NIMCET 2007 — Computer PYQ

The correct option is (b) $1374$.

Detailed Solution

To convert a number from Hexadecimal (Base-16) to Octal (Base-8), the easiest and most efficient method is to first convert the hexadecimal number into Binary (Base-2), and then group those binary digits into sets of three to get the octal equivalent.

Step 1: Convert Hexadecimal to Binary

Each hexadecimal digit corresponds to a $4\text{-bit}$ binary number. Let's break down $3{\text{DC}}_{16}$:

• $3\to 0011$

• $\text{D}(\text{which represents }13)\to 1101$

• $\text{C}(\text{which represents }12)\to 1100$

Combining these gives the complete binary representation:

$$3{\text{DC}}_{16}=001111011100_2$$

Step 2: Convert Binary to Octal

To convert the binary number into octal, group the bits into sets of three, starting from right to left (Least Significant Bit to Most Significant Bit):

$$001111011100$$

Now, convert each $3\text{-bit}$ group into its equivalent decimal/octal digit:

• $001\to 1$

• $111\to 7$

• $011\to 3$

• $100\to 4$

Combining these digits together gives:

$$1374_8$$

Conclusion: Therefore, $3{\text{DC}}_{16}=1374_8$.