GATE CS 2017 Set 2 Q.1 (CS Q.1): Number Representations and Computer Arithmetic

The representation of the value of a 16-bit unsigned integer $Y$ in hexadecimal number system is $\text{BCA9}$ . The representation of the value of $Y$ in octal number system is

571244

736251

571247

136251

Official answer and solution

Official answer: D
From: Official GATE 2017 answer key

Solution

Convert the 16-bit hexadecimal number to binary, then group the binary digits into groups of 3 bits from right to left to obtain the octal representation.

Convert each hexadecimal digit of $\text{BCA9}_{16}$ into its 4-bit binary equivalent:

$\text{B}_{16} = 1011_2$
$\text{C}_{16} = 1100_2$
$\text{A}_{16} = 1010_2$
$9_{16} = 1001_2$

Concatenating these gives the 16-bit binary string:

Y = 1011\ 1100\ 1010\ 1001_2

Group the binary string into 3-bit groups starting from the least significant bit (right to left), padding with leading zeros on the left:

$001_2 = 1$
$011_2 = 3$
$110_2 = 6$
$010_2 = 2$
$101_2 = 5$
$001_2 = 1$

Reading the octal digits from left to right yields $136251_8$ .

Final answer

Common trap

Grouping from left to right instead of right to left leads to incorrect digit boundaries.

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

Source

Paper: GATE 2017 Computer Science and Information Technology (CS) Session 2
Question: 1 of 65, printed as CS Q.1
Section: Computer Science and Information Technology

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