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Given below are two statements: Statement - I: (25)16=(00100101)2(25)_{16} = (00100101)_2(25)16​=(00100101)2​Statement - II: (00011011)2=(1
Question

Given below are two statements:
Statement - I: (25)16=(00100101)2(25)_{16} = (00100101)_2
Statement - II: (00011011)2=(1B)16(00011011)_2 = (1B)_{16}​​
In the light of the above statements, choose the most appropriate answer from the options given below: ​​

A.

Both Statement I and Statement II are correct.

B.

Both Statement I and Statement II are incorrect.

C.

Statement I is correct but Statement II is incorrect.

D.

Statement I is incorrect but Statement II is correct.

Correct option is A

Statement - I: (25)16=(00100101)2\bf{(25)_{16} = (00100101)_2}​ (True):
To convert a hexadecimal number to binary, you can convert each hexadecimal digit to its 4-bit binary equivalent.
(2)16=(0010)2(2)_{16} = (0010)_2​​
(5)16=(0101)2(5)_{16} = (0101)_2​​
So, (25)16=(00100101)2(25)_{16} = (00100101)_2​​
Statement - II: (00011011)2=(1B)16(00011011)_2 = (1B)_{16}​ (True):
To convert a binary number to hexadecimal, you can group the binary digits into sets of 4 and convert each set to its hexadecimal equivalent.
(0001)2=(1)16(0001)_2 = (1)_{16}​​
(1011)2=(B)16(1011)_2 = (B)_{16}​​
So, (00011011)2=(1B)16(00011011)_2 = (1B)_{16}​​
Therefore, the correct answer is:
(a) Both Statement I and Statement II are correct.

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