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Given below are two statements:Statement I: The value of hexadecimal number 21 is 33 in the decimal number system.Statement II: The value of binary number 1110 is 14 in the decimal number system.In the light of the above statements, choose the correct answer from the options given below:

A.
Both Statement I and Statement II are true
B.
Both Statement I and Statement II are false
C.
Statement I is correct but Statement II is false
D.
Statement I is incorrect but Statement II is true

Solution:

Calculation steps:Conversiton from hexadecimal to decimal(21)?? = (2 × 16¹) + (1 × 16?) = (33)??The value of hexadecimal number 21 is 33 in the decimal number system is true. Conversiton from binary to decimal(1110)? = (1 × 2³) + (1 × 2²) + (1 × 2¹) + (0 × 2?) = (14)??The value of binary number 1110 is 14 in the decimal number system. Therefore both Statement I and Statement II are true. Number systemDescriptionExampleBinaryA binary number system is used to store data and perform the calculation in computersIt expresses in base 2It contains only two symbols '0' and '1'Before starting any operation the first thing is to convert the value into binary formatEach digit in binary is known as a bit20, 21, 22. . . . . 1111OctalThe base is 8The symbols are 0 to 7Each value is expressed in the power of 880, 81, 82, . . . . . 17DecimalThe base is 10It is a positional value systemAny numerical quantity in this system can be represented in 10 digitsThe value lies between 0 to 9100, 101, 102, . . . . . 15HexadecimalThe base is 1616 symbols are 0 to 9 and A to FEach value is expressed in the power of 16160, 161, 162, . . . . . F

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