GATE CS 2023 Q22 — Number Representations (Fixed and Floating Point)

To find the radix-5 representation of the number, we first convert it from radix-4 to decimal (base-10), and then convert that decimal value to radix-5.

$$(132)_4 = 1 \times 4^2 + 3 \times 4^1 + 2 \times 4^0$$$$= 16 + 12 + 2 = 30_{10}$$

We divide the decimal number successively by $5$ and record the remainders:

• $30 \div 5 = 6$ with a remainder of $0$
• $6 \div 5 = 1$ with a remainder of $1$
• $1 \div 5 = 0$ with a remainder of $1$

Reading the remainders from bottom to top (most significant to least significant digit) gives $(110)_5$.

Therefore, the same number in radix-5 representation is 110.