Question
Given below are two statements:
Statement I: (1011101)2 = (135)8
Statement II: (71)8 = (111001)2
In the light of the above statements, choose the most appropriate answer from the options given below:
Options :
Both Statement I and Statement II are true.
Both Statement I and Statement II are false.
Statement I is true but Statement II is false.
Statement I is false but Statement II is true.
Answer :
Both Statement I and Statement II are true.
Solution :
To convert binary number (base 2) into octal (base 8), following steps are followed:
1. Multiply each number of binary with square series of 2 from last number
2. Divide the sum with 8 continuously with respect to quotient
3. Write the remainders in inverse order to get the answer
Example-1: 1011101 base 2
1 × 20 + 0 × 21 + 1 × 22 + 1 × 23 + 1 × 24 + 1 × 25 + 1 × 26
= 1 + 0 + 4 + 8 + 16 + 0 + 64
= 93
93/8 = R-5, Q-11
11/8 = R-3, Q-1
1/8 = R-1, Q-0
Base 8/octal number of binary 1011101 = 135
Hence, statement I is correct.
Example-2: 111001 base 2
1 × 20 + 0 × 21 + 0 × 22 + 1 × 23 + 1 × 24 + 1 × 25 + 1 × 26
= 1 + 0 + 0 + 8 + 16 + 32
= 57
57/8 = R-1, Q-7
7/8 = R-8, Q-7
Octal number for 111001 base 10 = 71
Hence, statement II is also correct
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