Given below are two statements. In the light of the above statements, choose the correct answer from the options given below.

Statement I:(167) in base 10 equals (101000111) in base 2.

Statement II:(11010110) in base 2 equals (214) in base 10.

ABoth Statement I and Statement II are true

BBoth Statement I and Statement II are false

CStatement I is true but Statement II is false

DStatement I is false but Statement II is true ✓ Correct

Correct answer: (D) Statement I is false but Statement II is true

Explanation

Statement 1 is false, because (167) in base 10 is 10100111 in binary, not 101000111.

Adding 128+32+4+2+1 gives 167, which needs only eight binary digits.

The nine-digit value 101000111 actually equals 327, not 167.

Statement 2 is true, as (11010110) in base 2 equals 128+64+16+4+2 = 214.

That total of 214 matches the given decimal value exactly.

Checking the number of bits is a quick way to spot such conversion errors.

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