GATE CS 2023 Q.32: Number Representations and Computer Arithmetic

A particular number is written as $132$ in radix- $4$ representation. The same number in radix- $5$ representation is _______.

Your answer

Official answer and solution

Solution

Convert $(132)_4$ to decimal, then convert the decimal value to radix 5.

Convert $(132)_4$ to decimal:
$(132)_4 = 1 \times 4^2 + 3 \times 4^1 + 2 \times 4^0 = 16 + 12 + 2 = 30_{10}$
Convert $30_{10}$ to radix 5 by successive division:
- $30 \div 5 = 6$ with remainder $0$
- $6 \div 5 = 1$ with remainder $1$
- $1 \div 5 = 0$ with remainder $1$

Reading the remainders from bottom to top yields $110_5$ .

Final answer

110

Common trap

Reading remainders in forward order instead of reverse, or miscalculating $3 \times 4^1$ .

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

GATE questions are the work of the organising institutes. This site is independent and is not affiliated with them.