IGDTUW 2025 — Computer PYQ

The correct answer is (b) $(36.246{)}_8$.

Conversion Methodology

To convert a hexadecimal number to octal, the easiest intermediate step is to convert the hexadecimal number to binary, and then convert that binary sequence into octal.

Step 1: Convert Hexadecimal to Binary (each hex digit = 4 bits)

• $1_{16}=0001_2$

• $E_{16}=1110_2$

• $5_{16}=0101_2$

• $3_{16}=0011_2$

Concatenating these, we get:

$$(1E.53{)}_{16}=(00011110.01010011{)}_2$$

Step 2: Convert Binary to Octal (group by 3 bits)

Starting from the radix point (decimal point) and moving outwards:

• Left side (integer part): $001,111,10$ $\to$ pad with zeros $\to$ $011,111,010$ (Wait, re-aligning: $001$ $111$ $0\to$ $000$ $011$ $110=036_8$)

• Let's re-group carefully: $00011110.01010011$

• Grouping in threes: $011110.010100110$

• Adding leading zeros: $011,110.010,100,110$

Step 3: Convert triplets to Octal digits

• $011_2=3_8$

• $110_2=6_8$

• $010_2=2_8$

• $100_2=4_8$

• $110_2=6_8$

Result: $(36.246{)}_8$