$$1\times2^{3}+1\times2^{2}+0\times2+1\times2^{0}; 8+4+0+1=13y_{4}$$
$a=13$
$$12+0+1=13y_{4}$$
$$12+1=13y_{4}$$
$$13=13y_{4}$$
$$13y_{4}=13$$
$$y_{4}=\frac{13}{13}$$
$$y_{4}=1$$
$$a=1\times 8+1\times 2^{2}+0\times 2+1\times 2^{0}$$
$$a=8+1\times 2^{2}+0\times 2+1\times 2^{0}$$
$$a=8+1\times 4+0\times 2+1\times 2^{0}$$
$$a=8+4+0\times 2+1\times 2^{0}$$
$$a=12+0\times 2+1\times 2^{0}$$
$$a=12+0+1\times 2^{0}$$
$$a=12+1\times 2^{0}$$
$$a=12+1\times 1$$
$$a=12+1$$
$$a=13$$
$$y_{4}=1$$ $$a=13$$
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