Logic Gates: Two Marks Important Questions and Answers

Applied Physics CSIE II: 

UNIT II: Logic Gates

IMPORTANT PART ‒ A QUESTIONS AND ANSWERS

 

1. What is a Logic gate?

Logic gates are the basic elements that make up a digital system. The electronic gate is a circuit that is able to operate on a number of binary inputs in order to perform a particular logical function.

 

2. What are the basic digital logic gates?

The three basic logic gates are

• AND gate

• OR gate

• NOT gate

 

3. Which gates are called as the universal gates? What are its advantages?

The NAND and NOR gates are called as the universal gates. These gates are used to perform any type of logic application like NOT, AND & OR.

 

4. State the associative property of boolean algebra.

The associative property of Boolean algebra states that the OR ing of several variables results in the same regardless of the grouping of the variables. The associative property is stated as follows:

A+ (B+C) = (A+B) +C

 

5. State the commutative property of Boolean algebra.

The commutative property states that the order in which the variables are OR ed makes no difference and similarly the order in which the variables are AND ed makes no difference. The commutative property is:

A+B=B+A

A⚫B=B⚫A

 

6. State the distributive property of Boolean algebra.

The distributive property states that AND ing several variables and OR ing the result With a single variable is equivalent to OR ing the single variable with each of the several Variables and then AND ing the sums.

The distributive property is: A+BC = (A+B) (A+C)

 

7. State De Morgan's theorem.

De Morgan's theorems are very useful for simplifying Boolean expressions, especially when dealing with inverted (complemented) sums or products.

First De Morgan's Theorem

The complement of a product is equal to the sum of the complements.

Second De Morgan's Theorem

The complement of a sum is equal to the product of the complements.

 

8. Reduce A (A + B)

A (A + B) = AA + AB

= A (1+ B) [1 + B = 1]

= A.

 

9. Reduce A'B'C' + A'BC' + A'BC

A'B'C' A'BC' + A'BC

= A'C'(B' + B) + A'B'C

[A + A' = 1]

= A'C' A'BC           

= A'(C' + BC)

[A A'B = A + B]

= A'(C' + B)

 

10. Define Karnaugh map

Karnaugh introduced a simple graphical method for Boolean function simplification. This method is called the Karnaugh Map (K‒Map) method.

A K‒Map is a diagram made up of 2n cells, where n is the number of variables. Each cell represents a possible combination of the variables, and any two adjacent cells differ by only one bit.

 

11. What are the limitations of K‒map?

i. Generally, it is limited to five variable map (i.e.) more than five variable involving expressions are not reduced.

ii. The map method is restricted in its capability since they are useful for simplifying only Boolean expression represented in standard form.

iii. The minimum expression obtained might not be unique

 

12. List the advantages and disadvantages of BCD code.

The advantages of BCD code are

(i) Any large decimal number can be easily converted into corresponding binary number

(ii) A person needs to remember only the binary equivalents of decimal number from 0 to

(iii) Conversion from BCD into decimal is also very easy.

The disadvantages of BCD code are

(i.) The code is least efficient. It requires several symbols to represent even small numbers.

(ii) Binary addition and subtraction can lead to wrong answer required BCD addition.

(iii) Special codes are required for arithmetic operations.

(iv) This is not a self‒complementing code.

(v) Conversion into other coding schemes requires special methods

 

13. Convert the number 18₁₀ to the binary system.

 

14. Convert 11101₂ to the decimal number system.

11101₂ = (1 × 2⁴) + (1 × 2³) + (1 × 2²) + (0 × 2¹) + (1 × 2⁰)

11101₂ = 16+ 8 + 4 + 0 + 1

11101₂ = 29₁₀

 

15. What is AND gate? Give its Symbol, truth table and Expression

The AND gate gives an output of 1 only if both inputs are 1. If any input is 0, the output is 0. For an n‒input AND gate, the output is 1 only when all inputs are 1; otherwise, it is 0.

 

16. What is OR gate? Give its Symbol, truth table and Expression

The OR gate is one of the most commonly used digital logic gates. Its output becomes high (1) if any one of its inputs is high (1). If all the inputs are low (0), then the output will be low (0).

