GATE CS 2005 Q17 — Number Representations (Fixed and Floating Point)

To convert an octal number to its hexadecimal equivalent, the most efficient method is to first convert the octal number to binary, and then group the binary digits into groups of four to find the hexadecimal representation.

Step 1: Convert Octal to Binary
Each octal digit corresponds to a $3$-bit binary number:

• $6 \rightarrow 110$
• $5 \rightarrow 101$
• $7 \rightarrow 111$

Step 2: Convert Binary to Hexadecimal
Group the binary bits into groups of four, starting from the right (least significant bit). Add leading zeros if necessary: $$\underbrace{0001}_{1} \quad \underbrace{1010}_{\text{A}} \quad \underbrace{1111}_{\text{F}}$$ Converting each $4$-bit group to its hexadecimal digit:

• $0001_2 = 1_{16}$
• $1010_2 = \text{A}_{16}$
• $1111_2 = \text{F}_{16}$