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

Statement I:(1011101) in base 2 equals (135) in base 8.

Statement II:(71) in base 8 equals (111001) in base 2.

ABoth Statement I and Statement II are true ✓ Correct

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 answer: (A) Both Statement I and Statement II are true

Explanation

Statement 1 is true, since (1011101) in base 2 equals 93 and (135) in base 8 also equals 93.

Working it out, 64+16+8+4+1 gives 93 for the binary value.

For the octal side, 1 times 64 plus 3 times 8 plus 5 also gives 93.

Statement 2 is true, since (71) in base 8 equals 57 and (111001) in base 2 also equals 57.

Here 7 times 8 plus 1 is 57, and 32+16+8+1 is likewise 57.

Grouping binary digits in threes converts directly to octal.

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