CSE 1st Year: NOR Gate Truth Table

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Questions and Answers

What is the output of a two-input NOR gate when both inputs are 1?

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0 (correct)

1 and 0 alternating

Which equation correctly describes the operation of a NAND gate with inputs A and B?

A NAND B = A AND B

A NAND B = A + B

A NAND B = NOT(A AND B) (correct)

A NAND B = A OR B

What is the output of a two-input NAND gate when both inputs are 0?

1 (correct)

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alternates between 0 and 1

What is the primary characteristic of a NOR gate?

It only produces a logic 1 output when all inputs are 0. Signup and view all the answers

Which of the following statements about NAND gates is true?

NAND gates require all inputs to be high to output a low signal. Signup and view all the answers

In the truth table of a NOR gate, what is the output for inputs A=0 and B=1?

0 Signup and view all the answers

When combining logic gates, what role does a NAND gate serve?

It can be used to construct any other type of logic gate. Signup and view all the answers

How can the output of a two-input NAND gate be expressed mathematically?

$C = NOT(A AND B)$ Signup and view all the answers

What is the output when both inputs of an XNOR gate are 1?

1 Signup and view all the answers

Which operation does an XNOR gate implement?

Exclusive NOR operation Signup and view all the answers

What is the Boolean expression of the output Y for an XNOR gate with inputs A and B?

Y = NOT(A XOR B) Signup and view all the answers

In the truth table of an XOR gate, what is the output when both inputs are 0?

0 Signup and view all the answers

How many inputs does an XNOR gate take?

Two inputs Signup and view all the answers

What will be the output of an XNOR gate if the inputs are 0 and 1?

0 Signup and view all the answers

Which of the following statements is true about the operation of an XNOR gate?

It is a combination of XOR and NOT gates Signup and view all the answers

What output does an XNOR gate produce when both inputs are equal to 1?

1 Signup and view all the answers

What is the output of an XNOR gate when both inputs are 0?

1 Signup and view all the answers

In Boolean algebra, how is a minterm defined?

The product of N distinct literals Signup and view all the answers

When does the Boolean function F(A,B,C,D) = A + BC' + D return a high output?

When A=1, or BC'=1, or D=1 Signup and view all the answers

How many rows would a truth table have for a Boolean function with 4 input variables?

16 Signup and view all the answers

Which of the following devices do not typically utilize logic gates in their circuits?

Traditional clocks Signup and view all the answers

What is the sum of N distinct literals known as in Boolean algebra?

Maxterm Signup and view all the answers

What will the XNOR output be when inputs A = 1 and B = 0?

0 Signup and view all the answers

What is the value of the Boolean function F=xy'z+p when x=1, y=0, z=1, and p=0?

1 Signup and view all the answers

What is the final expression for the K-map of the 3 variables F(A,B,C)=∏M(0,3,6,7)?

(A'+B')(B'+C')(A+B+C) Signup and view all the answers

Which grouping results from the green group in the K-map of F(A,B,C,D)=∏M(3,5,7,8,10,11,12,13)?

C'DB Signup and view all the answers

What is the significance of 'Don’t Care' conditions in K-maps?

They allow flexibility in grouping cells. Signup and view all the answers

Which of the following represents a 'Don’t Care' condition in K-maps?

X Signup and view all the answers

What is the correct resultant product expression of F(A,B,C,D) from the red group?

(C’+D’+A) Signup and view all the answers

For the K-map with 4 variables, how many product terms are derived from the combination of cell groups?

4 Signup and view all the answers

Which grouping is NOT utilized in the simplification of F(A,B,C,D)=∏M(3,5,7,8,10,11,12,13)?

A'B'C' Signup and view all the answers

What is the term that results from taking the complement of the yellow group's findings in the K-map of 3 variables?

ABC Signup and view all the answers

What is the result of minimizing the SOP function f = Σm(1, 5, 6, 11, 12, 13, 14) + d(4) using K-Maps?

BC' + BD' + A'C'D + AB'CD Signup and view all the answers

How should don’t care conditions be treated when converting a POS expression to SOP form?

They are kept as they are. Signup and view all the answers

In the POS function F(A, B, C, D) = Σm(0, 1, 2, 3, 4, 5) + d(10, 11, 12, 13, 14, 15), what is the minimal POS form?

(A' + C)(B' + C') Signup and view all the answers

What is the significance of ‘don’t care’ conditions in digital circuit design?

They help reduce power consumption. Signup and view all the answers

Which of the following statements about don’t cares is false?

They should always be considered as valid inputs. Signup and view all the answers

When minimizing functions using K-Maps, how do don’t cares affect the grouping of terms?

They can be included to make larger groups. Signup and view all the answers

In the example function F(A, B, C, D) with don’t cares d(12, 13, 14, 15), which minterms are missing from the POS expression?

6, 7, 8, 9 Signup and view all the answers

What is the first step in converting a standard SOP function with don’t cares to a POS expression?

Identify the missing minterms. Signup and view all the answers

Study Notes

Truth Table of NOR Gate

A two-input NOR gate produces an output of 1 only when both inputs are 0.
Relationships:
- A=0, B=0 → A NOR B = 1
- A=0, B=1 → A NOR B = 0
- A=1, B=0 → A NOR B = 0
- A=1, B=1 → A NOR B = 0

NAND Gate Overview

Commonly used universal logic gate performing inverted AND operations.
Configuration:
- NAND Gate = AND Gate + NOT Gate
Outputs low (logic 0) only when all inputs are high (logic 1).