The Boolean expression for an OR gate is written using a plus sign (+)

Y = A+B

 

17. Give its Symbol, truth table and expression of NOT Gate.

In digital electronics, the NOT gate is a basic logic gate that has one input and one output. It is also called an inverter because it reverses the input signal.

If the input is low (0), the output becomes high (1).

If the input is high (1), the output becomes low (0).

 Y=

 

18. Give the Boolean expression of XOR gate and write its truth table.

In digital electronics, the XOR gate is a special logic gate used to perform a modulo‒2 sum. It is also known as the Exclusive OR (or) Ex‒OR gate.

If the two inputs are A and B, and the output is Y, the Boolean expression is:

 

19. Why is NAND and NOR gate called a universal gate?

NAND and NOR gates are called as universal gates because it is used to construct any logic gates using only NAND gates or only NOR gates.

The NAND and NOR gate can be constructed all the basic gates AND, OR and NOT.

 

20. Give the Boolean expression of XNOR gate

 

21. What is NAND Gate?

The NAND gate is universal logic gate. It is formed by connecting an AND gate followed by a NOT gate in series. A NAND gate can have two or more inputs and gives one output.

The Boolean expression for a two‒input NAND gate is: 

  Y=

 

22. Differentiate between OR gate and XOR gate

OR Gate

1. OR gate gives output 1 if any one or more inputs are 1.

2. Boolean expression: Y = A + B

3. Truth table output for (1,1) is 1.

4. Used for simple addition‒like logic.

XOR Gate

1. XOR gate gives output 1 only if the inputs are different.

2. Boolean expression: Y = A  B

3. Truth table output for (1,1) is 0.

4. Used for parity checking and arithmetic circuits (adders).

 

23. Give any two applications of logic gates.

1. Digital Circuits:

Logic gates are used in designing adders, subtractors, multiplexers, and comparators in digital systems.

2. Computers and Processors:

Logic gates are used in ALU (Arithmetic Logic Unit) to perform arithmetic and logical operations in microprocessors.

 

24. Realize NOT gate using NAND gate.

NAND gate both inputs are connected together and create NOT function.

 

25. What is the logic level representation of 1 and 0 in digital electronics?

Logic "0" means 0 volts in a circuit. It is also called as LOW, OFF, or False.

Logic "1" means +5 volts in a circuit. It is also called as HIGH, ON, or True.

 

26. Define Boolean variable and Boolean function with an example.

Boolean Variable

A Boolean variable is a variable that can take only two values: 0 or 1.

Example: A=0 or B=1

Boolean Function (or) Boolean Expression

A Boolean function is an expression formed by combining Boolean variables using logic operations such as AND, OR, and NOT,

Example: F (A,B) =+B

 

27. Simplify using Boolean laws: A+ AB

A+AB = A(1+B)

= A

 

28. What is a minterm? Give an Example.

A minterm is a product (AND term) in which each variable appears exactly once, either in its true form or complemented form.

A minterm represents a single combination of input values for which the function output is 1. It is also called as Sum of Product (SOP)

Example

For variables A and B, and all possible minterms are: , A, B,AB 

 

29. What is Maxterm? Give an example.

A Maxterm is a sum term (OR term) in which each variable appears exactly once, either in its true form or complemented form.

A maxterm corresponds to an input combination for which the function output is 0.It is also called as Product of Sum (POS)

For variables C and D, and all possible Maxterms are:

C+D,C+,+,+D

 

30. Define Grouping Rules in K‒Map

In a Karnaugh map, groups are formed to simplify Boolean expressions. The basic grouping rules are:

i. Groups must contain 1s in powers of two

Groups can have 1, 2, 4, 8, 16... cells only (i.e., 2ⁿ cells).

ii. Groups must be adjacent

Only cells that are next to each other horizontally or vertically can be grouped.

(Diagonal grouping is not allowed.)

iii. Groups should be as large as possible

Always form the largest possible group to achieve maximum simplification.

iv. Wrapping is allowed

K‒maps are cyclic; cells on the edges can be grouped with cells on the opposite edges.