Assertion (A): Boolean algebra and Binary number system are different ...
Boolean algebra and Binary number system are different from each other because in Boolean algebra
1 + 1 = 1 while in the binary number system 1 + 1 = 10. There are lot of other examples to prove this.
Reason is also a correct statement because AND, OR and NOT are the three basic operations which are used in Boolean algebra. However, reason is not the correct explanation of assertion.
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Assertion (A): Boolean algebra and Binary number system are different ...
Assertion: Boolean algebra and Binary number system are different from each other.
Reason: There are some basic operations like AND, OR and NOT which are performed in Boolean algebra.
Explanation:
Boolean algebra and Binary number system are related to each other, but they are not the same. The following are the differences between Boolean algebra and Binary number system:
1. Definition:
- Boolean algebra is a branch of mathematics that deals with logical operations and its applications in digital circuits.
- Binary number system is a numerical system that uses only two digits, 0 and 1, to represent any number.
2. Operations:
- Boolean algebra involves logical operations such as AND, OR, NOT, NAND, NOR, XOR, and XNOR.
- Binary number system involves arithmetic operations such as addition, subtraction, multiplication, and division.
3. Representation:
- Boolean algebra uses symbols such as 0, 1, and X to represent logical values.
- Binary number system uses digits 0 and 1 to represent numerical values.
4. Application:
- Boolean algebra is used to design and analyze digital circuits, computer algorithms, and programming languages.
- Binary number system is used to perform arithmetic operations in digital circuits, computer programming, and communication systems.
Therefore, the assertion is true, and the reason is also true, but it does not explain the assertion correctly. Hence, option (B) is the correct answer.
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