GATE Electrical 2024 | GA | Question: 3

Question

​​​​The decimal number system uses the characters $0,1,2, \ldots, 8,9$, and the octal number system uses the characters $0,1,2, \ldots, 6,7$.

For example, the decimal number $12\left(=1 \times 10^{1}+2 \times 10^{0}\right)$ is expressed as $14\left(=1 \times 8^{1}+4 \times 8^{0}\right)$ in the octal number system.

The decimal number $108$ in the octal number system is

• A. $168$
• B. $108$
• C. $150$
• D. $154$

Answer 1

The Correct Answer is Option D) 154 .

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When we convert the decimal number 108 to binary, we will get the binary equivalent as 001101100.( I padded two zeros on the left to make the number of digits a multiple of 3 , so that we can form groups of 3 digits ) .

We can form groups of 3 digits from the right and write the octal value for each of group .

001 is 1 in octal . 101 is 5 in octal . 100 is 4 in octal .

Therefore, the octal equivalent of decimal number 108 will be 154.

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