Test: Combinational Circuits - Electrical Engineering (EE) MCQ

An n-bit flash type ADC requires:

1. 2ⁿ -1 comparators

2. 2ⁿ resistors

3. One 2ⁿ × n priority encoder

Here n = 4, hence the size of comparator 2⁴ × 4

Calculation:

For the given MUX, the output is given by,

Given I₀ = X, I₁ = Y, I₂ = X and I₃ = 0

= X ⊕ Y (X-OR gate)

So, option (c)

Explanation:

Multiplier

• A multiplier is a combinational logic circuit that we use to multiply binary digits.
• We use a multiplier in several digital signal processing applications.
• We use it to design calculators, mobiles, processors, and digital image processors.

Process

• The first product obtained from multiplying A₀ with the multiplicand is called as partial product 1.
• And the second product obtained from multiplying A₁ with the multiplicand is known as the partial product 2.

The structure of multiplication is explained below:

There are 6 product terms so to get all those 6 AND gates are required.

To get the addition of B₁A₀ and B₀A₁ we require one-half adder and this produces a carry also.

To get the addition of B₂A₀, B₁A₁ and C₁ we require Full adder because of 3 inputs and this also produces a carry.

To get the B₂A₁ and C₂ we require one-half adder because of 2 inputs.

Conclusion:

Total 6 AND gates, 2 Half adders and 1 Full adder are required.

Concept:

For a 2 × 1 MUX is shown above, the output function F is expressed as:

i.e. when S₁ = 0, I₀ is transmitted to the output.

And when S₁ = 1, I₁ is transmitted to the output.

Application:

The output of the 1^st MUX will be:

The final output will be:

To implement 2ⁿ × 1 MUX using 2 × 1 MUX, the total number of 2 × 1 MUX required is (2ⁿ - 1).

∴ The number of 2 × 1 multiplexer required to implement 16 × 1 MUX will be:

n = 16 - 1 = 15

Or we can follow the below steps to calculate the same:

1st stage = 16/2 = 8

2nd  stage = 8/2 = 4

3rd stage = 4/2 = 2

4th stage = 2/2 = 1

The sum will give the total number of MUX required to implement 16 × 1 multiplexer using 2 × 1, i.e.

n = 8 + 4 + 2 + 1 = 15
Important Point

Concept:

For a 2 × 1 MUX is shown above, the output function F is expressed as:

i.e. when S₁ = 0, I₀ is transmitted to the output.

And when S₁ = 1, I₁ is transmitted to the output.

Application:
The given circuit is redrawn as:


Now, the required function f will be:

An encoder converts information from one format or code to another. An encoder can be used to encode the decimal number to binary number.

Additional Information

Accumulator:

• An accumulator is a general-purpose register of microprocessor. It is used to store result of most arithmetic and Logical Operations performed in 8085.

Some examples of decimal to binary conversion are:

• 0 → 0
• 1 → 01
• 2 → 10
• 3 → 11
• 4 → 100
• 5 → 101
• 6 → 110
• 7 → 111
• 8 → 1000
• 9 → 1001

ALU:

• ALU stands for arithmetic logic unit. ALU contains circuits that perform arithmetic operations such as Addition/subtraction and Logical operations such as XOR, AND etc

Memory:

• Memory is a storage device that is used to store data as well as instructions that are to be executed by the microprocessor.

Y = 1

Concept:

From the given figure:

 

The above circuit is of Half adder:

• ​Sum (S) can be obtained by: A XOR B = A⨁ B
• Carry (C) can be obtained by: A AND B = A ∙ B​​​​​​

From the above truth table, it can conclude that:


Fig: K-Map simplification of Half Adder

Normally we see a half circle mark on IC's one edge. That edge is the top of the IC.

And if we keep IC in the below manner,

 

Then the first left side pin is Pin no. 1

Here, pin no. 1 is A

Additional Information

• Integrated Circuits are made up of Silicon.
• Integrated circuits are the chips of Silicon on which transistors,
  logical gates, resistors or capacitors are embedded.
• First IC was developed by Jack Kilby and Robert Noyce in 1958,
  but the concept was introduced by Geoffrey Dummer in 1952.
• These building blocks of a circuit can act as microprocessors, amplifiers, memory etc.