subtractors - Download Free PDF
Last updated on Jul 9, 2025
Latest Subtractors MCQ Objective Questions
Subtractors Question 1:
Which of the following is true about the Half Subtractor circuit?
Answer (Detailed Solution Below)
Subtractors Question 1 Detailed Solution
Half 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 |
Subtractors Question 2:
A half subtractor is an arithmetic circuit which performs subtraction operation on _______ input bits.
Answer (Detailed Solution Below)
Subtractors Question 2 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
Subtractors Question 3:
The circuit shown below is a :
Answer (Detailed Solution Below)
Subtractors Question 3 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:
Subtractors Question 4:
A full binary subtractor has _______ input lines and _______ output lines
Answer (Detailed Solution Below)
Subtractors Question 4 Detailed Solution
Subtractors Question 5:
The circuit shown in the given figure represents a/an:
Answer (Detailed Solution Below)
Subtractors Question 5 Detailed Solution
Concept-
De-Multiplexer-It is a combinational circuit that performs the reverse operation of Multiplexer. It has single input, ‘n’ selection lines and maximum of 2n outputs. The input will be connected to one of these outputs based on the values of selection lines.
Eg-Let the 1x8 De-Multiplexer has one input I, three (n=3) selection lines s2, s1 & s0 and outputs Y7 to Y0. outputs Y7 to Y0 are basically min terms for 3 input.
The Truth table of 1x8 De-Multiplexer is shown below.
|
Selection Inputs |
Outputs |
|||||||||
|
S2 |
S1 |
S0 |
Y7 |
Y6 |
Y5 |
Y4 |
Y3 |
Y2 |
Y1 |
Y0 |
|
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
|
0 |
0 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
|
0 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
|
0 |
1 |
1 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
0 |
|
1 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
0 |
0 |
|
1 |
0 |
1 |
0 |
0 |
1 |
0 |
0 |
0 |
0 |
0 |
|
1 |
1 |
0 |
0 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
|
1 |
1 |
1 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
Full substractor:- It is a combinational logic circuit it contains 3 input (A, B, C) and two output (difference and Borrow)
Eg: In full subs tractor we perform A – B – C By which we get difference and Borrow
Truth table:-
|
A |
B |
C |
Difference (D) |
Borrow (Bout) |
|
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 |
D = ∑ m (1, 2, 4, 7)
B = ∑ m (1, 2, 3, 7)
Solution-
In given question
Y0 to y7 are minterms
\(\left. {\begin{array}{*{20}{c}} {{\rm{F}}1{\rm{\;}} = {\rm{\;}}\sum {\rm{\;m\;}}\left( {1,{\rm{\;}}2,{\rm{\;}}4,{\rm{\;}}7} \right){\rm{\;}} \to {\rm{\;difference}}}\\ {{\rm{F}}2{\rm{\;}} = {\rm{\;}}\sum {\rm{\;m\;}}\left( {1,{\rm{\;}}2,{\rm{\;}}3,{\rm{\;}}7} \right){\rm{\;}} \to {\rm{\;Borrow}}} \end{array}} \right\}{\rm{Full\;supstractor}}\)
Top Subtractors MCQ Objective Questions
A half subtractor is an arithmetic circuit which performs subtraction operation on _______ input bits.
Answer (Detailed Solution Below)
Subtractors 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)
Subtractors 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 |
\( Difference = A⊕B = A\bar B + \bar AB \)
\(Borrow = X=\bar AB\)
Answer (Detailed Solution Below)
Subtractors Question 8 Detailed Solution
Download Solution PDFConcept:
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:
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)
Subtractors Question 9 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
The circuit is formed as shown below. The output S and C implements;
Answer (Detailed Solution Below)
Subtractors Question 10 Detailed Solution
Download Solution PDFCalculation:
The output expression of S is written as:-
S = A̅ B + AB̅
The Truth Table for S is:
|
A |
B |
S |
|
0 |
0 |
0 |
|
0 |
1 |
1 |
|
1 |
0 |
1 |
|
1 |
1 |
0 |
The expression of C is given as:-
C = A̅ B
The truth table is as shown:-
|
A |
B |
C |
|
0 |
0 |
0 |
|
0 |
1 |
1 |
|
1 |
0 |
0 |
|
1 |
1 |
0 |
A binary full-subtractor:
Answer (Detailed Solution Below)
Subtractors Question 11 Detailed Solution
Download Solution PDFA binary full-subtractor contains two half-subtractors and one OR gate.
Truth table for the full- subtractor is
|
A |
B |
Bin |
M |
N |
|
0 |
0 |
0 |
0 |
0 |
|
0 |
1 |
0 |
1 |
1 |
|
1 |
0 |
0 |
0 |
1 |
|
1 |
1 |
0 |
0 |
0 |
|
0 |
0 |
1 |
1 |
1 |
|
0 |
1 |
1 |
1 |
0 |
|
1 |
0 |
1 |
0 |
0 |
|
1 |
1 |
1 |
1 |
1 |
Difference(D) = A̅ B̅ Bin + A̅ B B̅in + AB̅ B̅in + ABBin
D = Bin ⊕ (A ⊕ B)
Borrow(B) = A̅ B̅ Bin + A̅ B B̅in + A̅ B Bin + ABBin
B = (A̅ B̅ + AB)Bin + A̅ B
B = (A̅ ⊕ B)Bin + A̅ B
Subtractors Question 12:
A half subtractor is an arithmetic circuit which performs subtraction operation on _______ input bits.
Answer (Detailed Solution Below)
Subtractors 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
Subtractors Question 13:
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)
Subtractors Question 13 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 |
\( Difference = A⊕B = A\bar B + \bar AB \)
\(Borrow = X=\bar AB\)
Subtractors Question 14:
The circuit shown below is a :
Answer (Detailed Solution Below)
Subtractors Question 14 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:
Subtractors Question 15:
Consider the following circuit diagram
A 4-bit subtractor, four 4-bit three-state buffers (with bus input and output), and one inverter is used to subtract two numbers (Y - X), X = 0101 and Y = 0010
If A = 0, then D and Bout are respectively
Answer (Detailed Solution Below)
Subtractors Question 15 Detailed Solution
Concept:
The truth table for a tristate buffer is as shown:
|
Enable Input |
Input |
Output |
|
0 |
0 |
Hi – Z |
|
0 |
1 |
Hi – Z |
|
1 |
0 |
0 |
|
1 |
1 |
1 |
Observation:
If the “Enable” input signal is 1, the input is simply passed to the output.
If the “Enable” input signal is 0, the tristate buffer passes a high impedance signal that disconnects its output from the circuit.
Application:
When A = 0, Buffer 1 and Buffer 3 are enabled, and buffer 2 and 4 are disabled.
The input to the 4-bit subtractor will be Y and X respectively, such that the output is:
D = Y – X = 0010 – 0101
= 1101 with a borrow of 1, i.e. Bout = 1