IGDTUW 2025 — Computer PYQ

The correct answer is (b) $(6612{)}_8$.

Conversion Methodology

To convert a binary number to octal, we group the binary digits into sets of three, starting from the rightmost bit (the least significant bit). If the total number of bits is not a multiple of three, we add leading zeros to the left.

Step 1: Group the bits into sets of three

Binary number: $110,110,001,010$

Step 2: Convert each triplet to its decimal (octal) equivalent

We use the positional weight $2^2,2^1,2^0$ (which is $4,2,1$) for each group:

• $110_2=(1\times 4)+(1\times 2)+(0\times 1)=6_8$

• $110_2=(1\times 4)+(1\times 2)+(0\times 1)=6_8$

• $001_2=(0\times 4)+(0\times 2)+(1\times 1)=1_8$

• $010_2=(0\times 4)+(1\times 2)+(0\times 1)=2_8$

Step 3: Combine the results

Combining these digits in order gives us:

$$(110110001010{)}_2=(6612{)}_8$$