Question

2011
A number written as 213 in quadral system (number sys
epresented in hexal system (number system with base 6) as
(A) 23
(B) 39
(C) 103​

Answer 1

$option : (c) \: 103$

Explanation:

$(213)_{4} = 2 \times {4}^{2} + 1 \times {4}^{1} + 3 \times {4}^{0} \\ \: \: \: \: \: \: \: \: \: \: = 2 \times 16 + 1 \times 4 + 3 \times 1 \\ = 32 + 4 + 3 \\ = 39 \\ Now, \: \: 39 = 1 \times {6}^{2} + 0 \times {6}^{1} + 3 \times {6}^{0} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 1 \times 36 + 0 \times 6 + 3 \times 1 \\ = 36 + 0 + 3 \\ = 39 \\ = \boxed{ (103) _{6}}$