Test: Comparators - Electrical Engineering (EE) MCQ

Comparator: 
A comparator is a combinational circuit that gives the output in terms of input signals.
It is used to compare numbers and represent their relationship with each other.
It compares the signals as A > B, A < B, and A = B.
1-bit comparator:
A 1-bit comparator circuit is shown below.

In this circuit, we can compare two input signals
The truth table for the 1-bit comparator is

The expression for A = B: A ⊙ B
The expression for A > B: A B̅ 
The expression for A < B: A̅ B

Y = (A₀ ⊕ B₀) + (A₁ ⊕ B₁) + (A₂ ⊕ B₂) + (A₃ ⊕ B₃) 
Given that output is 1.
To get the output y = 1, all the inputs of OR gate should not be zero.
From the options, A₃ A₂ A₁ A₀ = 0010, B₃ B₂ B₁ B₀ = 1011 satisfies this condition.

x = x₁ x₀ y = y₁ y₀
The Boolean function S that satisfies condition,
If x > y, then s = 1.
We can represent the above condition through a truth table.

By using k-maps

Minimized form:
s = x₁y̅₁ + x₁x₀y̅₀ + x₀y̅₁y̅₀  

Concept:
The conversion time of different types of n-bit ADC is shown :

• From the above table, it is clear that the dual-slope is the slowest ADC and Flash Type is the fastest ADC.
• The conversion type of Flash type is independent of the number of bits 

Application:
n = 8

• Maximum conversion time in clock cycles of 8-bit Successive approximation type ADC  = n=  8
• Maximum conversion time in clock cycles of 8 bit Dual slope type ADC = 2ⁿ⁺¹ = 2⁹ = 512
• Maximum conversion time in clock cycles of 8 bit Successive approximation type ADC = 1

From the given circuit we can find the outputs expression as follows:

Now, we can observe that

So, the given circuit in question behaves like a comparator circuit. 

In an n-bit, compare the n columns of bits in one binary number (let it be A) and n columns of bits of another number (let it be B).
For all possible values of bits in A and B truth table is taken for A > B, A < B and A = B.
So there are 2n inputs in the comparator.
For 2n inputs total possible combinations are 2²ⁿ
So total number of entries is 2²ⁿ.

By analysing the above truth table it is giving the expression for 1 bit comparator.

Y = AB + A̅B̅
It represents a XNOR gate
The truth table of XNOR gate is


The output is high when both the inputs are equal.
It represents a 1-bit comparator (or) equality detector.

The only possible combinations are
A = 01 and B = 0 0
A = 10 and B = 00, 01
A = 11 and B = 00, 01, 10
So there are only 6 combinations
Tips and Tricks:

where n = 2 bit

Total no. of input combination of A & B are = 2³ x 2³ = 64
In 64 combination only in 8 combination A = B situation occurs. So the no. of combination for which A ≠ B is 64 - 8 = 56
Only of these 56 combinations only in 28 combinations A > B situation occur.
So, the no of 1 in K map will be 28