10 Questions
किसके द्वारा डिजिटल तर्क की विशेष प्रक्रियाओं का प्रतिनिधित्व किया जाता है?
लिखित बूल तर्क
NAND (Not AND) को कैसे लिखा जाता है?
(AB)'
अगर A=1, B=0 है, तो A OR B का परिणाम क्या होगा?
1
NOT A को कैसे लिखा जाता है?
A'
कौन-सा सटीक है - 'क्रमवार्ती तर्क' के साथ मिश्रित करने के लिए?
सत्यता सारणी
यदि एक सर्किट के लिए एक सत्यता सारणी में 4 इनपुट होते हैं, तो सत्यता सारणी क्या प्रदर्शित करती है?
इनपुट के आधार पर सर्किट का आउटपुट
एक सत्यता सारणी क्या प्रतिनिधित्व करती है?
सर्किट के आउटपुट
सत्यता सारणी में 0 और 1 का मतलब क्या है?
सकारात्मक और नकारात्मक
सत्यता सारणी क्या प्रकट करती है?
सर्किट का आउटपुट
क्या है सत्यता सारणी में 1 का महत्व?
सकारात्मक मान
Study Notes
Boolean Logic: A Comprehensive Guide to Truth Tables
Boolean logic is the foundation of digital circuitry and is essential to the functioning of modern computers. It is a system of rules that allows for complex decisions to be made based on simple "yes/no" questions. This article provides a detailed explanation of Boolean logic and focuses on the subtopic of truth tables.
Truth Tables
Truth tables are a practical tool used to explain the output of a circuit based on the possible inputs to that circuit. They are simple plots that provide a clear understanding of the output in relation to the inputs. Truth tables can be expanded to accommodate any number of inputs and outputs, making them an invaluable resource in the realm of digital logic.
Example of a Truth Table
Consider a four-input circuit, which can be represented as follows:
| A | B | C | D | Output |
|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 1 |
| 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 1 | 1 | 1 |
| 0 | 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 1 | 1 |
| 0 | 1 | 1 | 0 | 1 |
| 0 | 1 | 1 | 1 | 1 |
| 1 | 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 1 | 1 |
| 1 | 0 | 1 | 0 | 1 |
| 1 | 0 | 1 | 1 | 1 |
| 1 | 1 | 0 | 0 | 1 |
| 1 | 1 | 0 | 1 | 1 |
| 1 | 1 | 1 | 0 | 1 |
| 1 | 1 | 1 | 1 | 1 |
In this example, the truth table shows that the output of the circuit is 0 when all inputs are 0, and it is 1 when any of the inputs are 1. This information is crucial for understanding the behavior of digital circuits.
Written Boolean Logic
Truth tables are not the only way to represent the logic of circuits. Written Boolean logic is another method that uses mathematical symbols to represent the unique operations involved in digital logic: AND, OR, XOR, and NOT.
Operators and Their Symbols
- AND: A AND B should be written as AB (or sometimes A • B)
- OR: A OR B should be written as A + B
- XOR: A XOR B should be written as A ⊕ B
- NOT: NOT A should be written as A' or A
NAND and NOR
Two additional useful operations in digital logic are NAND (Not AND) and NOR (Not OR).
- A NAND B is written as (AB)' , (A • B)' , or (AB)
- A NOR B is written as (A + B)' or (A + B)
Sequential Logic
While combinational logic is essential, it needs to be combined with sequential logic to create modern computing systems. Sequential circuitry adds memory to our logical systems, allowing for more complex decision-making processes.
Truth tables are a powerful tool for understanding the behavior of digital circuits. They provide a clear and concise representation of the output in relation to the inputs, making it easier to analyze and design circuits. By understanding the concepts of truth tables and written Boolean logic, one can gain a deeper appreciation for the fundamental principles that underpin modern digital systems.
This quiz covers the fundamental concepts of Boolean logic, focusing on truth tables, written Boolean logic, NAND, NOR operations, and sequential logic in digital circuits. Test your knowledge on how to analyze and create truth tables, use different logical operators, and understand the importance of sequential circuitry.
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