Answer to Question #311796 in Discrete Mathematics for tia

Question

1.  Convert the following to their decimal equivalence:

2022₈

ACE₁₆

Answer 1

Solution (a)

${\left( {2022} \right)_8} = {\left( {2 \times {8^3} + 0 \times {8^2} + 2 \times {8^1} + 2 \times {8^0}} \right)_{10}} \\$

${\left( {2022} \right)_8} = {\left( {2 \times 512 + 0 \times 8 + 2 \times 8 + 2 \times 1} \right)_{10}} \\$

${\left( {2022} \right)_8} = {\left( {1024 + 0 + 16 + 2} \right)_{10}} \\$

${\left( {2022} \right)_8} = {\left( {1042} \right)_{10}} \\$

Solution (b)

${\left( {ACE} \right)_{16}} = {\left( {A \times {{16}^2} + C \times {{16}^1} + E \times {{16}^0}} \right)_{10}}$

${\left( {ACE} \right)_{16}} = {\left( {10 \times 256 + 12 \times 16 + 14 \times 1} \right)_{10}}$

${\left( {ACE} \right)_{16}} = {\left( {2560 + 192 + 14} \right)_{10}}$

${\left( {ACE} \right)_{16}} = {\left( {2766} \right)_{10}}$