Truth Table of XOR Gate

An exclusive OR (XOR) gate outputs 1 when inputs differ.
Relationships:
- A=0, B=0 → A XOR B = 0
- A=0, B=1 → A XOR B = 1
- A=1, B=0 → A XOR B = 1
- A=1, B=1 → A XOR B = 0

XNOR Gate Properties

XNOR gate outputs high (logic 1) when both inputs are similar.
Defined as:
- XNOR Gate = XOR Gate + NOT Gate
Serves as a similarity detector in circuits.

Truth Table of XNOR Gate

Relationships:
- A=0, B=0 → A XNOR B = 1
- A=0, B=1 → A XNOR B = 0
- A=1, B=0 → A XNOR B = 0
- A=1, B=1 → A XNOR B = 1

Applications of Logic Gates

Essential components in digital circuits.
Utilized in:
- Computers
- Microprocessors
- Microcontrollers
- Digital/Smart watches
- Smartphones

Boolean Functions

Define logical operations through binary variables.
Represented by Boolean Expressions.
Example: F = xy'z + p outputs 1 when conditions are met.

Methods of Simplification: K-map

Minterms and Maxterms:
- Minterm: Product of distinct literals (outputs 1).
- Maxterm: Sum of distinct literals (outputs 0).

K-map for Three Variables

For F(A, B, C) = ∏M(0, 3, 6, 7), significant terms derived through grouping.

K-map for Four Variables

For F(A, B, C, D) = ∏M(3, 5, 7, 8, 10, 11, 12, 13), grouping leads to minimal expression.

Don’t Care Conditions in K-Maps

"Don’t Care" conditions allow flexibility in grouping, leading to simplification of Boolean expressions.
They can be treated as 1, 0, or ignored, enhancing group sizes.

Significance of "Don’t Care" Conditions

Simplifies output expression, accounting for invalid inputs.
Reduces the number of gates needed in circuit design, making it more economical.
Lowers power consumption by minimizing switching states and memory space.

Examples of Minimizing Functions with K-Maps

Applying SOP and POS forms illustrates simplifications effectively.
Utilize don’t care conditions for optimal circuit design and expression reduction.

Studying That Suits You

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Description

Test your knowledge on the truth table of the NOR gate with this quiz. It covers the relationships between inputs and output for a two-input NOR gate. This is ideal for students in their first year of Computer Science Engineering.

CSE 1st Year: NOR Gate Truth Table

Podcast

Questions and Answers

What is the output of a two-input NOR gate when both inputs are 1?

Which equation correctly describes the operation of a NAND gate with inputs A and B?

What is the output of a two-input NAND gate when both inputs are 0?

What is the primary characteristic of a NOR gate?

Which of the following statements about NAND gates is true?

In the truth table of a NOR gate, what is the output for inputs A=0 and B=1?

When combining logic gates, what role does a NAND gate serve?

How can the output of a two-input NAND gate be expressed mathematically?

What is the output when both inputs of an XNOR gate are 1?

Which operation does an XNOR gate implement?

What is the Boolean expression of the output Y for an XNOR gate with inputs A and B?

In the truth table of an XOR gate, what is the output when both inputs are 0?

How many inputs does an XNOR gate take?

What will be the output of an XNOR gate if the inputs are 0 and 1?

Which of the following statements is true about the operation of an XNOR gate?

What output does an XNOR gate produce when both inputs are equal to 1?

What is the output of an XNOR gate when both inputs are 0?

In Boolean algebra, how is a minterm defined?

When does the Boolean function F(A,B,C,D) = A + BC' + D return a high output?

How many rows would a truth table have for a Boolean function with 4 input variables?

Which of the following devices do not typically utilize logic gates in their circuits?

What is the sum of N distinct literals known as in Boolean algebra?

What will the XNOR output be when inputs A = 1 and B = 0?

What is the value of the Boolean function F=xy'z+p when x=1, y=0, z=1, and p=0?

What is the final expression for the K-map of the 3 variables F(A,B,C)=∏M(0,3,6,7)?

Which grouping results from the green group in the K-map of F(A,B,C,D)=∏M(3,5,7,8,10,11,12,13)?

What is the significance of 'Don’t Care' conditions in K-maps?

Which of the following represents a 'Don’t Care' condition in K-maps?

What is the correct resultant product expression of F(A,B,C,D) from the red group?

For the K-map with 4 variables, how many product terms are derived from the combination of cell groups?

Which grouping is NOT utilized in the simplification of F(A,B,C,D)=∏M(3,5,7,8,10,11,12,13)?

What is the term that results from taking the complement of the yellow group's findings in the K-map of 3 variables?

What is the result of minimizing the SOP function f = Σm(1, 5, 6, 11, 12, 13, 14) + d(4) using K-Maps?

How should don’t care conditions be treated when converting a POS expression to SOP form?

In the POS function F(A, B, C, D) = Σm(0, 1, 2, 3, 4, 5) + d(10, 11, 12, 13, 14, 15), what is the minimal POS form?

What is the significance of ‘don’t care’ conditions in digital circuit design?

Which of the following statements about don’t cares is false?

When minimizing functions using K-Maps, how do don’t cares affect the grouping of terms?

In the example function F(A, B, C, D) with don’t cares d(12, 13, 14, 15), which minterms are missing from the POS expression?

What is the first step in converting a standard SOP function with don’t cares to a POS expression?

Study Notes

Truth Table of NOR Gate

NAND Gate Overview

Truth Table of XOR Gate

XNOR Gate Properties

Truth Table of XNOR Gate

Applications of Logic Gates

Boolean Functions

Methods of Simplification: K-map

K-map for Three Variables

K-map for Four Variables

Don’t Care Conditions in K-Maps

Significance of "Don’t Care" Conditions

Examples of Minimizing Functions with K-Maps

Studying That Suits You

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