The representation of the value of a 16-bit unsigned integerXin a hexadecimal number system isBCA9. The representation of the value ofXin octal number system is:a)571244b)736251c)571247d)136251Correct answer is option 'D'. Can you explain this answer?

Question

Answer

Representation of a 16-bit unsigned integer in hexadecimal:

The given value of the 16-bit unsigned integer Xin is represented in the hexadecimal number system as BCA9.

To convert this value to the octal number system, we need to convert it from hexadecimal to binary first, and then from binary to octal.

Converting from hexadecimal to binary:

Each hexadecimal digit can be represented by a 4-bit binary number. So, we can convert each digit of the hexadecimal number to its equivalent 4-bit binary representation.

Hexadecimal digit B is equal to binary 1011.
Hexadecimal digit C is equal to binary 1100.
Hexadecimal digit A is equal to binary 1010.
Hexadecimal digit 9 is equal to binary 1001.

So, the binary representation of the given hexadecimal number BCA9 is 1011 1100 1010 1001.

Converting from binary to octal:

To convert the binary representation to octal, we divide the binary number into groups of 3 bits starting from the rightmost side. If there are any remaining bits, we pad them with leading zeros.

1011 1100 1010 1001 can be divided into groups as follows:
001 011 100 101 010 010 01

Now, we can convert each group of 3 bits to its equivalent octal digit:

001 is equal to octal 1.
011 is equal to octal 3.
100 is equal to octal 4.
101 is equal to octal 5.
010 is equal to octal 2.
010 is equal to octal 2.
01 is equal to octal 1.

So, the octal representation of the given 16-bit unsigned integer Xin is 1345221.

Therefore, the correct answer is option D: 136251.

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